Lidé

prof. Ing. Mirko Navara, DrSc.

Všechny publikace

Form of contextuality predicting probabilistic equivalence between two sets of three mutually noncommuting observables

  • DOI: 10.1103/PhysRevA.109.022222
  • Odkaz: https://doi.org/10.1103/PhysRevA.109.022222
  • Pracoviště: Strojové učení
  • Anotace:
    We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases within the Hilbert space, featuring a state-independent sum of probabilities. In other words, regardless of the initial state preparation, the total probability remains constant but may be distinct from unity. The measurement contextuality in this setup arises from the quantum realizations of the hypergraph, which adhere to a specific bound on the linear combination of probabilities. In contrast, classical realizations can surpass this bound. The violation of quantum bounds stems from the inability of classical ontological models, specifically the set theoretic representation of the hypergraph corresponding to the quantum observables’ collections, to adhere to and explain the observed statistics.

Maximum likelihood estimator of quantum probabilities

  • DOI: 10.1007/s10773-023-05469-8
  • Odkaz: https://doi.org/10.1007/s10773-023-05469-8
  • Pracoviště: Strojové učení
  • Anotace:
    Classical probability theory is based on assumptions which are often violated in practice. Therefore quantum probability is a proposed alternative not only in quantum physics, but also in other sciences. However, so far it mostly criticizes the classical approach, but does not suggest a working alternative. Maximum likelihood estimators were given very low attention in this context. We show that they can be correctly defined and their computation in closed form is feasible at least in some cases.

Relations between the shapes of triangular norms and their generators

  • Autoři: Houšková, K., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Copulas. Theory and Applications. Linz: Johannes Kepler University, 2023. p. 42-46. ISBN 978-3-903480-02-5.
  • Rok: 2023
  • Pracoviště: Strojové učení
  • Anotace:
    We study relations between the shape of a strict triangular norm and its generators. In particular, we introduce the class of balanced generators.

The Fibonacci sequence in the description of maximal discrete Archimedean t-norms

  • DOI: 10.1016/j.fss.2022.08.012
  • Odkaz: https://doi.org/10.1016/j.fss.2022.08.012
  • Pracoviště: Strojové učení
  • Anotace:
    There are many arguments for counting with more than two “truth values”; this allows to imitate human reasoning of facts which are not binary. For theoretical reasons, it is natural to use the whole real interval as the scale. However, this brings practical problems: it is difficult, and even impossible, to represent exact values. Often only a small scale of values suffices to express what we need. Therefore, finite chains are frequently used as domains of fuzzy logical operations. Their representation and manipulation are easy. In this paper, we focus on triangular norms (t-norms). The choice of a finite domain admits some operations (Gödel, Łukasiewicz), while it excludes others (all strict ones, including the product). A disadvantage of the Gödel (minimum) t-norm is that repetition of arguments does not change their meaning. This is often desirable to emphasize the statement. (“Words, words, words!”) Thus we do not consider the Gödel operations sufficient for representation of all fuzzy logical statements in human reasoning. Together with them, we discard all operations with idempotent elements other than 0, 1, thus we restrict attention to Archimedean t-norms (and t-conorms as their duals, not treated explicitly in the sequel). A disadvantage of many Archimedean t-norms is that, when applied to several arguments, the result is very often zero. Then, it gives no clue in comparing the outcomes, e.g., in giving priorities to alternatives evaluated by fuzzy rules. For instance, when the continuous Łukasiewicz t-norm is applied to 5 entries, it is nonzero only on 1/5! = 1/120 of the volume of its 5-dimensional domain; in its discrete versions, nonzero results are even more rare. Thus we are interested in Archimedean t-norms with values “as large as possible”, here in the maximal Archimedean t-norms (=those which are not majorized by other Archimedean t-norms). It was shown in previous works that there is an abundance of discrete t-norms; their number grows fast with the number of elements of the underlying chain (no exponential bound seems to be known). There is also an abundance of Archimedean t-norms. In contrast to that, when we counted the number of maximal Archimedean t-norms, it grows asymptotically exponentially with a mild base. What is more interesting, these numbers follow the Fibonacci sequence. We have found a description of maximal Archimedean t-norms and explained also the processes behind their construction and the role of the Fibonacci sequence. These results link the t-norms to a construction using a kind of additive generators, although this could not be used without modifications. We do not describe all Archimedean t-norms and their numbers, but we have completed at least a significant step towards this goal, too.

Generalised Kochen-Specker Theorem in Three Dimensions

  • DOI: 10.1007/s10701-021-00476-3
  • Odkaz: https://doi.org/10.1007/s10701-021-00476-3
  • Pracoviště: Strojové učení
  • Anotace:
    We show that there is no non-constant assignment of zeros and ones to points of a unit sphere in R^3 such that for every three pairwisely orthogonal vectors, an odd number of them is assigned 1. This is a new strengthening of the Bell-Kochen-Specker theorem, which proves the non-existence of hidden variables in quantum theories.

On Frink Ideals in Orthomodular Posets

  • DOI: 10.1007/s11083-020-09537-0
  • Odkaz: https://doi.org/10.1007/s11083-020-09537-0
  • Pracoviště: Katedra matematiky, Strojové učení
  • Anotace:
    Let S denote the class of orthomodular posets in which all maximal Frink ideals are selective. Let R (resp. T) be the class of orthomodular posets defined by the validity of the following implications: P is an element of R if the implication a, b is an element of P, a boolean AND b = 0 double right arrow a <= b' holds (resp., P is an element of T if the implication a. b = a boolean AND b' = 0 double right arrow a = 0 holds). In this note we prove the following slightly surprising result: R subset of S subset of T. Since orthomodular posets are often understood as quantum logics, the result might have certain bearing on quantum axiomatics.

Quantum logics defined by divisibility conditions

  • DOI: 10.1007/s10773-018-3977-y
  • Odkaz: https://doi.org/10.1007/s10773-018-3977-y
  • Pracoviště: Katedra matematiky, Strojové učení
  • Anotace:
    Let p be a prime number and let S be a countable set. Let us consider the collection DivSp of all subsets of S whose cardinalities are multiples of p and the complements of such sets. Then the collection DivSp constitutes a (set-representable) quantum logic (i.e., DivSp is an orthomodular poset). We show in this note that each state on DivSp can be extended over the Boolean algebra exp S of all subsets of S.

Quantum structures without group-valued measures

  • Autoři: prof. Ing. Mirko Navara, DrSc., Voráček, V.
  • Publikace: International Journal of Theoretical Physics. 2021, 60(2), 687-695. ISSN 0020-7748.
  • Rok: 2021
  • DOI: 10.1007/s10773-019-04058-y
  • Odkaz: https://doi.org/10.1007/s10773-019-04058-y
  • Pracoviště: Strojové učení
  • Anotace:
    Quantum structures with small dimensions of state spaces are not only mathematical curiosities. They enriched the mathematical theory by new tools. We have significantly optimized some of these constructions. Related questions have been studied also in graph theory.

Generators of fuzzy logical operations

  • Autoři: prof. Ing. Mirko Navara, DrSc., Petrík, M.
  • Publikace: Algebraic Techniques and Their Use in Describing and Processing Uncertainty. Cham: Springer, 2020. p. 89-112. Studies in Computational Intelligence. vol. 878. ISSN 1860-949X. ISBN 978-3-030-38565-1.
  • Rok: 2020
  • DOI: 10.1007/978-3-030-38565-1_8
  • Odkaz: https://doi.org/10.1007/978-3-030-38565-1_8
  • Pracoviště: Strojové učení
  • Anotace:
    We deal with fuzzy logical operations with values in the real unit interval. Many of them can be considered equivalent up to an isomorphism (i.e., increasing bijection) of the set of values. This is the case of all involutive fuzzy negations; an elegant proof was given by Nguyen and Walker (A first course in fuzzy logic, 2nd edn. Chapman & Hall/CRC, Boca Raton, 2000 [23]) . The situation is more tricky for binary operations, triangular norms, triangular conorms, and fuzzy implications. For the most common classes of these operations, the existence of their (additive or multiplicative) generators is known; however, their computation can be often unfeasible. We proved that a rather general subclass allows computing the generators from partial derivatives. Here we summarize preceding results in this direction (mostly with simplified proofs) and add several new ones.

Boolean subalgebras of orthoalgebras

  • Autoři: Harding, J., Heunen, Ch., Lindenhovius, B., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS. 2019, 36(3), 563-609. ISSN 0167-8094.
  • Rok: 2019
  • DOI: 10.1007/s11083-019-09483-6
  • Odkaz: https://doi.org/10.1007/s11083-019-09483-6
  • Pracoviště: Strojové učení
  • Anotace:
    We develop a direct method to recover an orthoalgebra from its poset of Boolean subalgebras. For this a new notion of direction is introduced. Directions are also used to characterize in purely order-theoretic terms those posets that are isomorphic to the poset of Boolean subalgebras of an orthoalgebra. These posets are characterized by simple conditions defining orthodomains and the additional requirement of having enough directions. Excepting pathologies involving maximal Boolean subalgebras of four elements, it is shown that there is an equivalence between the category of orthoalgebras and the category of orthodomains with enough directions with morphisms suitably defined. Furthermore, we develop a representation of orthodomains with enough directions, and hence of orthoalgebras, as certain hypergraphs. This hypergraph approach extends the technique of Greechie diagrams and resembles projective geometry. Using such hypergraphs, every orthomodular poset can be represented by a set of points and lines where each line contains exactly three points.

