Some new hybrid hesitant fuzzy weighted aggregation operators based on Archimedean and Dombi operations for multi-attribute decision making

Abstract

Hesitant fuzzy set (HFS) is more flexible and general tool in comparison to fuzzy set theory. There is not yet reported an aggregation operator (AO) which can provide desirable generality, flexibility and compatibility in adjusting risk preferences while aggregating attribute values under hesitant fuzzy (HF) environment, although based on algebraic t-norm and t-conorm, Einstein t-norm and t-conorm, Hammacher t-norm and t-conorm, Dombi t-norm and t-conorm and Frank t-norm and t-conorm; weighted AOs have been developed earlier to attempt to meet above such eventualities. So, the primary objective of this paper is to develop some general, flexible as well as compatible AOs that can be exploited to solve MADM problems with HF information. From this perspective, at the very beginning, we develop new operations between HFEs by uniting the features of Archimedean and Dombi operations. Next, based on these operations, we develop HF Archimedean-Dombi weighted arithmetic and geometric AOs, HF Archimedean-Dombi ordered weighted arithmetic and geometric AOs and HF Archimedean-Dombi hybrid arithmetic and geometric AOs. We have shown that the existing HF-algebraic weighted AOs, HF-Einstein weighted AOs and HF-Hammacher weighted AOs are special cases of our developed AOs. We discuss in detail some intriguing properties of the proposed AOs. Next, we establish a procedure of MADM endowed by the proposed operators under HF environment. Then, we present a practical example concerning the personnel selection to gloss the decision steps of the proposed method. We also conduct a validity test to show that our proposed AOs are authentic and legal. Moreover, we exhibit a sensitivity investigation with diverse criteria weight sets to examine the stability of our proposed intriguing approach. Also, we draw attention toward a comparison between the existing decision-making methods with the proposed method to prove the superiority of our model.