Journal ArticleDOI
Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment
Zeshui Xu,Wei Zhou +1 more
TLDR
This paper proposes a hesitant fuzzy number with probabilities, called the hesitant probabilistic fuzzy number, and construct its score function, deviation function, comparison laws, and its basic operations and a practical case is provided to demonstrate consensus building with a group of DMs under the HPFE environment.Abstract:
As a generalized fuzzy number, the hesitant fuzzy element (HFE) has been receiving increased attention and has recently become a popular topic. However, we find that the occurring probabilities of the possible values in the HFE are equal, which is obviously impractical. Consequently, in this paper, we propose a hesitant fuzzy number with probabilities, called the hesitant probabilistic fuzzy number, and construct its score function, deviation function, comparison laws, and its basic operations. It is well known that in the context of a group of decision makers (DMs), one of the basic approaches to built consensus is to aggregate individual evaluations or individual priorities. Thus, to use the hesitant fuzzy numbers for consensus building with a group of DMs, we further propose a method called maximizing score deviation method to obtain the DMs’ weights under the HPFE environment, based on which two extended and four new ordered weighted operators are provided to fuse the HPFE information and build the consensus of the DMs. We also analyze the differences among these ordered weighted operators and provide their application scopes. Finally, a practical case is provided to demonstrate consensus building with a group of DMs under the HPFE environment using the proposed approaches.read more
Citations
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Journal ArticleDOI
A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters
Zhibin Wu,Zhibin Wu,Jiuping Xu +2 more
TL;DR: A LGDM consensus model in which the clusters are allowed to change and the decision makers provide preferences using fuzzy preference relations is proposed, and an emergency decision to choose a rescue plan is illustrated to validate the proposed method and demonstrate distinctive characteristics compared with the existing approaches.
Journal ArticleDOI
Multi-criteria decision-making method based on dominance degree and BWM with probabilistic hesitant fuzzy information
TL;DR: This paper discusses the probabilistic distribution function of PHFE and the dominance degree matrix between two PHFEs and the best worst method (BWM), and develops models based on additive consistency and multiplicative consistency of fuzzy preference relations to derive the criteria weights.
Journal ArticleDOI
Group consistency and group decision making under uncertain probabilistic hesitant fuzzy preference environment
TL;DR: This study proposes the uncertain probabilistic hesitant fuzzy element (UPHFE), a generalized fuzzy number, which includes four types of HFEs, and introduces the UPHFPRs and these methods into a group decision-making process, for which two operators are proposed to aggregate the UHFEs and ensure that the aggregated preference relations can remain UPHfPRs.
Journal ArticleDOI
Grey Relational Analysis Method for Probabilistic Linguistic Multi-criteria Group Decision-Making Based on Geometric Bonferroni Mean
TL;DR: This work extends the geometric Bonferroni mean to the probabilistic linguistic environment and designs an approach for the application of multi-criteria group decision-making with PLTSs, and introduces the grey relational analysis method.
Journal ArticleDOI
Probability Calculation and Element Optimization of Probabilistic Hesitant Fuzzy Preference Relations Based on Expected Consistency
TL;DR: This paper presents an iterative optimization algorithm to improve their expected consistency by optimizing some elements in the PHFPRs and the priorities of the alternatives, and demonstrates the probability calculation method for the PHFPEs based on a proposed variable, which is called the expected consistency.
References
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Book
Fuzzy sets
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Journal ArticleDOI
On ordered weighted averaging aggregation operators in multicriteria decisionmaking
TL;DR: A type of operator for aggregation called an ordered weighted aggregation (OWA) operator is introduced and its performance is found to be between those obtained using the AND operator and the OR operator.
Journal ArticleDOI
Hesitant fuzzy sets
TL;DR: It is proved that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set, and it is proved also that the operations proposed are consistent with the ones of intuitionist fuzzy sets when applied to the envelope.
Journal ArticleDOI
Hesitant fuzzy information aggregation in decision making
Meimei Xia,Zeshui Xu +1 more
TL;DR: The relationship between intutionistic fuzzy set and hesitant fuzzy set is discussed, based on which some operations and aggregation operators for hesitant fuzzy elements are developed and their application in solving decision making problems is given.