Dialogue between Mirko Navara and Vilem Novak

  • Pracoviště: Strojové učení
  • Anotace:
    The two people participating in this interview have much in common. Both studied engineering before they decided to do (only) mathematics. They both wrote textbooks on fuzzy sets in Czech. And, as you see, they share a lot of common opinions on this topic and its importance, although, despite their extensive lists of coauthors, they have no common pa- per.

Formulas for generators of R-implications

  • DOI: 10.1016/j.fss.2018.09.011
  • Odkaz: https://doi.org/10.1016/j.fss.2018.09.011
  • Pracoviště: Strojové učení
  • Anotace:
    We study implications on the unit interval. Like triangular norms and conorms, these implications also may have generators (additive or multiplicative). Although there are constructive proofs of the existence of generators of these operations, they rarely lead to closed formulas. Thus we lack a practical tool for computations of the generators. Recently we have shown that the generators of triangular norms can often be computed from the partial derivatives of the original operations. Here we apply a similar technique to R-implications. Some of the formulas have analogies for triangular norms, some do not. Besides, we show (and avoid) another potential problem of computation of generators of triangular norms, not mentioned before.

Imperfect information as a source of non-symmetry in the two envelope problem

  • Autoři: prof. Ing. Mirko Navara, DrSc., Šindelář, J.
  • Publikace: International Journal of Approximate Reasoning. 2019, 112 37-54. ISSN 0888-613X.
  • Rok: 2019
  • DOI: 10.1016/j.ijar.2019.05.011
  • Odkaz: https://doi.org/10.1016/j.ijar.2019.05.011
  • Pracoviště: Strojové učení
  • Anotace:
    We present new views on the two envelope problem (also called the exchange paradox). We consider it as a game of a single player (and a banker) or a constant-sum game of two players, each of them having different imperfect information.

Orthoalgebras as pastings of Boolean algebras

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: International Journal of Theoretical Physics. 2017, 56(12), 4126-4132. ISSN 0020-7748.
  • Rok: 2017

Principles of inclusion and exclusion for interval-valued fuzzy sets and IF-sets

  • DOI: 10.1016/j.fss.2016.08.009
  • Odkaz: https://doi.org/10.1016/j.fss.2016.08.009
  • Pracoviště: Strojové učení
  • Anotace:
    The principle of inclusion and exclusion is one of basic tools of classical set theory. Many previous papers have presented its generalizations to fuzzy sets or IF-sets (Atanassov’s intuitionistic fuzzy sets) with G{\"o}del or product operations. In our previous work we clarified these questions for fuzzy sets with intersections and unions based on continuous triangular norms and conorms. Here we extend these results to interval-valued fuzzy sets and IF-sets."

Sasaki projections

  • Autoři: Gabriëls, J., Gagola III, S.M., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Algebra universalis. 2017, 77(3), 305-320. ISSN 0002-5240.
  • Rok: 2017
  • DOI: 10.1007/s00012-017-0428-1
  • Odkaz: https://doi.org/10.1007/s00012-017-0428-1
  • Pracoviště: Strojové učení
  • Anotace:
    We collect, correct, and extend results on the properties of the Sasaki projection in orthomodular lattices. We bring arguments as to why this operation can extend tools for simplification of formulas and automated computing.

The role of information in the two envelope problem

  • Autoři: prof. Ing. Mirko Navara, DrSc., Šindelář, J.
  • Publikace: ITAT 2017: Information Technologies – Applications and Theory. Aachen: CEUR Workshop Proceedings, 2017. p. 112-119. vol. 1885. ISBN 9781974274741.
  • Rok: 2017
  • Pracoviště: Strojové učení
  • Anotace:
    We offer a new view on the two envelope problem (also called the exchange paradox). We describe it as a zero-sum game of two players, having only partial information. We first explain a standard situation and show that the mean gain - when defined - is really zero. However, there are even more paradoxical situations in which the information obtained by the players supports the exchange of envelopes. We explain that this does not lead to a contradiction and we demonstrate it also by computer simulation. The reason for this paradox is that the mean gain does not exist and that the players have different information, supporting their contradictory decisions.

Axiomatic approach to probability of fuzzy events

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Functional Equations and Inequalities. Linz: Universitätsdirektion, Johannes Kepler University, 2016. pp. 66-72.
  • Rok: 2016
  • Pracoviště: Strojové učení
  • Anotace:
    We discuss the requirements on a fuzzy stochastic system describing probabilities of fuzzy events. We present (and sometimes reject) alternative ways. We show the principal contribution of D.~Butnariu and E.~P.~Klement to this research and we summurize the state-of-the-art and perspectives.

Perfect Pavelka Logic

States on symmetric logics: extensions

  • DOI: 10.1515/ms-2015-0141
  • Odkaz: https://doi.org/10.1515/ms-2015-0141
  • Pracoviště: Strojové učení
  • Anotace:
    We continue the study of symmetric logics, i.e., collections of subsets generalizing Boolean algebras and closed under the symmetric difference. We contribute to several open questions. One of them is whether there is a non-Boolean symmetric logic such that all states on it are Delta-subadditive.

Convex combinations of fuzzy logical operations

  • DOI: 10.1016/j.fss.2014.10.013
  • Odkaz: https://doi.org/10.1016/j.fss.2014.10.013
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    One may ask when (non-trivial) convex combinations of fuzzy logical operations result in operations of the same type. This question has been intensively studied for triangular norms and it still remains open for continuous ones. An equivalent prob- lem is obtained for triangular conorms. We show equivalence with the analogous problem for S-implications. Negative answers are obtained for strong fuzzy negations and for R-implications corresponding to continuous triangular norms. The situation for Q-implications and related problems are discussed.

Infinitesimals and Pavelka logic

  • Autoři: Turunen, E., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: International Joint Conference IFSA - EUSFLAT 2015. Asturias: European Centre for Soft Computing, 2015. pp. 1027-1033. Advances in Intelligent Systems Research. ISSN 1951-6851. ISBN 978-94-6252-077-6.
  • Rok: 2015
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Rational Pavelka Logic does not admit infinitesimals. We argue that infinitesimals are important in logic and we present an alternative approach which admits them. It is built up in a similar style, but based on the Chang's perfect MV-algebra. We prove a partial result towards the completeness of this logic. We also discuss a combined approach using more complex perfect MV-algebras.

Measures on interval-valued fuzzy sets and IF-sets and principle of inclusion and exclusion

  • Autoři: Kuková, M., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of the 8th International Summer School on Aggregation Operators. Katowice: University of Silesia, 2015, pp. 163-168. ISBN 978-83-8012-519-3.
  • Rok: 2015
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    In our previous work, we proved that the only continuous operations on fuzzy sets fulfilling the principle of inclusion and exclusion are Gödel and product operations and their ordinal sums. We have made a similar observation on t-representable measures on interval-valued fuzzy sets and IF-sets. Here we complete these results and discuss also operations which are not t-representable.

New properties of Sasaki projections

  • Autoři: Gagola III, S., Gabriëls, J., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Topology, Algebra, and Categories in Logic 2015. Salerno: University of Salerno, 2015. pp. 107-109.
  • Rok: 2015
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We extend results on the properties of the Sasaki projection in orthomodular lattices. We bring arguments as to why this operation can extend tools for simplification of formulas and automated computing.

Quantum logics of idempotents of unital rings

  • Autoři: Bikchentaev, A.M., prof. Ing. Mirko Navara, DrSc., Yakushev, R.
  • Publikace: International Journal of Theoretical Physics. 2015, 54(6), 1987-2000. ISSN 0020-7748.
  • Rok: 2015
  • DOI: 10.1007/s10773-014-2405-1
  • Odkaz: https://doi.org/10.1007/s10773-014-2405-1
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We introduce some new examples of quantum logics of idempotents in a ring. We continue the study of symmetric logics, i.e., collections of subsets generalizing Boolean algebras and closed under the symmetric difference.

States on systems of sets that are closed under symmetric difference

  • DOI: 10.1002/mana.201500029
  • Odkaz: https://doi.org/10.1002/mana.201500029
  • Pracoviště: Katedra matematiky, Katedra kybernetiky
  • Anotace:
    We consider extensions of certain states. The states are defined on the systems of sets that are closed under the formation of the symmetric difference (concrete quantum logics). These systems can be viewed as certain set-representable quantum logics enriched with the symmetric difference. We first show how the compactness argument allows us to extend states on Boolean algebras over such systems of sets. We then observe that the extensions are sometimes possible even for non-Boolean situations. On the other hand, a difference-closed system can be constructed such that even two-valued states do not allow for extensions.

Weaker forms of associativity in orthomodular lattices

  • Autoři: Gagola III, S. M., Gabriëls, J. M., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Algebra universalis. 2015, 73(3-4), 249-266. ISSN 0002-5240.
  • Rok: 2015
  • DOI: 10.1007/s00012-015-0332-5
  • Odkaz: https://doi.org/10.1007/s00012-015-0332-5
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We have found that there are 8 nonassociative operations in orthomodular lattices satisfying the identities of alternative algebras. For these operations, we clarified the validity of other similar identities, including the Moufang identities.

