Deriving a Ranking From Hesitant Fuzzy Preference Relations Under Group Decision Making

Abstract

In this paper, we explore the ranking methods with hesitant fuzzy preference relations (HFPRs) in the group decision making environments. As basic elements of hesitant fuzzy sets, hesitant fuzzy elements (HFEs) usually have different numbers of possible values. In order to compute or compare HFEs, we have two principles to normalize them, i.e., the α -normalization and the β -normalization. Based on the α -normalization, we develop a new hesitant goal programming model to derive priorities from HFPRs. On the basis of the β -normalization, we develop the consistency measures of HFPRs, establish the consistency thresholds to measure whether or not an HFPR is of acceptable consistency, and then use the hesitant aggregation operators to aggregate preferences in HFPRs to obtain the ranking results.

Missing values estimation and consensus building for incomplete hesitant fuzzy preference relations with multiplicative consistency

“…For the β -normalization, Zhu et al 2 introduced the following method to add some elements to a HFE.…”

“…Due to the advantages of handing imprecision by two or more sources of vagueness appear simultaneously 2 , HFSs have attracted great attention by researchers and have been widely applied in decision making 3,4,5,6 . Rodríguez et al 7 extended the HFSs to linguistic environment, and introduced hesitant fuzzy linguistic term set (HFLTS).…”

“…Zhu et al 2 explored the ranking methods with HFPRs in the group decision making (GDM) environments. Liao et al 22 investigated the multiplicative consistency of HFPRs and its application in GDM.…”

Decomposition and Intersection of Two Fuzzy Numbers for Fuzzy Preference Relations

“…Zhang et al [11] presented a fuzzy probabilistic preference relation. Zhu et al [12] proposed hesitant fuzzy preference relations. Wang [13] adopted the relative preference degrees of the fuzzy numbers over average.…”

A note on operations of hesitant fuzzy sets

“…In decision making problems, experts are usually hesitant and irresolute for one thing or another which makes it difficult to reach a final agreement, such cases motivate experts to use hesitant fuzzy sets for decision makings [7,35], e.g., permit several membership values for a single thing in the reference set. For solving decision making prob-…”