Abstract
Preference relations are generally used to cope with multi-attribute group decision making (MAGDM), which express the experts’ preference information through pairwise comparisons. To make decision rationale, one of the vital issues related to preference relations is how to make the preference information logical. The logicality level of preference information is usually described by the consistency of preference relation. Thus, developing methods to check and improve the consistency of preference relations is necessary and significant. In this paper, we give a general description of multiplicative transitivity property for fuzzy preference relation (FPR). Then, based on the new multiplicative transitivity function which can repair some counterintuitive cases of the traditional one, we define the stably multiplicative consistency, the stably mean multiplicative consistency (SMMC), and the acceptable SMMC for interval-valued hesitant FPR (IVHFPR). Additionally, several algorithms are developed to improve the SMMC of IVHFPR. A practical example concerning the respiratory illness diagnosis is given to demonstrate the applicability of IVHFPR with SMMC.
Highlights
Multi-attribute group decision making (MAGDM) can be described as the process of calculating the ranking result of several alternatives Al = {A1, A2, · · ·, AK } with respect to a set of attributes At = {a1, a2, · · ·, aM }, based on a group of experts’ evaluation information
We focus on discussing the multiplicative consistency of interval-valued hesitant fuzzy preference relation (IVHFPR) from a new perspective of multiplicative transitivity property of fuzzy preference relation (FPR)
Considering that the researches on multiplicative consistency of the interval-valued hesitant FPR (IVHFPR) are rare, in this paper, we aim to investigate the methods of improving the multiplicative consistency of the IVHFPR
Summary
We focus on discussing the multiplicative consistency of interval-valued hesitant fuzzy preference relation (IVHFPR) from a new perspective of multiplicative transitivity property of fuzzy preference relation (FPR). As matters stand with the algorithms to improve the multiplicative consistency of FPRs, much work has been done for intuitionistic FPR (IFPR) [9]–[11], interval-valued FPR (IVFPR) [12], [13], and hesitant FPR (HFPR) [14], et al While the related researches for the IVHFPR were rare. With all the mentioned above, our main work in this paper is as follows: For the FPR, we give a new multiplicative transitivity function for repairing some counterintuitive cases of the traditional ones in Refs.
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