Complex intuitionistic fuzzy classes

A complex fuzzy class is characterized by a pure complex fuzzy grade of membership. Pure complex fuzzy classes are paramount in providing rich semantics for cases where the fuzzy data is periodic with a fuzzy period. Often, however, the available data is contaminated by noise, opposing expert opinions, ambiguity, and false information. This opens the door for using intuitionistic fuzzy sets theory: representing the false information via a degree of non-membership. Several researchers have identified the benefits of integrating the two concepts of complex fuzzy sets and intuitionistic fuzzy sets. Nevertheless, complex fuzzy sets allow for only one component of the degree of membership to be fuzzy. In this paper, we introduce the concept of complex intuitionistic fuzzy classes, which are characterized by pure complex intuitionistic fuzzy grade of membership. We define the basic terms and operations on complex intuitionistic fuzzy classes and provide a motivating example of relevant application.