Preprint Article Version 1 This version is not peer-reviewed

Grey Relational Analysis for Hesitant Fuzzy Sets and Interval-Valued Hesitant Fuzzy Sets with Applications to MADM Problems

Version 1 : Received: 13 October 2017 / Approved: 17 October 2017 / Online: 17 October 2017 (12:35:18 CEST)

How to cite: Guan, X.; Sun, G.; Yi, X.; Zhao, J. Grey Relational Analysis for Hesitant Fuzzy Sets and Interval-Valued Hesitant Fuzzy Sets with Applications to MADM Problems. Preprints 2017, 2017100118 (doi: 10.20944/preprints201710.0118.v1). Guan, X.; Sun, G.; Yi, X.; Zhao, J. Grey Relational Analysis for Hesitant Fuzzy Sets and Interval-Valued Hesitant Fuzzy Sets with Applications to MADM Problems. Preprints 2017, 2017100118 (doi: 10.20944/preprints201710.0118.v1).

Abstract

Quantitative and qualitative fuzzy measures have been proposed to hesitant fuzzy sets (HFSs) from different points. However, few of the existing HFSs fuzzy measures refer to the grey relational analysis (GRA) theory. Actually, the GRA theory is very useful in the fuzzy measure domain, which has been developed for such the intuitionistic fuzzy sets. Therefore, in this paper, we apply the GRA theory to the HFSs and interval-valued hesitant fuzzy sets (IVHFS) domain. We propose the HFSs grey relational degree, HFSs slope grey relational degree, HFSs synthetic grey relational degree and IVHFSs grey relational degree, which describe the closeness, the variation tendency and both the closeness and variation tendency of HFSs and closeness of IVHFSs, respectively, 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 and IVHFSs MADM problems. Finally, combined with two practical MADM examples about energy policy selection with HFSs information and emergency management evaluation with IVHFSs information, we obtain the most desirable decision results, and compared with the previous methods, the validity, effectiveness and accuracy of the proposed grey relational degree for HFSs and IVHFSs are demonstrated in detail.

Subject Areas

Grey relational analysis (GRA); Hesitant Fuzzy Sets (HFSs); Interval-valued hesitant fuzzy sets (IVHFS); grey relational degree; grey relational based MADM methodology

Readers' Comments and Ratings (0)

Leave a public comment
Send a private comment to the author(s)
Rate this article
Views 0
Downloads 0
Comments 0
Metrics 0
Leave a public comment

×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.