Consistency of Aggregation Function-Based m-Polar Fuzzy Digraphs in Group Decision Making

This study investigates the consistency problem of m-polar fuzzy preference relations, presented by m-polar fuzzy digraphs, during the consensus phase in group decision making. At first, a conjunction-based framework is presented to generalize the concept of m-polar fuzzy relation on an m-polar fuzzy set. Consequently, the definition of m-polar fuzzy graphs is developed by using an arbitrary conjunctive aggregation operator rather than the minimum. This change enables us to measure the strength of the relation between each pair of objects in an m-polar fuzzy graph based on the membership values of both not necessarily the lowest one. Next, by using the aggregation functions, new types of reflexivity, symmetry, antisymmetry and transitivity are given on an m-polar fuzzy relation. Then, m-polar fuzzy preference relation is derived, where the preferences are in the form of aggregation-based transitivite, and modeled by the m-polar fuzzy digraph. A theorem is given to consider the sufficient conditions for preservation of the consistency of aggregation-based m-polar fuzzy preferences during the consensus process. Lastly, an algorithm is designed to model the final consistence priority by using digraphs. A numerical example is also given to illustrate the proposed method.