Image development in the framework of ξ – complex fuzzy morphisms

Abstract

The study of complex fuzzy sets defined over the meet operator (ξ – CFS) is a useful mathematical tool in which range of degrees is extended from [0, 1] to complex plane with unit disk. These particular complex fuzzy sets plays a significant role in solving various decision making problems as these particular sets are powerful extensions of classical fuzzy sets. In this paper, we define ξ – CFS and propose the notion of complex fuzzy subgroups defined over ξ – CFS (ξ – CFSG) along with their various fundamental algebraic characteristics. We extend the study of this idea by defining the concepts of ξ – complex fuzzy homomorphism and ξ – complex fuzzy isomorphism between any two ξ – complex fuzzy subgroups and establish fundamental theorems of ξ – complex fuzzy morphisms. In addition, we effectively apply the idea of ξ – complex fuzzy homomorphism to refine the corrupted homomorphic image by eliminating its distortions in order to obtain its original form. Moreover, to view the true advantage of ξ – complex fuzzy homomorphism, we present a comparative analysis with the existing knowledge of complex fuzzy homomorphism which enables us to choose this particular approach to solve many decision-making problems.