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A Mathematical Setting for Fuzzy Logics
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 1997The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the algebra of truth values is the real numbers in the unit interval equipped with minimum, maximum and -x=1-x for conjunction, disjunction and negation ...
Carol L. Walker +2 more
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Special Issue on Mathematical Fuzzy Logic
Journal of Logic and Computation, 2011Editoriale
Cintula P., Metcalfe G., Noguera C.
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A General Omitting Types Theorem in Mathematical Fuzzy Logic
IEEE Transactions on Fuzzy Systems, 2021This article is a contribution to the theoretical study of weighted structures in fuzzy logic. We consider an important item from classical model theory: the construction of models that do not have any collection satisfying certain prescribed properties, that is, an omitting types theorem. We generalize the work done by Cintula and Diaconescu (Omitting
Guillermo Badia, Carles Noguera
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What is mathematical fuzzy logic
Fuzzy Sets and Systems, 2006The paper comments on the development and present state of fuzzy logic as a kind (branch) of mathematical logic. It is meant just as a contribution to the discussion on what fuzzy logic is, not as a systematic presentation of mathematical fuzzy logic.
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Mathematical Philosophy and Fuzzy Logic
2020Mathematics in general is an abstraction. Of course, if it is not an easy subject, but in the same time it is rewarding one. We have to keep in mind that Mathematics is a part of our culture. In developed, developing and underdeveloped countries nobody can count himself truly good educated without Mathematical Concepts.
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2017
The term “fuzzy logic” (FL) is a generic one, which stands for a broad variety of logical systems. Their common ground is the rejection of the most fundamental principle of classical logic—the principle of bivalence—according to which each declarative sentence has exactly two possible truth values—true and false.
Radim Belohlavek +2 more
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The term “fuzzy logic” (FL) is a generic one, which stands for a broad variety of logical systems. Their common ground is the rejection of the most fundamental principle of classical logic—the principle of bivalence—according to which each declarative sentence has exactly two possible truth values—true and false.
Radim Belohlavek +2 more
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Mathematical aspects of fuzzy sets and fuzzy logic
Fuzzy Sets and Systems, 2005The paper considers some of the main trends of the development of mathematical fuzzy logic and of formalized fuzzy set theory which came out in the history of fuzzy sets, and which aim to give solid theoretical foundations for fuzzy set theory.
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Mathematical morphology, order filters and fuzzy logic
Proceedings of 1995 IEEE International Conference on Fuzzy Systems. The International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and The Second International Fuzzy Engineering Symposium, 2002In this paper, we try to establish connections between three different fields, which are mathematical morphology, order filters, and fuzzy logic. It is found that strong similarities between them exist, with respect to their algebraic structure, and tools which are common in fuzzy logic appear to be particular cases of some concepts of mathematical ...
M. Schmitt, M. Grabisch
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Mathematical fuzzy logic with many dual hedges
Proceedings of the Fifth Symposium on Information and Communication Technology - SoICT '14, 2014This paper proposes an axiomatization of mathematical fuzzy logic with many dual hedges. We extend an axiomatization of mathematical fuzzy logic with one truth-stressing and one truth-depressing hedges as an expansion of a core fuzzy logic with new unary connectives by Esteva et al.
Van Hung Le, Fei Liu, Dinh-Khang Tran
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Fuzzy description logics in the framework of mathematical fuzzy logic
2015Fuzzy Description Logics (DLs) are a logical formalism for the representation of structured knowledge affected by imprecision or vagueness. The chapter provides insights in terms of Mathematical Fuzzy Logic.
Bobillo F +5 more
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