Fusion of telescopic and Doppler radar data

  • Autoři: prof. Ing. Mirko Navara, DrSc., Matoušek, M., Mgr. Ondřej Drbohlav, Ph.D.,
  • Publikace: Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference. Kihei: Maui Economic Development Board, 2014, ISSN 2152-4629. Available from: http://www.amostech.com/TechnicalPapers/2014/Poster/NAVARA.pdf
  • Rok: 2014
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The most usual ways of observation of satellites and space debris and measur ement of their orbits are telescopic images, radar reflections, laser measurements. We use two of these three modalities, we combine telescopic images with response of Doppler radars. We u se single images from a terrestrial telescope. Our radar is passive, we receive the signal of a distant terrestrial transmitter. The receiver has a non-directional antenna and only Doppler shift is employed to gain information about an object's movement. Due to sensitivity limitati ons, our approach is applicable to large objects (RCS 5 m2 ) at distances 2000 km. Our method requires simultaneous detections by a telescope and a radar during the same fly-over, not necessarily at exactly the same time.

Identities valid in orthomodular lattices

  • Autoři: Gagola III, S., Gabriëls, J., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Biennial IQSA Conference Quantum Structures. Olomouc: Univerzita Palackého v Olomouci, 2014. pp. 32-33.
  • Rok: 2014
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We investigated possibilities of finding tools reducing operations in orthomodular lattices into normal forms.

New results about symmetric difference in quantum structures

  • Autoři: Bikchentaev, A., prof. Ing. Mirko Navara, DrSc., Yakushev, R.
  • Publikace: Biennial IQSA Conference Quantum Structures. Olomouc: Univerzita Palackého v Olomouci, 2014. pp. 71-72.
  • Rok: 2014
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We summarize recent results on set-representable orthomodular posets which are closed under set-theoretical symmetric difference. We clarify properties of states on them.

Symmetric differences and probabilities

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Symmetric differences and probabilities on set-representable quantum structures.

The role of symmetric difference in quantum structures

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: FSTA14: Twelfth International Conference on Fuzzy Set Theory and Applications. Liptovský Mikuláš: Akadémia ozbrojených síl, 2014. pp. 88-89. ISBN 978-80-8040-488-8.
  • Rok: 2014
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We summarize the recent advances in the study of orthomodular posets which admit set representations closed under the symmetric difference.

Alternative proof of Mulholland's theorem and new solutions to {M}ulholland inequality

  • Autoři: Petrík, M., prof. Ing. Mirko Navara, DrSc., Sarkoci, P.
  • Publikace: ISMVL 2013: IEEE 43rd International Symposium on Multiple-Valued Logic. Piscataway: IEEE, 2013. pp. 346-351. ISSN 0195-623X. ISBN 978-0-7695-4976-7.
  • Rok: 2013
  • DOI: 10.1109/ISMVL.2013.1
  • Odkaz: https://doi.org/10.1109/ISMVL.2013.1
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Mulholland inequality is a real functional inequality presented in 1950 in a paper by Mulholland as a generalization of the Minkowski inequality. In his paper, Mulholland has also provided a sufficient condition for the inequality to be satisfied. However, until now, it has remained an open problem whether this sufficient condition is also necessary. This paper investigates a geometric interpretation of Mulholland inequality and offers a class of functions satisfying the inequality which is strictly larger compared to the class delimited by the Mulholland's condition. Thus, it is proven that the condition is not necessary.

Computer proof of monotonicity of operations on orthomodular lattices

Continuous t-norms and t-conorms satisfying the principle of inclusion and exclusion

  • Autoři: Kuková, M., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: AGOP2013: Aggregation Functions in Theory and in Practise. Heidelberg: Springer, 2013. pp. 179-186. Advances in Intelligent Systems and Computing. ISBN 978-3-642-39164-4.
  • Rok: 2013

Fuzzy implications satisfying convexity relations

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: EUSFLAT 2013: Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology. Paris: Atlantis Press, 2013. p. 187-192. Advances in Intelligent Systems Research. ISSN 1951-6851. ISBN 9789078677789.
  • Rok: 2013
  • DOI: 10.2991/eusflat.2013.33
  • Odkaz: https://doi.org/10.2991/eusflat.2013.33
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    It is an open question whether a non-trivial convex combination of triangular norms (resp. conorms) can be a triangular norm (resp. conorm). We investigate the analogous question for S-implications and R-implications.

Principles of inclusion and exclusion for fuzzy sets

  • DOI: 10.1016/j.fss.2013.02.014
  • Odkaz: https://doi.org/10.1016/j.fss.2013.02.014
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Many previous papers have presented generalizations of the principle of inclusion and exclusion to fuzzy sets or IF-sets (Atanassov's intuitionistic fuzzy sets) with G"odel or product operations. We clarify for which fuzzy intersections and unions, based on continuous triangular norms and conorms, the principle of inclusion and exclusion holds.

The role of statistics---present and future

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We summarize the current role of statistics in science. We argue that its importance in education is underestimated. Further, we bring arguments for development of generalizations of statistics to phenomena exceeding the classical model---quantum and fuzzy events.

Various generalizations of the principle of inclusion and exclusion

  • Autoři: Kuková, M., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Applications of Algebra 17. Czestochowa: Jan Dlugosz University, 2013. pp. 20-21.
  • Rok: 2013
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The principle of inclusion and exclusion is generalized to fuzzy sets and IF-sets.

What observables can be

  • Autoři: Kuková, M., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Theory of Functions, Its Applications, and Related Questions. Kazan: Kazan Federal University, 2013. pp. 62-70. Transactions of the Mathematical Institute of N.I.~Lobachevsky. ISBN 978-5-00019-095-1.
  • Rok: 2013
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Different approaches to quantum logics resulted in different mathematical structures generalizing Boolean Sigma-algebras. In all of them, observables (as a generalization of random variables) play a crucial role. Depending on the quantum structure, observables may have quite different mathematical description. In all of these approaches, the generalized theory encounters difficulties because the classical approach tojoint distributions cannot be applied.

An algebraic generalization of the notion of tribe

  • DOI: 10.1016/j.fss.2011.02.001
  • Odkaz: https://doi.org/10.1016/j.fss.2011.02.001
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Tribes became a successful basis of measure theory on fuzzy sets. During their investigation, new requirements occurred. We discuss possible modifications of the original definition of a tribe, with emphasis on point-free notions.

Associativity of operations on orthomodular lattices

Algebras characterized by their lattices of subalgebras

  • Autoři: Harding, J., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Abstracts of Lectures, Tutorials, and Talks. International Conference on Order, Algebra, and Logics. Krakow: Jagiellonian University in Krakow, 2011. pp. 21.
  • Rok: 2011
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We show that an orthomodular lattice is determined by its lattice of subalgebras, as well as by its poset of Boolean subalgebras.

Computation with fuzzy quantities

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011) and LFA-2011. Paris: Atlantis Press, 2011. pp. 209-214. ISBN 978-90-78677-00-0.
  • Rok: 2011
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Solving systems of equations (even linear ones) in standard fuzzy arithmetic may be a problem. We suggest an alternative approach which transfers the task to a linear space where the solution may be standard. Fuzzy intervals form a proper subset (in fact, a cone) in this linear space.

Several definitions of probability on systems of fuzzy sets

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: ODAM 2011: Olomoucian Days of Applied Mathematics. Olomouc: Univerzita Palackého v Olomouci, 2011. pp. 48. ISBN 978-80-244-2684-6.
  • Rok: 2011
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We suggest a new algebraic approach to probability on systems of fuzzy sets and compare it to previous attempts.

Subalgebras of orthomodular lattices

  • Autoři: Harding, J., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS. 2011, 28(3), 549-563. ISSN 0167-8094.
  • Rok: 2011
  • DOI: 10.1007/s11083-010-9191-z
  • Odkaz: https://doi.org/10.1007/s11083-010-9191-z
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Sachs (Can J Math 14:451-460, 1962) showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determined by its lattice of subalgebras Sub(L), as well as by its poset of Boolean subalgebras BSub(L). The domain BSub(L) has recently found use in an approach to the foundations of quantum mechanics initiated by Butterfield and Isham (Int J Theor Phys 37(11): 2669-2733, 1998, Int J Theor Phys 38(3): 827-859, 1999), at least in the case where L is the orthomodular lattice of projections of a Hilbert space, or von Neumann algebra. The results here may add some additional perspective to this line of work.

Vector techniques in fuzzy arithmetic

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We propose a new method of computation with fuzzy quantities and solutions of systems of linear equations in the domain of fuzzy quantities. We transform the task to computation with vectors and then find those vectors which correspond to fuzzy quantities.

Characterization of spaces of filtering states

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: International Journal of Theoretical Physics. 2010, 49(12), 3209-3215. ISSN 0020-7748.
  • Rok: 2010
  • DOI: 10.1007/s10773-009-0213-9
  • Odkaz: https://doi.org/10.1007/s10773-009-0213-9
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Filtering states on orthomodular lattices have been introduced by G.T. Rüttimann as an opposite of completely additive states. We prove that, for any semi-exposed face F of a compact convex set C, there is an orthomodular lattice L and an affine homeomorphism f of C onto the state space of L such that f(F) is the space of filtering states.

Explicit formulas for generators of triangular norms

  • Autoři: prof. Ing. Mirko Navara, DrSc., Petrík, M., Sarkoci, P.
  • Publikace: Publicationes Mathematicae. 2010, 77(1-2), 171-191. ISSN 0033-3883.
  • Rok: 2010
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The paper shows a direct correspondence between the first partial derivatives of a continuous Archimedean triangular norm and the first derivatives of its additive generator. An explicit formula for the additive generator is obtained.

Fuzzy algebras need not be MV-algebras

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We propose a notion of a fuzzy algebra which generalizes MV-algebras and tribes of fuzzy sets.

