A new method of multi‐attribute group decision making based on hesitant fuzzy soft expert information

Abstract

Interesting insights into uncertain multi‐attribute decision‐making systems have come from the theory of hesitant fuzzy sets. Outputs become more reliable when a decision‐maker is not forced to produce one single assessment in the presence of hesitation. Hesitancy in fuzzy environments grants more flexibility to the decision‐maker, therefore enhancing the validity of all subsequent results. Due to these facts, hesitation has become a landmark in the enhancement of fuzzy‐soft‐inspired theories, and techniques using models such as hesitant fuzzy soft sets or hesitant (fuzzy) ‐soft sets have thrived. However, the literature lacks a comparable improvement for fuzzy soft expert information. The main goal of this paper is the integration of both hesitation and fuzziness with the characteristics of soft expert sets. The resulting hybrid model is therefore called hesitant fuzzy soft expert set, and its utilization for multiple attribute group decision‐making (MAGDM) will be investigated too. To that purpose, we first study the required algebraic operations and properties (subsethood and equality, complement, union, intersection, plus AND and OR operation). Respective numerical examples illustrate their utilization. We also establish some important laws for hesitant fuzzy soft expert sets, including commutativity, associativity, distributivity, and De Morgan's laws. Moreover, we define four novel types of level soft expert sets for fuzzy soft expert sets, and three types of fuzzy soft expert sets for hesitant fuzzy soft expert sets, which are: ‐level soft expert sets, level soft expert sets regarding fuzzy threshold, mid‐level soft expert sets and top‐level soft expert sets. Armed with these tools, we present a natural algorithm for MAGDM under hesitant fuzzy soft expert information that is accompanied by an illustrative application that concerns a selection problem for the samples of electric vehicles manufactured by different companies. This is followed by a comparison with existing mathematical tools such as hesitant fuzzy soft sets and fuzzy soft expert sets, in order to show the advantages of our work over them. In the end, we provide some future research directions.