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. 2022;52(15):18226-18247.
doi: 10.1007/s10489-022-03749-0. Epub 2022 Jul 15.

Interactive group decision making method based on probabilistic hesitant Pythagorean fuzzy information representation

Gang Sun  1 , Weican Hua  2 , Guijun Wang  2
Affiliations

Interactive group decision making method based on probabilistic hesitant Pythagorean fuzzy information representation

Gang Sun et al. Appl Intell (Dordr). 2022.

Abstract

Interactive group evaluation is a decision-making method to obtain group consensus by constantly modifying the initial weight of experts. Probabilistic hesitant Pythagorean fuzzy set (PrHPFS) is to be added the corresponding probability values for each membership degree and non-membership degree on the hesitant Pythagorean fuzzy set (HPFS). It is not only a generalization of HPFS and the Pythagorean fuzzy set (PFS), but also a more comprehensive and accurate reflection of the initial decision information given by experts. Especially, it can deal with the decision-making problem of multi-attribute fuzzy information in a wider area. In this paper, some basic definitions and related operations of the probabilistic hesitant Pythagorean fuzzy numbers (PrHPFNs) are first reviewed, and propose score function and accuracy function in PrHPFNs environment. Secondly, the concepts of Hamming distance measure, weighted distance measure and degree of similarity are put forward in PrHPFNs space, and the degree of similarity of two probabilistic hesitant Pythagorean fuzzy matrices (PrHPFMs) is suggested through the aggregation operator formula of PFNs. Finally, an interactive group decision-making method is designed based on the PrHPFM and the degree of similarity under the PrHPFNs environment, the effectiveness of the method is verified by an example, so as to overcome the hesitant psychological state of experts and achieve the consistent consensus evaluation of group preference.

Keywords: Degree of similarity; Hamming distance measure; Interactive group decision making; Probabilistic hesitant Pythagorean fuzzy number (PrHPFN); Pythagorean fuzzy number (PFN).

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Conflict of interest statement

Conflict of interestThe authors declare that they have no conflict of interest.

Figures

Fig. 1
Fig. 1
The flow chart of the proposed group interactive decision-making method
Fig. 2
Fig. 2
The flow chart of the technical route of the proposed method
Fig. 3
Fig. 3
An intuitive flow chart of the whole decision-making process
Fig. 4
Fig. 4
Influence of adjusting expert weights to PrHPFM similarities
Fig. 5
Fig. 5
Influence of adjusting expert weights to score values
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