Abstract
Hesitant fuzzy sets (HFSs) are widely applied in pattern recognition, classification, clustering, and multiple attribute decision making. In order to get more accurate decision results, the order relation of HFSs is particularly important. In this paper, some defects of the existing order relations for HFSs are discussed. In order to solve these problems, by employing a distance measure and the TOPSIS method, we propose a new order relation extraction method based on a new additive consistency fuzzy preference relation for hesitant fuzzy elements (HFEs). Then, the proposed additive consistency fuzzy preference relation is applied to integrate group decision information. In multi-attribute group decision making (MAGDM), it is particularly important to ensure the consensus of the decision-makers (DMs), and the consistency of the decision process is the precondition for DMs to reach consensus. The proposed method can maintain the consistency of the decision process for MAGDM under hesitant fuzzy environments, so as to get the consensus of DMs, besides, it can overcome the limitations of the existing order relations for HFSs. At the end of this paper, a numerical example is used to illustrate the effectiveness and feasibility of the new approach, and some comparative analyses are given. The obtained results confirm the theoretical and numerical analyses and emphasize the advantages, which can ensure the consistency of the whole decision process and avoid the original decision information change and loss of the proposed method, so as to be more in line with the actual situation.
Highlights
Many studies on the fuzzy set theory have been conducted (Kacprzyk & Orlovski, 1987; Turksen, 1986) and have achieved great success (Roy & Maji, 2007; Deschrijver & Kerre, 2003; Erceg, 1979), since the fuzzy set theory was advanced by Zadeh (1965)
Ni, Chen, Li, and Zhou (2016) further constructed several information measure formulas for interval-valued hesitant fuzzy elements (IVHFEs) on the basis of the continuous ordered weighted averaging operator to deal with multi-attribute group decision making (MAGDM) whose attribute values are IVHFs forms
We have studied MAGDM problems in which the preference information offered by experts are hesitant fuzzy sets (HFSs)
Summary
Many studies on the fuzzy set theory have been conducted (Kacprzyk & Orlovski, 1987; Turksen, 1986) and have achieved great success (Roy & Maji, 2007; Deschrijver & Kerre, 2003; Erceg, 1979), since the fuzzy set theory was advanced by Zadeh (1965). Zhu, C., Zhu, L., and Zhang (2016) discussed multi-attribute decision making problems with linguistic hesitant fuzzy information and proposed a series of linguistic hesitant fuzzy power aggregation operators. The weighted hesitant fuzzy geometric Bonferroni mean (WHFGBM) and the weighted hesitant fuzzy Choquet geometric Bonferroni mean (WHFCGBM) are proposed Another application involves using the distance or similarity measure to aggregate decision information. Jin, Ni, Chen, Li, and Zhou (2016) further constructed several information measure formulas for interval-valued hesitant fuzzy elements (IVHFEs) on the basis of the continuous ordered weighted averaging operator to deal with MAGDM whose attribute values are IVHFs forms. Zhang, Wang, and Tian (2015b) proposed two group decision making support models with hesitant fuzzy preference relations (HFPRs) based on Tanino’s additive consistency concept and the b-normalization based method and used them to MAGDM.
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