Multi-Attribute Decision-Making Using Hesitant Fuzzy Dombi–Archimedean Weighted Aggregation Operators

Abstract

Multi-attribute decision-making (MADM) has been receiving great attention in recent years due to two major issues which are basically to describe attribute values and secondly to aggregate the described information to generate a ranking of alternatives. For the first case it entails the hesitant fuzzy elements (HFEs) as a more flexible and general tool in comparison to fuzzy set theory and for the second one, we allow the aggregation operator (AO) as an effective tool. Having said that there is not yet reported an AO which can provide desirable generality and flexibility in aggregating attribute values under hesitant fuzzy (HF) environment, although many AOs have been developed earlier to attempt to meet above such eventualities. So, the primary objective of this paper is to develop some general as well as flexible AOs that can be exploited to solve MADM problems with the HF information. From this perspective, at the very beginning, we develop some operations between HFEs by uniting the features of Dombi and Archimedean operations. Next, we bring up some HF weighted AOs based on Dombi and Archimedean operations. We discuss in detail some intriguing properties of the proposed AOs. Secondly, we emphasize establishing a procedure of MADM endowed by the proposed operators under the HF environment. Finally, we present a practical example concerning human resource selection to gloss the decision steps of the proposed method and at the same time, we explore the feasibility of the new method.

Keywords

• Hesitant fuzzy set
• Archimedean t-norm and t-conorm
• Dombi t-norm and t-conorm
• Dombi–Archimedean weighted aggregation operators
• multi-attribute decision-making