Multiple Attributes Group Decision‐Making Approaches Based on Interval‐Valued Dual Hesitant Fuzzy Unbalanced Linguistic Set and Their Applications

Abstract

Aiming at multiple attributes group decision-making (MAGDM) problems that characterize uncertainty nature and decision hesitancy, firstly, we propose the interval-valued dual hesitant fuzzy unbalanced linguistic set (IVDHFUBLS) in which two sets of interval-valued hesitant fuzzy membership degrees and nonmembership degrees are employed to supplement the most preferred unbalanced linguistic term, as an effective hybrid expression tool to elicit complicate preferences of decision-makers more comprehensively and flexibly than existing tools based on classic linguistic term set. Basic operations for IVDHFUBLS are further defined; also a novel distance measure is developed to avoid potential information distortion that could be brought about by traditional complementing methodology for hesitant fuzzy set and its derivatives. In view of the fundamental role of aggregation operators in MAGDM modelling, we next develop some extended power aggregation operators for IVDHFUBLS, including power aggregation operator, weighted power aggregation operator, and induced power ordered weighted aggregation operator; their desirable properties and special cases are also analyzed theoretically. Subsequently, with support of the above methods, we develop two effective approaches for our targeted complex decision-making problems and verify their effectiveness and practicality by numerical studies.

Multiple Attributes Group Decision-Making under Interval-Valued Dual Hesitant Fuzzy Unbalanced Linguistic Environment with Prioritized Attributes and Unknown Decision-Makers’ Weights

“…However, till now, regarding MADM based on compound hesitant fuzzy linguistic expressions, only Qi et al [47] introduced the expression tool of interval-valued dual hesitant fuzzy unbalanced linguistic set (IVDHFUBLS) and investigated its power aggregation operators. Despite merits of ULTS into IVDHFUBLS, the group decision-making approach in Qi et al [47] only applies to decision scenarios with mutually supportive assessments in decision matrices; nevertheless, the weighting methods for both attributes and decision-makers were derived from and specific to the mutually supportive relations. For more clarity, representative hesitant fuzzy linguistic MADM methods from above discussion and their properties have been compared in Table 1.…”

“…Therefore, based on the prioritized average (PA) operator [49], in the following, we firstly develop PA operator for IVDHFUBLS to address prioritization relations among attributes. To gain more generality of decision-makers' weighting method rather than the problem-specific limitedness of the one devised in Qi et al [47], we then develop a deviation-maximizing method to objectively derive decision-makers' weights. Finally, on the strength of these methods, we manage to construct a practical and effective IVDHFUBLS-based multiple attributes group decision-making approach.…”

“…By fusing the merits of both unbalanced linguistic term set [44] and interval-valued dual hesitant fuzzy set (IVDHFS) [32], most recently, Qi et al [47] introduced the effective hybrid expression tool called interval-valued dual hesitant fuzzy unbalanced linguistic set (IVDHFUBLS), as shown in following definition.…”

“…So, coherently, to tackle complex decision-making more effectively under ill-structured scenarios with decision hesitancy, there are actual needs to develop hybrid hesitant fuzzy linguistic expression tools that are capable of inheriting advantages of both ULTS and hesitant fuzzy sets. However, thus far, to the best of our knowledge, only Qi et al [47] developed the interval-valued dual hesitant fuzzy unbalanced linguistic set (IVDHFUBLS) and its power aggregation operators. Although IVDHFUBLS manages to be more effective and flexible in depicting complicated assessments with interval values for both membership degrees and non-membership degrees to a designated unbalanced linguistic label, their MAGDM approaches were only developed to cope with the special type of decision-making problems with mutually supportive assessments in decision matrices.…”

“…Nevertheless, there is still a lack of investigation on prioritized operators in hesitant fuzzy unbalanced linguistic environments. Therefore, aiming at resolving these types of practical multiple attributes decision-making problems with prioritization relation among evaluating attributes, on the basis of IVDHFUBLS [47], we focus on studying prioritized average operators for IVDHFUBLS and corresponding effective MAGDM approaches.…”