In this paper, using fuzzy complex valued functions and fuzzy complex valued fuzzy measures ([11]) and interval-valued Choquet integrals ([2-6]), we define Choquet integral with respect to a fuzzy complex valued fuzzy measure of a fuzzy complex valued function and investigate some basic properties of them.

Fuzzy rough n-ary subhypergroups are introduced and characterized.

Complex numbers can capture compound features and convey multifaceted information; thereby providing means for solving complicated problems. In this paper, we combine the degree of membership and a degree of non-membership of members of Intuitionistic Fuzzy Sets via complex numbers to characterize these fuzzy sets. This approach enables extending several concepts such as classical fuzzy sets, P...

Fuzzy Logic, introduced by Zadeh along with his introduction of fuzzy sets, is a continuous multi-valued logic system. Hence, it is a generalization of the classical logic and the classical discrete multi-valued logic (e.g. Łukasiewicz’ three/many-valued logic). Throughout the years Zadeh and other researches have introduced extensions to the theory of fuzzy setts and fuzzy logic. Notable exten...

In this note, we show by counterexamples that some results of Qiu and colleagues [On the restudy of fuzzy complex analysis: Part I. The sequence and series of fuzzy complex numbers and their convergences, Fuzzy Sets and Systems 115 (2000) 445–450; On the restudy of fuzzy complex analysis: Part II. The continuity and differentiation of fuzzy complex functions, Fuzzy Sets and Systems 120 (2001) 5...

Since the product of complex numbers and rectangular fuzzy (RFCN) is not necessarily a RFCN in former linear system (FCLS), scalar multiplication addition operations (FCN) based on new representation FCN are proposed. We also introduce method for solving FCLS, which can convert FCLS into two distinct systems. One an n×n system, other (mn)×(mn) real where n number unknown variables, m substituti...

The objective of this paper is to investigate the applications of complex fuzzy sets. The novelty of the complex fuzzy set lies in the range of values its membership function may attain. In contrast to a traditional fuzzy membership function, this range is not limited to [0, 1], but extended to the unit circle in the complex plane. Thus, the complex fuzzy set provides a mathematical framework f...

Abstract This paper presents a new complex system systemic. Here, we are working in a fuzzy environment, so we have to adapt all the previous concepts and results that were obtained in a non-fuzzy environment, for this fuzzy case. The direct and indirect influences between variables will provide the basis for obtaining fuzzy and/or non-fuzzy relationships, so that the concepts of coverage and i...