Abstract
The hesitant fuzzy 2-dimension linguistic element (HF2DLE) allows decision makers to express the importance or reliability of each term included in a hesitant fuzzy linguistic element as a linguistic term. This paper investigates a programming technique for multidimensional analysis of preference for hesitant fuzzy 2-dimension linguistic multicriteria group decision making. Considering the flexibility of HF2DLEs in expressing hesitant qualitative preference information, we first adopt HF2DLEs to depict both the evaluation values of alternatives and the truth degrees of alternative comparisons. To calculate the relative closeness degrees (RCDs) of alternatives, the Euclidean distances between HF2DLEs are defined. Based on RCDs and preference relations on alternatives, the group consistency and inconsistency indices are constructed, and a bi-objective hesitant fuzzy 2-dimension linguistic programming model is established to derive the criteria weights and positive and negative ideal solutions. Since the objective functions and partial constraint coefficients of the established model are HF2DLEs, an effective solution is developed, through which the RCDs can be calculated to obtain the individual rankings of alternatives. Furthermore, a single-objective assignment model is constructed to determine the best alternative. Finally, a case study is conducted to illustrate the feasibility of the proposed method, and its effectiveness is demonstrated by comparison analyses.
Highlights
Multicriteria group decision making (MCGDM), a hot research topic in decision science, is used to select the best compromise solution from a feasible set of alternatives based on the preference information provided by a group of decision makers (DMs) with respect to multiple quantitative or qualitative criteria
The remainder of this paper is organized as follows: In Section 2, we review some basic definitions related to hesitant fuzzy 2-dimension linguistic term set (HF2DLTS); Section 3 develops a hesitant fuzzy 2-dimension linguistic programming technique for multidimensional analysis of preference for MCGDM problems
A novel fuzzy programming method was proposed to solve MCGDM problems in which the evaluation values of alternatives and the truth degrees of pairwise comparisons between alternatives were denoted by hesitant fuzzy 2-dimension linguistic element (HF2DLE), and the preferences over alternatives and criteria were incomplete
Summary
Multicriteria group decision making (MCGDM), a hot research topic in decision science, is used to select the best compromise solution from a feasible set of alternatives based on the preference information provided by a group of decision makers (DMs) with respect to multiple quantitative or qualitative criteria. Considering two reference points of HF2DLPIS and HF2DLNIS simultaneously, the RCD involved in TOPSIS is used to replace the distance measure in the traditional LINMAP method to construct the hesitant fuzzy 2-dimension linguistic group consistency and inconsistency indices. (3) A bi-objective hesitant fuzzy 2-dimension linguistic programming model is constructed to determine the criteria weights, HF2DLPIS, and HF2DLNIS Since both the objective functions and partial constraints’ coefficients of the established model take the form of HF2DLEs, an effective solution method is technically developed to solve the constructed model.
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