Fuzzy logics with an additional involutive negation

  • Autoři: Cintula, P., Klement, E.P., Mesiar, R., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Fuzzy Sets and Systems. 2010, 161(3), 390-411. ISSN 0165-0114.
  • Rok: 2010
  • DOI: 10.1016/j.fss.2009.09.003
  • Odkaz: https://doi.org/10.1016/j.fss.2009.09.003
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    This paper surveys the present state of knowledge on propositional fuzzy logic with additional involutive negation. The involutive negation is added as a new propositional connective in to order to improve the expressive power of the standard mathematical fuzzy logics based on a continuous t-norm.

Reconstruction of additive generators from partial derivatives of continuous Archimedean t-norms

  • Autoři: prof. Ing. Mirko Navara, DrSc., Petrík, M., Sarkoci, P.
  • Publikace: ISMVL10: 40th IEEE International Symposium on Multiple-Valued Logic. Los Alamitos: IEEE Computer Society Press, 2010. pp. 241-244. ISSN 0195-623X. ISBN 978-0-7695-4024-5.
  • Rok: 2010
  • DOI: 10.1109/ISMVL.2010.52
  • Odkaz: https://doi.org/10.1109/ISMVL.2010.52
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The paper shows a direct correspondence between the first partial derivatives of a continuous Archimedean triangular norm and the first derivatives of its additive generator. An explicit formula for the additive generator is obtained. Application of the result is demonstrated on the problem of convex combinations of strict triangular norms.

Colouring of graphs and problems of quantum mechanics

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We summarize recent results on existence of measures on the orthomodular lattice of subspaces of a finitely-dimensional Hilbert space. We concentrate on measures with values in the two-element cyclic group., keywords = orthomodular lattice, Hilbert lattice, measure, group-valued measure, cyclic group, hidden variable, Kochen-Specker Theorem, graph colouring

Convex combinations of triangular norms

  • Autoři: prof. Ing. Mirko Navara, DrSc., Petrík, M., Sarkoci, P.
  • Publikace: 30th Linz Seminar on Fuzzy Set Theory: The Legacy of 30 Seminars-Where Do We Stand and Where Do We Go?. Linz: Universitätsdirektion, Johannes Kepler University, 2009. p. 85-87.
  • Rok: 2009
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Alsina, Frank, and Schweizer stated, as an open problem, a question whether a non-trivial convex combination of two triangular norms can ever be a triangular norm again. The piresentation gives an overview of the results done in this field presenting also the contributions of the authors.

Different representations of fuzzy vectors

  • Autoři: Liang, J., prof. Ing. Mirko Navara, DrSc., Vetterlein, T.
  • Publikace: Symbolic and Quantitative Approaches to Reasoning with Uncertainty. Heidelberg: Springer, 2009. pp. 700-711. Lecture Notes in Computer Science. ISSN 0302-9743. ISBN 978-3-642-02905-9.
  • Rok: 2009
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Fuzzy vectors were introduced as a description of imprecise quantities whose uncertainty originates from vagueness, not from a probabilistic model. Support functions are a classical tool for representation and computation with compact convex sets. The combination of these two techniques-support functions of fuzzy vectors---has been proposed by Puri and Ralescu. Independently, Bobylev proposed another type of support functions which allows a more economical representation. However, the form of the functions is not very intuitive. We suggest a new type of support functions which combines the advantages of both preceding approaches. We characterize the functions which are support functions of fuzzy vectors in the new sense.

Existence of states on quantum structures

  • DOI: 10.1016/j.ins.2008.06.011
  • Odkaz: https://doi.org/10.1016/j.ins.2008.06.011
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Orthomodular lattices occurred as generalized event structures in the models of probability for quantum mechanics. Here we contribute to the question of existence of states (=probability measures) on orthomodular lattices. We prove that known techniques do not allow to find examples with less than 19 blocks (=maximal Boolean subalgebras). This bound is achieved by the example by R. Mayet. Although we do not finally exclude the existence of other techniques breaking this bound, existence of smaller examples is highly unexpected.

Mathematical questions related to non-existence of hidden variables

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Foundations of Probability and Physics - 5. New York: American Institute of Physics, 2009. p. 119-126. AIP Conference Proceedings. ISSN 0094-243X. ISBN 978-0-7354-0636-0.
  • Rok: 2009
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The famous Gleason's Theorem gives a characterization of states on lattices of subspaces of Hilbert spaces. The attempts to simplify its proof have led to easy proofs of some consequences, mainly the non-existence of hidden variables (dispersion-free states). Here we simplify some of them. We also formulate related open problems concerning spaces with rational coordinates and group-valued measures.

Several approaches to conditional probability

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of the 4th International Workshop on Nonstandard Logics. Praha: ČVUT FEL, Katedra kybernetiky - Centrum strojového vnímání, 2009. pp. 19-20. Research Report of CMP. ISSN 1213-2365.
  • Rok: 2009
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    It is highly desirable to generalize the notion of conditional probability to events which are vague (fuzzy) or not simultaneously observable (quantum). We summarize the recent approaches, their advantages and drawbacks.

Tribes revisited

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: 30th Linz Seminar on Fuzzy Set Theory: The Legacy of 30 Seminars-Where Do We Stand and Where Do We Go?. Linz: Universitätsdirektion, Johannes Kepler University, 2009. pp. 81-84.
  • Rok: 2009
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Tribes became a successful basis of measure theory on fuzzy sets. During their investigation, new requirements occurred. We discuss possible modifications of the original definition of a tribe.

Valuations on the algebra of intervals

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: IFSA/EUSFLAT 2009: International Fuzzy Systems Association World Congress, European Society for Fuzzy Logic and Technology Conference. Lisboa: Instituto Suparior Téchnico Av. Rovisco Pais, 2009. pp. 550-554. ISBN 978-989-95079-6-8.
  • Rok: 2009
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Interval-valued fuzzy sets are based on the algebra of subintervals of the unit interval [0,1]. We study valuations as a special type of measures on this algebra. We present a description of all valuations which preserve the standard fuzzy negation and extend the identity on the elements of the form (x,x). Consequences for sublattices are formulated.

What is primary: negation or implication?

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Witnessed Years: Essays in Honour of Petr Hajek. London: King's College, 2009. p. 227-241. Tributes. vol. 10. ISBN 978-1-904987-63-5.
  • Rok: 2009
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We compare R-fuzzy logics (based on an implication interpreted by the residuum of a triangular norm) and S-fuzzy logics (based on an involutive negation and using a different interpretation of implication). We show that the former approach (promoted by Petr H{' a}jek) leads to much richer logical results. Then we discuss extensions of R-fuzzy logics by an involutive negation as a new connective. These combine the features of both preceding approaches. We summarize recent results of this branch of research (which was also initiated by Petr Hájek).

Numerical Analysis with Maple

  • Pracoviště: Katedra matematiky, Katedra kybernetiky
  • Anotace:
    We summarize more than 10 years of our experience with a course of Numerical Analysis with the use of Maple. Besides software packages, we discuss also the principles of education.

Small quantum structures with small state spaces

  • DOI: 10.1007/s10773-007-9415-1
  • Odkaz: https://doi.org/10.1007/s10773-007-9415-1
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We summarize and extend results about ``small'' quantum structures with small dimensions of state spaces. These constructions have contributed to the theory of orthomodular lattices. More general quantum structures (orthomodular posets, orthoalgebras, and effect algebras) admit sometimes simplifications, but there are problems where no progress has been achieved.

Technical aspects of the use of Steiner point of fuzzy set

  • Autoři: Liang, J., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: FSTA 2008: Ninth International Conference on Fuzzy Set Theory and Applications. Liptovský Mikuláš: Akadémia ozbrojených síl, 2008. pp. 14-15. ISBN 978-80-8040-332-4.
  • Rok: 2008
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We have implemented the Steiner point of 2- dimensional fuzzy sets and we have made experiments. We expect that this could suggest further directions in the mathematical investigation of this topic.

Two methods of reconstruction of generators of continuous t-norms

  • Autoři: prof. Ing. Mirko Navara, DrSc., Petrík, M.
  • Publikace: IPMU 2008: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Málaga: Department of Applied Mathematics, School of Computer Sci., University of Málaga, 2008. pp. 1016-1021. ISBN 978-84-612-3061-7.
  • Rok: 2008
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We present two methods which allow to reconstruct the multiplicative and the additive generator of a continuous Archimedean triangular norm from its partial derivatives. The methods can be used for a strict triangular norm whose multiplicative generator has a non-zero derivative at 0, resp. for a continuous Archimedean triangular norm whose additive generator has a derivative continuous at [0,1] and non-zero at 1.

Cantor-Bernstein property

  • Autoři: Di Nola, A., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Abstracts of Lectures, Tutorials, and Talks. International Conference on Order, Algebra, and Logics. Nashville: Vanderbilt University, 2007. p. 22-23.
  • Rok: 2007
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We ask which algebras satisfy the Cantor-Bernstein theorem in its original form, without any additional condition. We summarize some results for orthomodular lattices and compare them to the situation in MV-algebras.

Cantor-Bernstein property for MV-algebras

  • Autoři: Di Nola, A., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Algebraic and Proof-theoretic Aspects of Non-classical Logics. Papers in Honor of Daniele Mundici on the Occasion of His 60th Birthday. Berlin: Springer-Verlag, 2007. p. 107-118. ISBN 978-3-540-75938-6.
  • Rok: 2007
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Generalizations of the Cantor -Bernstein theorem have been proved for different types of algebras. We ask which algebras satisfy the Cantor- Bernstein theorem without any additional assumption. In the case of orthomodular lattices, it has been proved that this class is rather large. We study the analogous question for MV-algebras and we find out interesting examples of MV-algebras which possess or do not possess this property.

