Ranking Objects from Individual Linguistic Dual Hesitant Fuzzy Information in View of Optimal Model-Based Consistency and Consensus Iteration Algorithm

Fanyong Meng (), Aiqing Zeng (), Jie Tang () and Witold Pedrycz ()
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Fanyong Meng: Nanjing University of Information Science and Technology
Aiqing Zeng: Hunan University of Technology and Business
Jie Tang: Nanjing University of Information Science and Technology
Witold Pedrycz: University of Alberta

Group Decision and Negotiation, 2023, vol. 32, issue 1, No 2, 5-44

Abstract: Abstract Linguistic variables are flexible and intuitive attraction for expressing the wording of decision makers. This paper introduces a new type of linguistic fuzzy sets called linguistic dual hesitant fuzzy sets to express the hesitancy of decision makers’ qualitative preferences and non-preferences. Considering the application in decision making, linguistic dual hesitant fuzzy preference relations (LDHFPRs) are introduced that permit the decision makers to apply several linguistic variables to indicate a qualitative preferred judgment and a qualitative non-preferred judgment, respectively. To rank objects from LDHFPRs rationally, a consistency concept is first presented. Then, two optimal models are built to judge the consistency of LDHFPRs. When LDHFPRs are inconsistent, an optimal model-based iteration algorithm for obtaining consistent LDHFPRs is offered. Based on consistent linguistic intuitionistic fuzzy preference relations, a method for calculating the weighted linguistic intuitionistic fuzzy priority vector is introduced. In the setting of group decision making (GDM), a consensus measure based on individually weighted consistent reverse complementary linguistic intuitionistic fuzzy preference relations is defined. When the consensus does not satisfy the requirement, a two-step optimal model-based method for increasing the consensus level is offered. Furthermore, an approach for GDM with LDHFPRs is developed. Finally, an illustrative example concerning the evaluation of basic services internet enterprise websites is provided to show the efficiency of the new method.

Keywords: Group decision making; LDHFPR; Optimal model; Consistency; Consensus analysis (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10726-022-09797-8

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