A Survey of Interval‐Valued Fuzzy Sets

Abstract

Handbook of Granular ComputingIn this introduction, we must indicate the three major problems, in our opinion, of the theory that is the object of our study: r A large number of contributions are generalized adaptations of the theoretical developments of fuzzy set theory.This prevents us from focusing on the nature of IVFSs themselves and studying the properties possessed exclusively by these sets.r In the early work on this theory, Gorzalczany presented the concept of the degree of compatibility between two IVFSs as an interval (see [9]).In some of the latest publications that we have read on interval-valued measures of information, these measures are defined as a point on [0, 1].With this modelization, what is achieved is that the relation between different interval-valued measures of information is a copy of the relation that exists between these concepts in fuzzy set theory.However, we consider that in this case we lose the information that would be provided by a modelization of these measures using intervals.

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