On interval fuzzy S-implications

“…In the following, basic concepts of an automorphism on the unit interval U , fuzzy negations and fuzzy subimplications are reported, mainly according to [12,25].…”

Section: Fuzzy Connectivesmentioning

confidence: 99%

Aggregating Fuzzy QL- and (S,N)-Subimplications: Conjugate and Dual Constructions

Reiser

Benitez

Yamin

et al. 2016

Tend. Mat. Apl. Comput.

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ABSTRACT. (S,N)-and QL-subimplications can be obtained by a distributive n-ary aggregation performed over the families T of t-subnorms and S of t-subconorms along with a fuzzy negation. Since these classes of subimplications are explicitly represented by t-subconorms and t-subnorms verifying the generalized associativity, the corresponding (S,N)-and QL-subimplicators, referred as I S,N and I S,T,N , are characterized as distributive n-ary aggregation together with related generalizations as the exchange and neutrality principles. Moreover, the classes of (S,N)-and QL-subimplicators are obtained by the median operation performed over the standard negation N S together with the families of t-subnorms and t-subconorms by considering the product t-norm T P as well as the algebraic sum S P , respectively. As the main results, the family of subimplications I S P ,N and I S P ,T P ,N extends the corresponding classes of implicators by preserving their properties, discussing dual and conjugate constructions.

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“…However, sometimes it is difficult to determine the membership degree to be used for certain problems. To work around this situation, several authors (e.g., as discussed in [14,15,16,17]) represent the membership degrees through real intervals, thus extending fuzzy sets to interval fuzzy sets.…”

Section: Interval Fuzzy Numbersmentioning

confidence: 99%

“…(15). So, we obtain the representation of interval fuzzy probabilities through their fuzzy generator probabilities as follows:P…”

Section: Proof the Proof Is Immediate Sincep (mentioning

confidence: 99%

An Approach to Interval Fuzzy Probabilities

Asmus

Dimuro

Bedregal

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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Fuzzy sets and logic have been largely used for the treatment of the uncertainty, vagueness and ambiguity found in the modeling of real problems. However, there may exist also the case when there is uncertainty related to the membership functions to be used in the modeling of fuzzy sets and fuzzy numbers, as there are many ways to define the shape of this kind of number. Thus, one can use, for example, the theory of interval fuzzy sets to address this uncertainty, considering different modelings of fuzzy numbers into a single interval fuzzy number. In this paper, we use interval fuzzy numbers to represent probabilities that are difficult to be estimated and where the modeling of fuzzy numbers is not trivial. To elaborate the calculation of interval fuzzy probabilities, we introduce an approach based on the one used by Buckley and Eslami for fuzzy probabilities, where the probabilities respect an arithmetic restriction. We discuss several properties of the proposed approach.

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On interval fuzzy S-implications

Cited by 119 publications

References 67 publications

Obtaining representable coimplications from aggregation and dual operators

Obtaining representable coimplications from aggregation and dual operators

Aggregating Fuzzy QL- and (S,N)-Subimplications: Conjugate and Dual Constructions

An Approach to Interval Fuzzy Probabilities

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