Dual hesitant fuzzy linguistic aggregation operators and their applications to multi-attribute decision making

Abstract

This paper studies the multi-attribute decision making (MADM) problems under two situations that the attributes are independent and correlative, respectively, in which the attribute values take the form of dual hesitant fuzzy linguistic elements and the weights of attributes take the form of real numbers. Firstly, the concept, operational laws, score function and accuracy function of dual hesitant fuzzy linguistic element (DHFLE) are defined. For the situation that the attributes are independent, some dual hesitant fuzzy linguistic geometric aggregation operators are proposed. Considering that there exists prioritization among the attributes, we propose several dual hesitant fuzzy linguistic prioritized aggregation operators based on the prioritized average (PA) operator. Moreover, some desirable properties and special cases of these operators are investigated in detail. Based on the proposed operators, two novel approaches to MADM with dual hesitant fuzzy linguistic information are proposed. Finally, a numerical example for investment alternative selection is given to illustrate the application of the proposed methods.

Hesitant Pythagorean fuzzy Maclaurin symmetric mean operators and its applications to multiattribute decision-making process

“…Apart from these, some other authors and their corresponding references have worked to present different types of algorithms under the HFSs environment. Wang et al proposed some weighted averaging and geometric aggregation operators under the DHFSs environment . presented the correlation coefficients of DHFSs and applied them to solve the multiple‐attribute decision‐making problems.…”

Tackling Complexity in Green Contractor Selection for Mega Infrastructure Projects: A Hesitant Fuzzy Linguistic MADM Approach with considering Group Attitudinal Character and Attributes’ Interdependency

“…Degraded form of IVDHFULS. Note that our approach is intrinsically adaptive to decision situations based on degraded forms of IVDHF UUBLS, such as the dual hesitant Complexity fuzzy linguistic sets introduced by Yang and Ju [54]. To further inspect feasibility of our approach, we here conduct comparative study on the same case adopted by Yang and Ju [54].…”

“…Note that our approach is intrinsically adaptive to decision situations based on degraded forms of IVDHF UUBLS, such as the dual hesitant Complexity fuzzy linguistic sets introduced by Yang and Ju [54]. To further inspect feasibility of our approach, we here conduct comparative study on the same case adopted by Yang and Ju [54]. We firstly convert their original decision matrix into the form of IVDHF UUBLS: crisp membership and nonmembership degrees are equivalently changed to intervals with same upper and lower limits (e.g., 0.2 turns out to be [0.2, 0.2]), and linguistic variables are rewritten as uncertain linguistic variables (e.g., 2 turns out to be [ 2 , 2 ]).…”

“…As a result, compound expression tools of hesitant fuzzy linguistic sets and their MADM approaches have attracted widespread interests. Such as, hesitant fuzzy linguistic set [38,53] and dual hesitant fuzzy linguistic set [39,54], among others. Comparatively, compound hesitant fuzzy linguistic expression tools attain more adaptability and feasibility in practical complex decision environments.…”

“…Second, under complicate decision-making environments, interdependency among attributes is a serious issue that needs to be addressed [60]. However, Choquet integral incorporated by Lin et al [38] can only capture interactions between adjacent coalitions, while the prioritized aggregation operator in [53,54] requires linear ordering of evaluative attributes that is often difficult for decision-makers to deduce up front in complex practices. Third, in order to deal with real-world complex problems, various degrees of optimism (degree of orness) of decision-makers should be coordinated as complex attitudinal characters and taken into account during decision-making [61].…”