Intuitionistic Fuzzy Implication Operators — An Expression and Main Properties

Abstract

In this paper we present the definition and properties of intuitionistic fuzzy implication operators. We study the expression obtained from said operators when fuzzy implication and coimplication operators are applied to different aggregations of degrees of truth and non-truth of the propositions.

A Survey of Interval‐Valued Fuzzy Sets

“…These methods are characterized by the fact that they always use the extremes of the intervals. However, in the construction method for interval-valued fuzzy implication operators that we shall present next (see [62]), other points The interval A(u) is the truth degree of the proposition 'u is A.' Let us take two values, the extremes of the intervals, K 0 (A(u)) and K 1 (A(u)).…”

“…In the following proposition, we present a construction method for interval-valued fuzzy implication operators in the sense of Definition 6 (see [62]). The aggregations that we use in this construction method are the following: an aggregation operator is a …”

“…In [62], there is a study of the conditions under which the constructions of Proposition 1 fulfill the properties I I V 6 -I I V 8 , among others. [30]); that is, [35]),…”

“…In [62], it is proved that the expression in Example 2 satisfies the properties I I V 6 , I I V 7 , and I I V 8 . Cornelis et al proved in [73] that this expression is an S-implicator on L ([0, 1]).…”

“…In [62], the properties usually required of interval-valued fuzzy implication operators are presented. These properties can be divided into two groups: the ones that result from adapting the properties of fuzzy implication operators to the interval-valued case and those that are interval-valued per se.…”