Abstract
Group decision making (GDM), which aims to obtain a sensible decision result with several decision makers, is a common occurrence in daily life. Since the uncertainty of the objects is a thorny issue in the process of GDM, it is important to eliminate uncertainty in order to achieve an optimal decision result. Considerations of some types of preference relations based on various fuzzy sets have been presented and investigated in previous studies; in this paper, we define the interval-valued hesitant multiplicative preference relation (IVHMPR) and the multiplicative consistency of IVHMPR. Based on these, we provide a detailed discussion on the connections between the interval-valued hesitant fuzzy preference relation (IVHFPR) and the IVHMPR. Then, we give a method to check the for unacceptable consistency of IVHFPR and IVHMPR, and improve them to make the consistency acceptable. Finally, an illustrative example of selecting the optimal treatment for a lung cancer patient is given to demonstrate our work in detail.
Highlights
The interval-valued hesitant fuzzy set (IVHFS) was presented by Chen et al [1] as a capable tool to describe the uncertainty in real practical application, especially in group decision making (GDM) circumstances
We first proposed the concepts of interval-valued hesitant multiplicative preference relation (IVHMPR), the expectation additive consistency of interval-valued hesitant fuzzy preference relation (IVHFPR), and the multiplicative consistency of IVHMPR
This work enriches the theory of IVHFSs and lays the foundation for the application of IVHFSs in practical Group decision making (GDM) problems with fuzzy preference relation (FPR) and multiplicative preference relation (MPR)
Summary
The interval-valued hesitant fuzzy set (IVHFS) was presented by Chen et al [1] as a capable tool to describe the uncertainty in real practical application, especially in group decision making (GDM) circumstances. Defined the concept of interval-valued hesitant fuzzy preference relation (IVHFPR) and applied it to the GDM situation based on some distance measurements and aggregation operations. HFS has a unique superiority in describing this hesitancy with regard to an interval fuzzy proposed a method to construct the acceptably multiplicatively consistent hesitant FPR, which does number This superiority is retained in IVHFS, it is a flaw of IVFS. Liu et al [24] introduced the density function to generated on the basis of the advantages of both IVFS and HFS It is arguably superior for describing determine the multiplicative consistency index of hesitant FPR to solve the problem of the existing uncertain information based on individual indetermination (relatively microscopic) and group method that there is no any theoretical evidence to give a consistency threshold. 7 concludes the paper. a special issue of IVHFPR in the decision-making process
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