Abstract
As an enhanced version of probabilistic hesitant fuzzy sets and dual hesitant fuzzy sets, probabilistic dual hesitant fuzzy sets (PDHFSs) combine probabilistic information with the membership degree and non-membership degree, which can describe decision making information more reasonably and comprehensively. Based on PDHFSs, this paper investigates the approach to group decision making (GDM) based on incomplete probabilistic dual hesitant fuzzy preference relations (PDHFPRs). First, the definitions of order consistency and multiplicative consistency of PDHFPRs are given. Then, for the problem that decision makers (DMs) cannot provide the reasonable associated probabilities of probabilistic dual hesitant fuzzy elements (PDHFEs), the calculation method of the associated probability is given by using an optimal programming model. Furthermore, the consistency level for PDHFPRs is tested according to the weighted consistency index defined by the risk attitude of DMs. In addition, a convergent iterative algorithm is proposed to enhance the unacceptable consistent PDHFPRs’ consistency level. Finally, a GDM approach with incomplete PDHFPRs is established to obtain the ranking of the alternatives. The availability and rationality of the proposed decision making approach are demonstrated by analyzing the impact factors of haze weather.
Highlights
Group decision making (GDM) determines the most ideal alternative according to evaluation information expressed by a group of decision makers (DMs) [1]
The above analysis motivate us to further study some issues related to probabilistic dual hesitant fuzzy preference relations (PDHFPRs), such as how to obtain the probability information of incomplete PDHFPRs, how to measure the consistency level of PDHFPRs, and how to use consistency to solve the GDM problem with PDHFPRs
A GDM approach with incomplete PDHFPRs is constructed, and the effectiveness and applicability of the proposed decision making approach are verified by analyzing the impact factors of haze weather
Summary
Group decision making (GDM) determines the most ideal alternative according to evaluation information expressed by a group of decision makers (DMs) [1]. Using DHFSs, DMs can provide hesitant evaluation information from the perspective of membership degrees (MDs) and non-membership degrees (NMDs). The occurrence possibilities of membership and non-membership values are not considered in DHFSs, and NMDs and their corresponding importance are not considered in PHFSs. DHFSs and PHFSs cannot fully express the evaluation information. In GDM problems, it may be more intuitive for DMs to provide evaluation information by using preference relation (PR). The above analysis motivate us to further study some issues related to PDHFPRs, such as how to obtain the probability information of incomplete PDHFPRs, how to measure the consistency level of PDHFPRs, and how to use consistency to solve the GDM problem with PDHFPRs. The rest of the sections are listed as follows: In “Related work”, the related work is briefly reviewed.
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