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.
Highlights
Multiattribute decision-making (MADM) is pervasive and active around human beings’ practical activities
Many researchers have devoted themselves to the fuzzy multiattribute decision-making (FMADM) with different types of fuzzy sets, from the traditional fuzzy set to the intuitionistic fuzzy sets (IFSs) and hesitant fuzzy sets (HFSs)
The motivation of this paper is to explore a novel synthetic grey relational degree for HFSs and develop a methodology based on TOPSIS to solve MADM problems with HFSs information
Summary
Multiattribute decision-making (MADM) is pervasive and active around human beings’ practical activities. It is an effect and basic method to solve large quantitative and qualitative problems as information fusion, pattern recognition, alternatives selection and evaluation, clustering analysis, military applications, and so forth. The fuzzy multiattribute decision-making (FMADM) is introduced and widely used to tackle this uncertainty since Zadeh [1] initially proposed the theory of fuzzy set in 1965. Many researchers have devoted themselves to the FMADM with different types of fuzzy sets, from the traditional fuzzy set to the intuitionistic fuzzy sets (IFSs) and hesitant fuzzy sets (HFSs). IFSs and HFSs are the two most popular fuzzy sets at present, which have been extensively paid attention to.
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