- and R-implications: A state-of-the-art survey

Baczyński, Michał; Jayaram, Balasubramaniam

doi:10.1016/j.fss.2007.11.015

Cited by 139 publications

(50 citation statements)

References 25 publications

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“…Moreover, the operations constructed in this way are in general non-functionally expressible implication functions. To see this, let us recall that an implication function I is said to satisfy the leftneutrality principle 1 , whenever…”

Section: Proposition 4 Let F G Be Aggregation Functions I An Implicmentioning

confidence: 99%

Constructing non-functionally expressible fuzzy implications

Massanet¹,

Mayor²,

Torrens³

2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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This article discusses a new method for the construction of non-functionally expressible fuzzy implications. In a recent work, we have considered non-functionally expressible fuzzy implications from an implication function acting on the inputs followed by an aggregation process. Now, we first perform an aggregation of the inputs and then an implication function between the aggregated values. The main part is devoted to analyse under which conditions the two construction processes coincide.

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Section: Proposition 4 Let F G Be Aggregation Functions I An Implicmentioning

confidence: 99%

Constructing non-functionally expressible fuzzy implications

Massanet¹,

Mayor²,

Torrens³

2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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“…The characterization of t-norms, which residuals satisfy the ordering property (OP) have been obtained by Baczyński and Jayaram [2]. …”

Section: A First Characterization Of R-implications Generated From Lementioning

confidence: 99%

R-implications and the Exchange Principle:A Complete Characterization

Jayaram¹,

Baczyński²,

Mesiar³

2011

Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011)

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It is well-known that the residual I T of a leftcontinuous t-norm T satisfies the exchange principle (EP), viz.,However, the left-continuity of T is only sufficient and not necessary, as many examples in the literature illustrate. In this work we study the necessary conditions on a t-norm T for its residual to satisfy (EP). The work presents a complete characterization of the class of t-norms whose residuals satisfy (EP).

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“…Coimplication functions are conceived as N -dual structures of implication functions extending the classical (co)implications [19,20,21,9,32] and [3]: Since Definition 6 imposes a very weak condition for a binary function to be a fuzzy (co)implication, several other extra properties are considered in the literature in addition to (J1) I1. The most used ones are listed below: …”

Section: Fuzzy (Co)implicationsmentioning

confidence: 99%