The primary motivation behind this paper is to present a brief overview of the bipolar complex intuitionistic fuzzy sets (in short BCIFS) which an extension set theory.

The homogeneity of binary functions on the unit interval [0, 1] is a very useful property in many real practical applications. This paper studies circle complex plane. generalization both rotational invariance and ratio scale for fuzzy operations. We show that function homogeneous if only it rotationally invariant invariant. Moreover, we consider simplification operators.

Let F*(K) be the set of all fuzzy complex numbers. In this paper some classical and measure-theoretical notions are extended to the case of complex fuzzy sets. They are fuzzy complex number-valued distance on F*(K), fuzzy complex number-valued measure on F*(K), and some related notions, such as null-additivity, pseudo-null-additivity, null-subtraction, pseudo-null-subtraction, autocontionuous f...

in this paper, the synchronization of a new hyperchaotic complex system based on t-s fuzzy model is proposed. first the considered hyperchaotic system is represented by t-s fuzzy model equivalently. then by using the parallel distributed compensation (pdc) method and by applying linear system theory and exact linearization (el) technique, a fuzzy controller is designed to realize the synchroniz...