Innovative New Framework of Complex Q-Fuzzy Set and Its Application

Abstract

The Q-fuzzy set (Q-FS) is a powerful general formal framework that generalises the notion of a fuzzy set (FS) when the domain of the FS extends from the universal set X to the product between X and Q. This article presents a novel complex Q-fuzzy set (CQ-FS) notion by extending the range of Q-fuzzy set (Q-FS) values to the unit circle in the complex plane by adding a further term called the phase term. This action characterises CQ-FS’s elements in terms of time. Based on these mathematical tools, we present the practical possibilities for basic operations on this concept, such as intersection, union, and complement, supported by numerical representations with some mathematical properties. Finally, we present a scenario for a decision-making problem in the medical field where our concept plays a dynamic role in representing the problem data, with time being a significant factor in determining symptom severity. To address this problem, we have developed a multi-step mathematical algorithm that helps the user create a simulation system for handling such issues within a decision-making environment.