It is an open question whether a non-trivial convex combination of triangular norms (resp. conorms) can be a triangular norm (resp. conorm). We investigate the analogous question for S-implications and R-implications.

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...

Given a coimplication function $J$ defined on the finite chain $L_n={0,...,n}$, a method for extending $J$ to the set of discrete fuzzy numbers whose support is an interval contained in $L_n$ (denoted by ${cal A}_1^{L_n}$) is given. The resulting extension is in fact a fuzzy coimplication on ${cal A}_1^{L_n}$...

A class of implication functions is constructed from fuzzy negations. The interest of this new class lies in its simplicity and in the fact that when $N$ is Id-symmetrical, the corresponding implication agrees with the residuum of a commutative semicopula.

Recently, in [4], [5], [6], and [8] we have discussed the distributivity equation of implications $mathcal{I}(x,mathcal{T}_1(y,z)) = mathcal{T}_2(mathcal{I}(x,y),mathcal{I}(x,z))$ over t-representable t-norms, generated from (classical) continuous Archimedean mbox{t-norms}, in interval-valued fuzzy sets...

This paper deals with the problem of the aggregation of implication functions. After characterizing those binary operations which merge two implication functions into an implication function, we study some aspects of the aggregated implication functions in terms of the two given ones. In particular,...

In this paper, an extension of Yager's implications is proposed by means of generalizing the internal factor x, in the case of f-generated implications, or 1/x, in the case of g-generated implications, to more general unary functions. The importance of this extension stems from the fact that both subclasses...

This paper deals with some dependencies between fuzzy connectives, on the pattern of laws in a classical propositional calculus, which allow to generate fuzzy implications. Fuzzy implications generated both by a triple: fuzzy conjunction, disjunction and negation, and by two fuzzy implications are considered....

Imprecise choices can be described using either a probabilistic or a fuzzy formalism. No relation between them has been studied so far. In this contribution we present a connection between the two formalisms that strongly makes use of fuzzy implication operators and t-norms. In this framework, Luce's...