Constructions of quantum structures

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Handbook of Quantum Logic and Quantum Structures. Amsterdam: Elsevier, 2007. p. 335-366. ISBN 978-0-444-52870-4.
  • Rok: 2007
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We collect results which allow to construct quantum structures, namely orthomodular lattices, orthomodular posets, orthoalgebras, and effect algebras. Particular attention is paid to the pasting. Although the text is self-contained and should be accessible also to beginners, it presents tools helpful to experts, too.

Extending States on Finite Concrete Logics (vol 44, 2005)

  • DOI: 10.1007/s10773-006-9298-6
  • Odkaz: https://doi.org/10.1007/s10773-006-9298-6
  • Pracoviště: Katedra matematiky, Katedra kybernetiky
  • Anotace:
    We summarize and extend results about ``small'' quantum structures with small dimensions of state spaces. These constructions have contributed to the theory of orthomodular lattices. More general quantum structures (orthomodular posets, orthoalgebras, and effect algebras) admit sometimes simplifications, but there are problems where no progress has been achieved.

How to use controller with conditionally firing rules

  • Autoři: prof. Ing. Mirko Navara, DrSc., Petrík, M.
  • Publikace: New Dimensions in Fuzzy Logic and Related Technologies. Proceedings of the 5th EUSFLAT Conference. Ostrava: Technická univerzita Ostrava, 2007. p. 87-94. ISBN 978-80-7368-387-0.
  • Rok: 2007
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    In previous work, a fuzzy controller with conditionally firing rules was suggested as an advantageous alternative to Mamdani Assilian controllers. Its features have been used without much understanding. Therefore we explicitly formulate the rules of its design in this tutorial which has not been available before.

Implementation of calculating Steiner point for 2-D objects

  • Autoři: Liang, J., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: ISKE07: Proceedings of the International Conference on Intelligent Systems and Knowledge Engineering. Paris: Atlantis Press, 2007. pp. 1592-1598. ISBN 978-90-78677-04-8.
  • Rok: 2007
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    This approach deals with the Steiner point calculation implementation and its application in image processing. Based on Steiner point definition and some properties, a numerical method is proposed for calculating the Steiner point of a 2-dimensional polytope. Also analysis of computational complexity and numerical precision of the integration is discussed. The invariance with respect to the Minkowski sum and translation is proved based on the promoted algorithm for polytopes. Some experiments on randomized 2-dimensional data and 2-D image processing are provided for testing the the algorithm.

MV-algebras with the Cantor-Bernstein property

  • Autoři: Di Nola, A., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Theoretical Advances and Applications of Fuzzy Logic and Soft Computing. Heidelberg: Springer, 2007. p. 861-868. ISBN 978-3-540-72433-9.
  • Rok: 2007
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We ask which MV-algebras satisfy the Cantor-Bernstein theorem in its original form, without any additional condition. Inspired by results for orthomodular lattices, we compare them to the situation in MV-algebras.

Probability and conditional probability on tribes of fuzzy sets

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Fuzzy Sets, Probability, and Statistics - Gaps And Bridges. Linz: Johannes Kepler University, 2007. p. 84-88.
  • Rok: 2007
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The classical probability theory and statistics tries to avoid experiments whose results are vague. However, also this type of information is useful and used in everyday life. To treat it, an extension of probability theory to events described by fuzzy sets is highly desirable. An intuitive definition has been suggested by Zadeh. Later on, an axiomatic approach has been introduced by Butnariu and Klement. Independently, measures on MV-algebras have been studied. Particularly interesting results have been obtained by Riečan and Mundici for MV-algebras with product. We show that these two approaches overlap significantly. Further, we outline conditional probabilities in this context.

Varieties of orthomodular lattices

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We summarize recent results on state spaces of orthomodular lattices. We obtain that the lattice of varieties of orthomodular lattices is of ``continuum height" and of ``infinite width".

Defuzzification using Steiner points

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    A defuzzification function assigns to each fuzzy set a crisp value in a way that this value may intuitively be understood as the ``centre'' of the fuzzy set. In the present paper, this vague concept is put into a mathematically rigorous form. To this end, we proceed analogously to the case of sharply bordered subsets, for which the Steiner point is frequently used. The function assigning to each convex subset its Steiner point is characterised by three properties; here, we study functions whose domains consist of fuzzy sets and which fulfil analogous properties. Although uniqueness can no longer be achieved, we give a complete characterisation of what we call Steiner points of fuzzy sets.

Fuzzy Control - Expectations, Current State, and Perspectives

  • Autoři: prof. Ing. Mirko Navara, DrSc., Petrík, M.
  • Publikace: Computational Intelligence, Theory and Applications. Berlin: Springer, 2006. p. 667-676. ISBN 3-540-34780-1.
  • Rok: 2006
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We analyse the reasons of success of fuzzy logic and fuzzy control. Their advantages as well as difficulties and drawbacks are discussed. We bring arguments why it is important to extend the use of fuzzy systems from home appliances to demanding applications with high requirements on reliability. The success or failure of this effort may decide the future role of fuzzy systems.

Kleene-isomorphic sigma-complete MV-algebras with product are isomorphic

  • Autoři: Cignoli, R., Mundici, D., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Journal of Multiple-Valued Logic and Soft Computing. 2006, 10(1-2), 1-8. ISSN 1542-3980.
  • Rok: 2006
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We prove that the Kleene structure in a sigma-complete MV-algebra with product is sufficient to recover the MV-structure.

Long-term experience with Maple: Advantages and challenges of Maple 10

Residuated logics based on strict t-norms with an involutive negation

  • Autoři: Cintula, P., Klement, E., Mesiar, R., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Mathematical Logic Quarterly. 2006, 52(3), 269-282. ISSN 0942-5616.
  • Rok: 2006
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    In general, there is only one fuzzy logic in which the standard interpretation of the strong conjunction is a strict triangular norm, namely, the product logic. We study several equations which are satisfied by some strict t-norms and their dual t-conorms. Adding an involutive negation, these equations allow us to generate countably many logics based on strict t-norms which are different from the product logic.

Varieties of algebras based on strict t-norms and involutive negations

  • Autoři: Cintula, P., Klement, E., Mesiar, R., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: FSTA06: Abstracts of 8th International Conference on Fuzzy Set Theory and Applications. Liptovský Mikuláš: Vojenská akadémia, 2006. pp. 8-9. ISBN 80-8040-284-1.
  • Rok: 2006
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Algebras based on triangular norms (and their residua) appeared naturally as models of fuzzy logics. They also form a basis for measure theory on collections of fuzzy sets. We conclude that there are (at least) countably many different fuzzy logics based on strict t-norms and involutive negations.

Convexity Conditions on T-Norms and their Additive Generators

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Let T be an Archimedean (continuous) t-norm and a in ]0, 1/2[. Fodor and Ovchinnikov have studied a relation between the inequality T (max(x-a, 0), min(x +a, 1)) / T (x, x) and the convexity of the additive generator of T. Here we clarify this relation and answer open problems from previous studies.

Decidability in Orthomodular Lattices

  • Autoři: Hyčko, M., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: International Journal of Theoretical Physics. 2005, 44(12), 2239-2248. ISSN 0020-7748.
  • Rok: 2005
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We discuss the possibility of automatic simplification of formulas in orthomodular lattices. We describe the principles of a program which decides the validity of equalities and inequalities, as well as implications between them and other important relations significant in quantum mechanics.

Extending States on Finite Concrete Logics

  • DOI: 10.1007/s10773-005-7083-6
  • Odkaz: https://doi.org/10.1007/s10773-005-7083-6
  • Pracoviště: Katedra matematiky, Katedra kybernetiky
  • Anotace:
    In this note we collect several observations on state extensions. They may be instrumental to anyone who pursues the theory of quantum logics. In particular, we find out when extensions (resp. signed extensions) exist in the "concrete" concrete logic of all even-element subsets of an even-element set. We also mildly add to the study of difference-closed logics by finding an extension theorem for subadditive states.

Probability Theory of Fuzzy Events

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: EUSFLAT 2005: Fourth Conference of the European Society for Fuzzy Logic and Technology and 11 Rencontres Francophones sur la Logique Floue et ses Applications. Barcelona: Universitat Politecnica de Catalunya, 2005. p. 325-329. ISBN 84-7653-872-3.
  • Rok: 2005
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We compare two approaches to probability on systems of fuzzy sets-measures on tribes as introduced by Butnariu and Klement and measures on MV-algebras with product studied by Riečan and Mundici. We show that these two approaches overlap significantly and they confirm the original proposal of probability measure on fuzzy sets by Zadeh.

Sequential Coordinate-Wise Algorithm for the Non-negative Least Squares Problem

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The paper contributes to the solution of the non-negative least squares problem. We propose a novel sequential coordinat-wise algorithm which is easy to implement and it is able to cope with larte scale problems. We derive stopping conditioons which allow to control te distance of the solution found to the optimal one in terms of the optimized objective function.

