Interval Type-2 Complex-Fuzzy Inferential System ― A New Approach to Modeling

Fuzzy rationale has been developed to deal with imprecision in information that happens in the real world usually. L.A. Zadeh proposed the important concept of type-2 fuzzy sets 10 years after the inception of regular fuzzy sets that are also known as type-1 fuzzy sets. The former uses real-valued membership degree to describe set-element relationship, while the latter uses fuzzy set to do so. The movement from type-1 to type-2 fuzzy sets and logic is a very important research direction for fuzzy systems and applications. In the meanwhile, another critical direction is the research of complex fuzzy sets (CFSs) and logic to generalize membership description to complex-valued degrees so that membership can be widely enriched in the complex plane. A CFS is also called type-1 CFS. In this paper, an interval type-2 complex-fuzzy inferential system is proposed, using interval type-2 complex fuzzy sets (IT2-CFS), each of which is newly synthesized by two type-1 CFSs. For optimization, a hybrid-learning method called the PSO-KFA method is used to equip with a selflearning ability for the proposed system. Through experimental results of function approximation, the proposed approach has shown promising result and performance.