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Fuzzy power sets and fuzzy implication operators
Fuzzy Sets and Systems, 1980The theory of fuzzy power sets, which has hitherto been insufficiently developed, is shown very naturally to require the use of a fuzzy implication operator (Section 1). Six such operators are gathered from the literature on multiple-valued logic (Section 2), and their effects on fuzzy power-set theory are compared throughout the rest of the paper ...
Bandler, Wyllis, Kohout, Ladislav
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ON A CLASS OF DISTRIBUTIVE FUZZY IMPLICATIONS
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2001We deal with the system of functional equations I(x,T(y,z))=T(I(x,y), I(x,z)), I(x,I(y,z))=I(T(x,y),z), where function T:[0,1]2→ [0,1] is a strict t-norm and I:[0,1]2→ [0,1] is an unknown function. Under some assumptions imposed on function I we obtain that I is almost conjugate with the Yager fuzzy implication.
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On rational fuzzy implication functions
2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2016The proposal of new classes of fuzzy implication functions must take into account the final expression of the operator to be potentially used in a concrete application. In particular, fuzzy implication functions with simple expressions have low computational cost and they reduce the spreading of numerical errors.
Sebastia Massanet +2 more
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Fuzzy implications based on semicopulas
Fuzzy Sets and Systems, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michal Baczynski 0001 +4 more
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Implicative Fuzzy Associative Memories
IEEE Transactions on Fuzzy Systems, 2006Associative neural memories are models of biological phenomena that allow for the storage of pattern associations and the retrieval of the desired output pattern upon presentation of a possibly noisy or incomplete version of an input pattern. In this paper, we introduce implicative fuzzy associative memories (IFAMs), a class of associative neural ...
Peter Sussner, Marcos Eduardo Valle
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Fuzzy Implications in the Mizar System
2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2021This paper is a description of first steps towards providing the computer-supported formalization of a relatively recent textbook by Baczynski and Jarayam “Fuzzy Implications”. We present some of the issues connected with the use of Mizar-computerized proof assistant together with its extensive repository of mathematical texts checked for their logical
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Fuzzy Implications Generating from Fuzzy Negations
2018A basic building block in the foundation of fuzzy neural networks is the theory of fuzzy implications. Fuzzy implications play a crucial role in this topic. The aim of this paper is to find a new method of generating fuzzy implications. based on a given fuzzy negation.
Georgios Souliotis +1 more
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Fuzzy positive implicative and fuzzy associative filters of lattice implication algebras
Fuzzy Sets and Systems, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Attribute Implications in a Fuzzy Setting
2006The paper is an overview of recent developments concerning attribute implications in a fuzzy setting. Attribute implications are formulas of the form A $\Longrightarrow$ B, where A and B are collections of attributes, which describe dependencies between attributes. Attribute implications are studied in several areas of computer science and mathematics.
Radim Belohlávek, Vilém Vychodil
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On interval fuzzy S-implications
Information Sciences, 2010Let \(\mathbb{U}=\{[a,b] \;| \;0\leq a\leq b\leq 1\}\) denote the set of subintervals of the unit interval. An interval S-implication is a function from \(\mathbb{U}^2\) to \(\mathbb{U}\) based on the functional \(\mathbb{I_{S,N}}(X,Y)=\mathbb{S}(\mathbb{N}(X),Y)\), where \(\mathbb{S}\) is an interval t-conorm and \(\mathbb{N}\) is an interval fuzzy ...
Benjamín R. C. Bedregal +3 more
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