Implicações Fuzzy intuicionistas intervalares obtidas por funções duais e agregadores intervalares

Abstract

This work is a theoretical study, in the strict sense of fuzzy logic, based on the concepts of the following approaches: intuitionistic fuzzy logic and interval fuzzy logic. The interval intuitionistic fuzzy logic not only deals with the indecision inherent in natural language variables modeling computer systems, but also collaborates with two other important interpretations. Firstly, the interpretation which is achieved when intervals may be considered as particular types of fuzzy sets, modeling the imprecision of a variable depending on the computational context by calculations and numerical errors, and by regarding information related to various experts concerned to its membership degree. Secondly, the indecision about the relationship of membership functions, when the membership degree is not restricted to the complement of the corresponding nonmembership degree of such modeled variable. It reinforces these interpretations by using the duality principle and aggregation operators, providing a more flexible modeling for the truth associated with each variable. Thus, a more realistic analysis of the veracity of this variable can be inferred as much as from its interval membership degree and from the complement related to its interval nonmembership degree. The interval extension of intuitionistic fuzzy connectives analysed in this work is focussed on interval intuitionistic fuzzy implications and their dual structures, the interval intuitionistic fuzzy coimplications. In particular, this work considers conjugate functions related to these connectives, obtained by the action of interval intuitionistic automophisms in order to provide an interpretation to the conditional rules based on interval intuitionistic fuzzy logic. The main contribution of this work is the introduction of a special class: the interval intuitionistic fuzzy implications obtained by a finite set of idempotent aggregation operators and a pair of mutual dual interval functions, named as interval fuzzy implications and coimplications. Moreover, a study of algebraic properties extended from fuzzy implications is developed, including an analysis of inherent properties from intuitionistic approach such as the relationships of the interval intuitionistic fuzzy index and the new classes mentioned above.