Grey Relational Analysis for Hesitant Fuzzy Sets and Its Applications to Multiattribute Decision-Making

Abstract

Due to the superiority in expressing the uncertain and vague information, the hesitant fuzzy set (HFS) is regarded as an important tool to deal with multiattribute decision-making (MADM) problems. Quantitative and qualitative fuzzy measures have been proposed to solve such problems from different points. However, most of the existing information measures for HFSs are related to such fuzzy measures as distance, similarity, entropy, and correlation coefficients. The grey relational analysis is omitted. Besides, the existing grey relational analysis for HFSs only considers the range or distance between HFSs data which is only a partial measure of the HFSs. Therefore, in this paper, we improve the grey relational analysis for HFSs and explore a novel slope grey relational degree by considering another factor of HFSs data: the slope. Further, we combine both the distance and slope factors of HFSs data to construct a synthetic grey relational degree that describes the closeness and variation tendency of HFSs simultaneously, greatly enriching the fuzzy measures of HFSs. Furthermore, with the help of the TOPSIS method, we develop the grey relational based MADM methodology to solve the HFSs MADM problems. Finally, combining with two practical MADM examples about energy policy selection and multisensor target recognition, we obtain the most desirable decision results. Compared with the previous methods, the validity, comprehensiveness, and discrimination of the proposed synthetic grey relational degree for HFSs are demonstrated in detail.

On generalized correlation coefficients of the hesitant fuzzy sets with their application to clustering analysis

“…Cheng (2018) developed a new method for autocratic decision making using group recommendations (ADMUGRs) on HFSs and implemented their proposed algorithm for green hotels selection problem. Guan et al (2018) studied grey relational analysis in hesitant fuzzy settings.…”

Multi-Attribute Decision Making with Interval-Valued Hesitant Fuzzy Information, a Novel Synthetic Grey Relational Degree Method

“…They can reflect only one aspect of the real measures. Sun et al (2018) and Guan et al (2018) presented a synthetic grey relational degree considering both sides by defining the slope grey relational degree, however, the slope grey relational degree can not be used for IVHFSs directly. Furthermore, the combination of synthetic grey relational degree is simple and can not reflect the influence of the whole index space of the grey theory.…”