Sufficient Triangular Norms in Many-valued Logics with Standard Negation

  • Autoři: Butnariu, D., Klement, E., Mesiar, R., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Archive for Mathematical Logic. 2005, 44(7), 829-849. ISSN 1432-0665.
  • Rok: 2005
  • DOI: 10.1007/s00153-004-0267-6
  • Odkaz: https://doi.org/10.1007/s00153-004-0267-6
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    In many-valued logics with the unit interval as the set of truth values, from the standard negation and the product (or, more generally, from any strict Frank t-norm) all measurable logical functions can be derived, provided that also operations with countable arity are allowed. The question remained open whether there are other t-norms with this property or whether all strict t-norms possess this property. We give a full solution to this problem (in the case of strict t-norms), together with convenient sufficient conditions. We list several families of strict t-norms having this property and provide also counterexamples (the Hamacher product is one of them). Finally, we discuss the consequences of these results for the characterization of tribes based on strict t-norms.

Sufficient triangular norms in many-valued logics with standard negation

  • Autoři: Butnariu, D., Klement, E.P., Mesiar, R., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: IEEE - SOFA 2005: IEEE International Workshop on Soft Computing Applications. New York: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2005. p. 8-9.
  • Rok: 2005
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Algebras based on triangular norms (and their residua) appeared naturally as models of fuzzy logics. They also form a basis for measure theory on collections of fuzzy sets. We conclude that there are (at least) countably many different fuzzy logics based on strict t-norms and involutive negations.

The Sigma-complete MV-algebras which Have Enough States

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We characterize Lukasiewicz tribes, i.e., collections of fuzzy sets that are closed under the standard fuzzy complementation and the Lukasiewicz t-norm with countably many arguments. As a tool, we introduce Sigma-McNaughton functions as the closure of McNaughton functions under countable MV-algebraic operations. We give a measure-theoretical characterization of Sigma-complete MV-algebras which are isomorphic to Lukasiewicz tribes.

The Steiner Point of Fuzzy Sets

  • Autoři: Vetterlein, T., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Fuzzy Logic, Soft Computing & Computational Intelligence. Eleventh International Fuzzy Systems Association World Congress. Beijing: Tsinghua University Press/Springer, 2005. p. 1256-1258. ISBN 7-302-11377-7.
  • Rok: 2005
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The Steiner point not the center of gravity should represent the location of structures (convex bodies) which grow uniformly in all directions. In this case, it gives the same location of the body during the growth. This is useful in biomedical applications. As the bodies sometimes do not have sharp boundaries, it is desirable to extend it to fuzzy sets. We clarify the possibility and problems of this generalization.

Theorem Proving in Fuzzy Logics

  • Autoři: Cintula, P., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: International Conference The Logic for Soft Computing IV & 4th Workshop of the ERCIM Working Group on Soft Computing. Ostrava: Technická univerzita Ostrava, 2005. p. 78-80.
  • Rok: 2005
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Computer algebra allows to perform many operations which were considered difficult, e.g., factorization, integration, symbolic solution of ODEs, etc. Logical operations are not always implemented. E.g., Maple 9 has a package logic which was missing in several preceding versions. Except for packages for fuzzy control, there seems to be no professional software for fuzzy logical tasks. Here we summarize current situation in computer algebra support of testing tautologies in fuzzy logics.

Triangular Norms and Measures of Fuzzy Sets

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms. Amsterdam: Elsevier Science, 2005. p. 345-390. ISBN 0-444-51814-2.
  • Rok: 2005
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The classical measure and probability theory is based on the notion of Sigma$-algebra of subsets of a set. Butnariu and Klement generalized it to fuzzy sets by considering collections of fuzzy sets called T-tribes (where T denotes a fixed triangular norm). Their concept of T-measure is fundamental in the fuzzification of classical measure theory. However, it has been successfully applied elsewhere, too (e.g., in finding solutions to games with fuzzy coalitions). Here we summarize results about characterization of measures on tribes. More generally, we study signed measures (called charges). Unlike preceding papers, we put emphasis on s-order continuous charges which preserve limits of increasing as well as decreasing sequences of fuzzy sets. We argue that this notion could be considered as a promising alternative to the original notion of Butnariu and Klement.

When a Residuum can be a Derived Operation of Fuzzy Logic

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Algebraic and Topological Methods in Non-Classical Logics II. Barcelona: University of Barcelona, 2005. p. 59-60.
  • Rok: 2005
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We answer the question when a residuum in a fuzzy logic can be derived from other connectives, mainly the conjunction and an involutive negation.

Automatic generation of fuzzy rules and its applications in medical diagnosis

  • Autoři: prof. Ing. Mirko Navara, DrSc., Peri, D.
  • Publikace: Proceedings of the 10th International Conference on Information Processing and Management of Uncertainty. Rome: Universita La Sapienza, 2004. p. 657-663. ISBN 88-87242-54-2.
  • Rok: 2004

Cantor-Bernstein theorems for quantum structures

Compactness of Fuzzy Logics

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Compactness is an important property of classical logic. It states that simultaneous satisfiability of an infinite set of formulas is equivalent to the satisfiability of all its finite subsets. In fuzzy logics, we have different degrees of satisfiability, hence the questions of compactness become more complicated. Here we give an overview of the recent results on compactness and we extend them to various fuzzy logics.

For n>=5 there is no nontrivial Z_2-measure on L(R^n)

On the permanence properties of interval homogeneous orthomodular lattices

Piron's and Bell's geometrical lemmas

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The famous Gleason's Theorem gives a characterization of measures on lattices of subspaces of Hilbert spaces. The attempts to simplify its proof lead to geometrical lemmas that possess also easy proofs of some consequences of Gleason's Theorem. We contribute to these results by solving two open problems formulated by Chevalier, Dvurečenskij and Svozil. Besides, our use of orthoideals provides a unified approach to finite and infinite measures.

Regular measures on tribes of fuzzy sets

Statistika - jejívýjimečná role ve vědě a argumenty pro revizi

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: 36. konferencia slovenských matematikov. Žilina: University of Žilina, 2004, pp. 14-15. ISBN 80-8070-320-5.
  • Rok: 2004
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Je zdůrazněna role statistiky nejen v matematice, ale jako nezbytného nástroje vědeckého zkoumání. Jsou důvody pro další zobecnění zahrnující vágnost (fuzzy výroky) a kvantovou neurčitost (pozorovanou nejen v kvantově mechanických systémech).

The role of computers in studies of quantum structures

  • Autoři: Hyčko, M., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Quantum Structures 2004. New Mexico: New Mexico State University, 2004, pp. 25.
  • Rok: 2004

Triangular norms and negations - which expressions do they allow?

  • Autoři: Butnariu, D., Klement, E., Mesiar, R., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Abstracts of the 7th International Conference on Fuzzy Sets Theory and Its Applications. Liptovský Mikuláš: Printing House of the Military Academy in Liptovský Mikuláš, 2004, pp. 25-26.
  • Rok: 2004

When a residuum can be computed from a t-norm and a negation

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of the 3rd International Workshop on Nonstandard Logics. Praha: ČVUT v Praze, FEL, 2004, pp. 12-14. ISBN 80-01-03003-2.
  • Rok: 2004

A Cantor-Bernstein theorem for S-complete MV-algebras

  • Autoři: De Simone, A., Mundici, D., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Czechoslovak Mathematical Journal. 2003, 53 (128)(2), 437-447. ISSN 0011-4642.
  • Rok: 2003
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The Cantor-Bernstein theorem was extended to S-complete boolean algebras by Sikorski and Tarski. Chang's MV-algebras are a nontrivial generalization of boolean algebras: they stand to the infinite-valued calculus of luk as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to S-complete MV-algebras, and compare it to a related result proved by Jakubí k for certain complete MV-algebras.

Characterization of T-measures

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    As a natural generalization of a measure space, Butnariu and Klement introduced T-tribes of fuzzy sets with T-measures. They made the first steps towards a characterization of monotonic real-valued T-measures for a Frank triangular norm T. Later on, Mesiar and the authors of this paper found independently two generalizations, one for vector-valued T-measures with respect to Frank t-norms (in particular for nonmonotonic ones), the other for monotonic real-valued T-measures with respect to general strict t-norms. Here we present a common generalization-a characterization of nonmonotonic T-measures with respect to an arbitrary strict t-norm. Moreover, we prove this for vector-valued T-measures. Using their characterization, we generalize Ljapunov Theorem to this context.

Convergence of the Expectation Maximization Algorithm for the Conditionally Independent Model to the Global Maximum

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    This contribution builds on M.I. Schlesinger's results. M.I. Schlesinger discovered that in a special case of a statistical model (conditional independence with two hidden states only) the EM algorithm converges to a global extreme. Under the same assumptions we shortened and simplified the proof of global convergence. We also smoothed away two minor imprecisions in the original proof and learned that they do not affect validity.

Convex structure of the space of fuzzy measures

Criteria that should be satisfied by Mamdani-Assilian controller

  • Autoři: Amato, P., Di Nola, A., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of International Conference on Fuzzy Information Processing Theories and Applications. Beijing: Tsinghua University Press/Springer, 2003, pp. 195-198. ISBN 7-302-06299-4.
  • Rok: 2003

Mathematical aspects of fuzzy control

  • Autoři: Amato, P., Di Nola, A., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Fuzzy Logic and Applications. 5th International Workshop, WILF 2003. Berlin: Springer, 2003, pp. 80-88. ISBN 3-540-31019-3.
  • Rok: 2003
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    In recent decades, fuzzy controllers were successfully applied to many tasks. Their use was based more on engineering intuition than on deep mathematical treatment. Here we collect several criteria that a fuzzy controller should satisfy in order to represent the meaning of the rule base. Surprisingly, these conditions are often ignored and violated. Sometimes this is caused only by wrong design, but there are cases when the principle of the controller does not admit to satisfy these criteria. We discuss them in more detail and formulate conclusions for selection of an appropriate type of fuzzy controller.

