A-Implicações Fuzzy Valoradas Intervalarmente

Abstract

In fuzzy logic, the interval valued fuzzy propositions can be combined using different aggregations (interval t-norms, interval t-conorms) and interval negations, generating new interval implications. The interval extension of fuzzy sets plays a crucial role in providing the foundation for the development of inference rules in expert systems based on interval valued fuzzy logic. Most fuzzy implication operators and their corresponding interval extensions are based on two types of representations: (i) the explicit representations defined in terms of aggregation operators,such as the classes of S-implications, QL-implications and D-implications; and (ii) implicit representations, considering forinstance R-implications. However, some fuzzy implication operations often applied in expert systems can not be classified in one of these two representations. In this new class of implications, referred to as A-implications, the relations with the aggregation operators are axiomatically defined based on algebraic properties. Therefore, to describe an interval extension of these operators, this study focuses on Yager s implications, Gh funtions and related properties of interval valued fuzzy implications, which can not be naturally represented explicitly or implicitly. Based on such study, this work introduces the canonical interval representation of the Yager s implications and Gh implication. In addition, it includes an analysis of the action of interval automorphisms on the class of interval valued A-implications and related algebraic properties which are verified by this interval constructions