In this paper, a new construction method of a fuzzy implication from two given ones, called e-generation method, is introduced. This method allows to con- trol, up to a certain level, the increasingness on the second variable of the fuzzy implication through an adequate scaling on that variable of the...

It is well-known that the residual IT of a leftcontinuous t-norm T satisfies the exchange principle (EP), viz., IT (x, IT (y, z)) = IT (y, IT (x, z)) for all x, y, z [0, 1]. However, the left-continuity of T is only sufficient and not necessary, as many examples in the literature illustrate. In this...

This paper deals with some dependencies between fuzzy conjunctions and fuzzy implications. More precisely, a fuzzy implication generated from a fuzzy conjunction and a fuzzy conjunction induced by a fuzzy implication is considered. In the case of a fuzzy conjunction only border conditions and monotonicity...

The aim of this work is to study N-dual structures of representable implications generated from a set M of aggregation functions and pairs of mutual dual functions, founded on the isomorphism between the unit interval and special instances of the Goguen's L-fuzzy sets. We discuss under which conditions...

In order to avoid combinatorial rule explosion in fuzzy reasoning, in this work we explore the distributive equations of implications. In details, by means of the section of I, we give out the sufficient and necessary conditions of solutions for the distributive equation of implication I(x, T1(y, z))...

A new family of implication operators, called probabilistic implications, is introduced. The suggested implications are based on conditional copulas and make a bridge between probability theory and fuzzy logic. It is shown that some well-known fuzzy implications appear as a particular probabilistic implications....

Given an implication function I defined on the finite chain L = {0, ..., n}, a method for extending I to the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers contained in L (denoted by AL

Ordered fuzzy numbers (OFN) invented by the second author and his two coworkers in 2002 make possible to utilize the fuzzy arithmetic and to construct the Abelian group of fuzzy numbers and then an ordered ring. The definition of OFN uses the extension of the parametric representation of convex fuzzy...