Complex fuzzy arithmetic aggregation operators

Abstract

A complex fuzzy set, characterized by complex-valued membership functions, is a generalization of a fuzzy set. In this paper, we present complex fuzzy arithmetic aggregation (CFAA) operators, complex fuzzy weighted arithmetic aggregation (CFWAA) operators. Based on the partial ordering of complex fuzzy values, we develop complex fuzzy ordered weighted arithmetic aggregation (CFOWAA) operators. Highly pertinent to complex fuzzy operations is the concept of rotational. This concept has been developed for complex fuzzy aggregation operators. We show that CFAA, CFWAA and CFOWAA operators possess the property of rotational invariance. Moreover, based on the relationship between Pythagorean membership grades and complex numbers, these operators are studied under Pythagorean fuzzy values.