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From (Deductive) Fuzzy Logic to (Logic-Based) Fuzzy Mathematics
2009It is indisputable that mathematical structures arising around vague/ fuzzy/ non-bivalent concepts have a broad range of applications; therefore they have been intensively investigated during the last five decades. The discipline studying these structures is, maybe unfortunately, called Fuzzy Mathematics .
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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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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. Grabisch, M. Schmitt
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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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Toward Problems for Mathematical Fuzzy Logic
2006 IEEE International Conference on Fuzzy Systems, 2006The paper discusses some open problems in the field of mathematical fuzzy logic which may have a decisive influence for the future development of fuzzy logic within the next decade.
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Mathematical Foundations of Fuzzy Logic
1999Our motivation to enter into the foundations of fuzzy logic is based on five aspects. First, fuzzy logic complements parity logic in a unique way and represents currently the most versatile branch of approximate and causal reasoning, in particular with respect to fuzzy cognitive maps in almost every field of psychology.
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Programming with Fuzzy Logic and Mathematical Functions
2006This paper focuses on the integration of the (also integrated) declarative paradigms of functional logic and fuzzy logic programming, in order to obtain a richer and much more expressive framework where mathematical functions cohabit with fuzzy logic features.
Ginés Moreno, Vicente Pascual
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Fuzzy Natural Logic: Towards Mathematical Logic of Human Reasoning
2015One of the often repeated proclaims appearing in the papers on fuzzy sets and fuzzy logic is their ability to model semantics of some linguistic expressions so that the inherent vagueness of the former is also captured. Recall that this direction of research was initiated by L.A.
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