Mathematical aspects of fuzzy control

  • Autoři: Amato, P., Di Nola, A., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: WILF 2003 International Workshop on Fuzzy Logic and Applications. Naples: ICAR - National Research Council, 2003, pp. 1-6.
  • Rok: 2003

Reformulation of fuzzy controller with conditionally firing rules

  • Autoři: Amato, P., Di Nola, A., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: International Conference on Computational Intelligence for Modelling, Control and Automation. Canberra: University of Canberra, 2003, pp. 140-151.
  • Rok: 2003

Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering

  • Autoři: Mrázek, P., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: International Journal of Computer Vision. 2003, 52(2/3), 189-203. ISSN 0920-5691.
  • Rok: 2003
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We develop a novel time-selection strategy for iterative image restoration techniques: the stopping time is chosen so that the correlation of signal and noise in the filtered image is minimized.

Two approaches to fuzzy propositional logics

  • Autoři: Hekrdla, J., Klement, E.P., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Journal of Multiple-Valued Logic and Soft Computing. 2003, 9(4), 343-360. ISSN 1542-3980.
  • Rok: 2003
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    We compare two approaches to fuzzy logics: R-fuzzy logics studied mainly by H'ajek, and S-fuzzy logics introduced by Butnariu, Klement and Zafrany. We improve some previous results and we discuss satisfiability, compactness and related questions in these logics. Special attention is paid to the comparison of their semantics.

Computer algebraic systems in proofs and visualization of results related to Gleason's Theorem

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Abstracts of the 6th International Conference on Fuzzy Sets Theory and Applications. Liptovský Mikuláš: Vojenská akadémia, 2002, pp. 95-96.
  • Rok: 2002

Consistency degrees in fuzzy logics

Fuzzy controllers with conditionally firing rules

On the Yosida-Hewitt decomposition and Rüttimann decomposition of states

Program for Generating Fuzzy Logical Operations and Its Use in Mathematical Proofs

Properties of fuzzy controller with conditionally firing rules

  • Autoři: prof. Ing. Mirko Navara, DrSc., Šťastný, J.
  • Publikace: Intelligent Technologies - Theory and Applications. Amsterdam: IOS Press, 2002. p. 111-116. ISBN 1-58603-256-9.
  • Rok: 2002

The Vitali-Hahn-Saks theorem for the product of quantum logics

Validation Sets in Fuzzy Logics

Which fuzzy logics satisfy the compactness property

  • Autoři: Cintula, P., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of 9th International Conference Information Processing and Management of Uncertainty in Knowledge-Based Systems. Annecy: ESIA - Université de Savoie, 2002, pp. 405-409. ISBN 2-9516453-5-X.
  • Rok: 2002

Compactness of Fuzzy Logics

  • Autoři: prof. Ing. Mirko Navara, DrSc., Bodenhofer, U.
  • Publikace: Proceedings 2nd International ICSC Congress on Computational Intelligence: Methods and Applications (CIMA 2001). Bangor: International Computing Sciences Conventions, 2001, pp. 654-657.
  • Rok: 2001

Conjunctions of Many-valued Criteria

  • Autoři: Bartušek, T., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of the International Conference Uncertainty Modelling'2001. Slovenská technická univerzita v Bratislave, 2001, pp. 67-77.
  • Rok: 2001

Consistent Positive Directional Splitting of Anisotropic Diffusion

  • Autoři: Mrázek, P., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of Computer Vision Winter Workshop. Ljubljana: Slovenian Pattern Recognition Society, 2001. p. 37-48. ISBN 961-90901-0-1.
  • Rok: 2001

Constrained Fuzzy Arithmetic

  • Autoři: Kreinovich, V., prof. Ing. Mirko Navara, DrSc., Žabokrtský, Z.
  • Publikace: Proceedings of Workshop on Soft Computing. Bratislava: Comenius University, 2001, pp. 1-3.
  • Rok: 2001

Convex Structure of the Space of T-Measures

Easy Proofs of Some Consequences of Gleason's Theorem

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of Summer School on Real Analysis and Measure Theory. Trieste: Universitá Trieste, 2001, pp. 91-94.
  • Rok: 2001

Enhancement of {M}amdani Fuzzy Controller

  • Autoři: prof. Ing. Mirko Navara, DrSc., Šťastný, J.
  • Publikace: Proceedings EUSFLAT 2001. Leicester: De Montfort University, 2001, pp. 168-170.
  • Rok: 2001

Generalizations of Cantor-Bernstein Theorem

  • Autoři: De Simone, A., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of International Conference on Non Classical Logic, Approximate Reasoning and Soft Computing. Napoli: University "Federico II", 2001, pp. 33-35.
  • Rok: 2001

How to Choose a Many-valued Conjunction

How to Make Constrained Fuzzy Arithmetic Efficient

On Interval Homogeneous Orthomodular Lattices

On Interval Homogeneous Orthomodular Lattices

Piron's and Bell's Geometrical Lemmas

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of Summer School on Real Analysis and Measure Theory. Trieste: Universitá Trieste, 2001, pp. 1-8.
  • Rok: 2001

Quantum Logics with Given Centers, State Spaces and Automorphism Groups

  • Autoři: Harding, J., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Quantum Structures V. Cesena-Cesenatico: International Quantum Structures Association, 2001, pp. 44-46.
  • Rok: 2001

Rüttimann Decompositions of States

  • Autoři: De Simone, A., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Quantum Structures V. Cesena-Cesenatico: International Quantum Structures Association, 2001, pp. 32-33.
  • Rok: 2001

Strict Triangular Norms and Characterization of T-Measures

  • Autoři: Barbieri, G., prof. Ing. Mirko Navara, DrSc., Weber, H.
  • Publikace: Proceedings EUSFLAT 2001. Leicester: De Montfort University, 2001. pp. 455-457.
  • Rok: 2001

Validation Sets in Fuzzy Logics

Yosida-Hewitt and Lebesgue Decompositions of States on Orthomodular Posets

  • Autoři: De Simone, A., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Journal of Mathematical Analysis and Its Applications. 2001, 255(1), 74-104. ISSN 0022-247X.
  • Rok: 2001

A New Type of a Fuzzy Controller

  • Autoři: Hekrdla, J., Moser, B., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Abstracts of 5th Int. Conf. Fuzzy Sets Theory Appl. Liptovský Mikuláš: Vojenská akadémia, 2000, pp. 100-101.
  • Rok: 2000

Cantor-Bernstein Theorems for Noncommutative Structures

Computational Problems of Constrained Fuzzy Arithmetic

  • Autoři: prof. Ing. Mirko Navara, DrSc., Žabokrtský, Z.
  • Publikace: The State of the Art in Computational Intelligence. Heidelberg: Physica-verlag, 2000. p. 95-98. ISBN 3-7908-1322-2.
  • Rok: 2000

Embeddings into Orthomodular Lattices with Given Centers, State Spaces and Automorphism Groups

Fuzzy Logics with Residuated Implication and Involutive Negation

  • Autoři: Esteva, F., Godo, L., Hájek, P., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Archive for Mathematical Logic. 2000, 39(1), 103-124. ISSN 0933-5846.
  • Rok: 2000

Mathematical Models of Uncertainty

Orthomodular Lattices with Rich State Spaces

Satisfiability in Fuzzy Logics

State Spaces of Orthomodular Structures

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Rendiconti dell'Istituto di Matematica dell'Universita di Trieste. 2000, 31(Suppl. 1), 143-201. ISSN 0049-4704.
  • Rok: 2000

Theory and Applications of Fuzzy Control

  • Autoři: prof. Ing. Mirko Navara, DrSc., Moser, B., Mrázek, P.
  • Publikace: Proceedings of Workshop 2000. Praha: České vysoké učení technické v Praze, 2000, pp. 38. ISBN 80-01-02229-3.
  • Rok: 2000

A survey of different triangular norm-based fuzzy logics

Characterization of measures based on strict triangular norms

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Journal of Mathematical Analysis and Its Applications. 1999, 236(2), 370-383. ISSN 0022-247X.
  • Rok: 1999

Comparing Semantics of Fuzzy Logics

Conditionally firing rules extend the possibilities of fuzzy controllers

  • Autoři: Moser, B., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of the International Conference Computational Intelligence for Modelling, Control and Automation. Amsterdam: IOS Press, 1999, pp. 242-245. ISBN 90-5199-474-5.
  • Rok: 1999

Constructions and Varieties of Orthomodular Lattices with Rich State Spaces

  • Autoři: Mayet, R., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings Workshop on Measure Theory and Real Analysis. Trieste: University of Trieste, 1999, pp. 76-89.
  • Rok: 1999

Diagonals of continuous triangular norms

Propositional fuzzy logics based on Frank t-norms

  • Autoři: Klement, E., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Fuzzy Sets, Logics and Reasoning about Knowledge. Dordrecht: Kluwer Academic Publishers, 1999, pp. 17-38. ISBN 0-7923-5977-1.
  • Rok: 1999

The Independence of the Center, State Space and Automorphism Group of Quantum Logics

  • Autoři: Harding, J., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Current Research in Operational Quantum Logic. Brussels: Free University of Brussels, 1999, pp. 100-110.
  • Rok: 1999

Two Descriptions of State Spaces of Orthomodulat Structures

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: International Journal of Theoretical Physics. 1999, 38(12), 3163-3178. ISSN 0020-7748.
  • Rok: 1999

Uncertainty and dependence in classical and quantum logic - the role of triangular norms

Varieties of orthomodular lattices determined by measures

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings 23rd Holiday Mathematics Symposium. Las Cruces: New Mexico State University, 1999, pp. 9-10.
  • Rok: 1999

Which triangular norms are convenient for fuzzy controllers?

