Matrix Theory for Complex Q-Fuzzy Sets and Their Applications in Administrative Decision-Making Problems

Abstract

The complex Q-fuzzy set (CQFS) is a novel method for solving the multiple-attribute decision-making problem, proposed as the Cartesian product of the universal set X and the set Q. The goal of this work is to investigate this idea in a matrix setting by introducing the concept of complex Q-fuzzy matrices (CQFM). We discuss some new elementary operations, including the complement of CQFM, the union, and the intersection between two CQFMs. Moreover, we will show important algebraic properties that link these processes within a theoretical framework and provide numerical examples based on CQFM. Then, we promote techniques for determining and adjoining as well as develop methods for computing composition functions to determine the greatest and least eigenvalues of CQFMs. Finally, we will present a scenario for an administrative problem related to evaluating a chain of restaurants according to our proposed concept, in which the importance of the mathematical tools provided in this work will be demonstrated in addressing this scenario.