  • Autoři: Moser, B., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings EUSFLAT-ESTYLF Joint Conf. 99. Palma de Mallorca: Universitat de les Illes Balears, 1999, pp. 75-78.
  • Rok: 1999

Comparison of Semantics of Fuzzy Logics

Computer algebra systems as a tool for computer proofs in quantum logic theory

  • Autoři: Hamouz, M., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings Conference Appl. Computer Algebra '98. Praha: České vysoké učení technické v Praze, Fakulta jaderná a fyzikálně inženýrská, 1998, pp. 1.
  • Rok: 1998

Computer algebra systems as a tool for mathematical proofs in quantum logics

  • Autoři: Hamouz, M., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings Conference Appl. Computer Algebra '98. Praha: České vysoké učení technické v Praze, Fakulta jaderná a fyzikálně inženýrská, 1998, pp. 1-7.
  • Rok: 1998

Considering Uncertainty and Dependence in Boolean, Quantum and Fuzzy Logics

Fuzzy Logics with Residuated Implication and Involutive Negation

  • Autoři: Esteva, F., Godo, L., Hájek, P., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Abstracts of Logic Colloquium '98. Praha: AV ČR, 1998, pp. 170.
  • Rok: 1998

Fuzzy Propositional Logic with Infinite Operations

  • Autoři: Hekrdla, J., Klement, E., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Fuzzy Sets Theory Applications - Abstracts. Liptovský Mikuláš: Vojenská akadémia, 1998, pp. 54.
  • Rok: 1998

Measures on Tribes of Fuzzy Sets and the Role of Frank t-Norms

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings 7th Int. Conf. Information Processing and Management of Uncertainty. Paris: Editions E.D.K, 1998, pp. 1756-1761. ISBN 2-84254-013-1.
  • Rok: 1998

Nearly Frank t-Norms and the Characterization of T-measures

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Non-Classical Measures and Their Applications to Decision Making. Linz: Universität Linz, 1998, pp. 9-16.
  • Rok: 1998

Quantum Logics with Given Centers and Variable State Spaces

Strong Negation: Its Relation to Intervals and Its Use in Expert Systems

  • Autoři: Starks, S.A., Kreinovich, V., Nguyen, H., Nguyen, H., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings 4th World Congress on Expert Systems Mexicon '98. Mexico City: ITESM, 1998, pp. 56-59.
  • Rok: 1998

The Role of Difference Operation in Quantum Structures

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Abstracts of 4th IQSA Biannual Meeting Quantum Structures '98. Liptovský Mikuláš: Vojenská akadémia, 1998, pp. 67.
  • Rok: 1998

Triangular Norms with Continuous Diagonals

Types of Uncertainty and the Role of the Frank t-Norms in Classical and Nonclassical Logics

A Characterization of Tribes with Respect to the Lukasiewicz t-norm

  • Autoři: Klement, E.P., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Czechoslovak Mathematical Journal. 1997, 47(122)(4), 689-700. ISSN 0011-4642.
  • Rok: 1997

All Strict Triangular Norms are "Equally Strong"

  • Autoři: prof. Ing. Mirko Navara, DrSc., Butnariu, D., Klement, E.P.
  • Publikace: Proceedings of the Conference on Fuzzy Logic and Applications. Tel-Aviv: Tel-Aviv University, 1997. pp. 116-124.
  • Rok: 1997

Boolean Representations of Fuzzy Quantum Spaces

Characterization of State Spaces of Orthomodular Structures

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings Summer School on Measure Theory and Real Analysis. Trieste: Universitá Trieste, 1997. pp. 97-123.
  • Rok: 1997

Decompositions of States on Orthomodular Posets

  • Autoři: prof. Ing. Mirko Navara, DrSc., De Simone, A.
  • Publikace: Proceedings International Seminar Fuzzy Sets, Quantum Structures and Related Topics. Bratislava: STU v Bratislave, 1997. pp. 14-15.
  • Rok: 1997

Difference Posets and Orthoalgebras

Fuzzy Logic Ideas in Pattern Recognition

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Czech Pattern Recognition Workshop '97. Prague: Czech Pattern Recognition Society, 1997. pp. 14-23.
  • Rok: 1997

How Prominent is the Role of {F}rank t-norms?

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings 7th IFSA World Congress. Praha: Academia, 1997. pp. 291-296. ISBN 80-200-0633-8.
  • Rok: 1997

How the State Spaces of Quantum Logics Can Be Described

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Abstracts: IQSA's Conference "Atlanta'97". Atlanta: Georgia Institute of Technology, 1997. pp. 5-6.
  • Rok: 1997

Less Simple Maple---Evaluation Rules, Bugs, and Advantages

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Computer Aided Education in Automation and Control. Bratislava: STU v Bratislave, 1997. pp. 74-97. ISBN 80-227-0978-6.
  • Rok: 1997

Matrix Composition of T-norms

  • Autoři: prof. Ing. Mirko Navara, DrSc., Drossos, C.
  • Publikace: Enriched Lattice Structures for Many-Valued and Fuzzy Logic. Linz: Universität Linz, 1997. pp. 95-100.
  • Rok: 1997

On Generating Finite Orthomodular Sublattices

Qualitative and Quantitative Valuation Structures

  • Autoři: prof. Ing. Mirko Navara, DrSc., Drossos, C.
  • Publikace: Enriched Lattice Structures for Many-Valued and Fuzzy Logic. Linz: Universität Linz, 1997. pp. 36-41.
  • Rok: 1997

Types of Uncertainly Types of Dependence

Coming from Distributive to Orthomodular

Constructions with t-Norms

Generalized t-conorms and closure operators

  • Autoři: Drossos, C., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of the 4th European Congress on Intelligent Techniques and Soft Computing EUFIT'96. Aachen: Verlag der Augustinus Buchhandlung, 1996. p. 22-26. ISBN 3-89653-187-5.
  • Rok: 1996

Quantum Logics Representable as Kernels of Measures

TS-tribes and TS-measures

  • Autoři: Mesiar, R., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Journal of Mathematical Analysis and Its Applications. 1996, 201(1), 91-102. ISSN 0022-247X.
  • Rok: 1996

Classes of Logics Representable as Kernels of Measures

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Classes of Logics Representable as Kernels of Measures

Classes of Logics Representable as Kernels of Measures

Dynamic Testing of A/D Plug-in Boards

Fuzzy Quantum Spaces and Boolean Representations

Non-classical Logics Representable as Kernels of Measures on Boolean Algebras

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Abstract 10th International Congress of Logic, Methodology and Philosophy of Science. Florence: ???, 1995. pp. 415.
  • Rok: 1995

States on orthoalgebras

Uniqueness of Bounded Observables

  • Autoři: prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Annales de l'Institut Henri Poincaré, Physique théorique. 1995, 63(2), 155-176. ISSN 0246-0211.
  • Rok: 1995

An orthomodular lattice admitting no group-valued measure

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    An orthomodular lattice admitting no group-valued measure exists

A Characterization of Triangular Norm Based Tribes

A characterization of triangular norm based tribes

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    A characterization of triangular norm based tribes

A Mathematical Model of Sound Transmision through the Middle Ear

  • Autoři: Navara, M., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Workshop 93. Praha: České vysoké učení technické v Praze, 1993. pp. 27-28.
  • Rok: 1993

Algebraic Approach to Fuzzy Quantum Spaces

Kernel Logics

Kernel logics

P-measures on Soft Fuzzy Sigma-algebras

Descriptions of state spaces of orthomodular lattices

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Descriptions of state spaces of orthomodular lattices

Independence of automorphism group, center, and state space of quantum logics

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Independence of automorphism group, center, and state space of quantum logics

States on soft fuzzy algebras |

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    States on soft fuzzy algebras | nite and countable additivity

A characterization of sigma-state spaces of orthomodular lattices

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    A characterization of sigma-state spaces of orthomodular lattices

Automorphisms of concrete logics

Orthosymmetry and Modularity in Ortholattices

The pasting Constructions for Orthomodular Posets

Almost Boolean orthomodular posets

Integration on generalized measure spaces

When is the integral on quantum probability spaces additive?

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    When is the integral on quantum probability spaces additive?

Construction of orthomodular lattices with given state spaces

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Construction of orthomodular lattices with given state spaces

Enlargements of logics (sigma-orthocomplete case)

ENLARGEMENTS OF QUANTUM-LOGICS

On constructions of orthomodular posets

  • Autoři: Rogalewicz, V., prof. Ing. Mirko Navara, DrSc.,
  • Publikace: Proceedings of the First Winter School on Measure Theory. Bratislava: AV SR, Matematický institut, 1988. pp. 133-137.
  • Rok: 1988

State isomorphism of orthomodular posets and hypergraphs

  • Autoři: prof. Ing. Mirko Navara, DrSc., Rogalewicz, V.
  • Publikace: Proceedings of the First Winter School on Measure Theory. Bratislava: AV SR, Matematický institut, 1988. pp. 93-98.
  • Rok: 1988

State space properties of finite logics

Quantum logics with Jauch-Piron states

Two-valued measures on sigma-classes

Za stránku zodpovídá: Ing. Mgr. Radovan Suk