Centroid Coordinate Ranking of Pythagorean Fuzzy Numbers and its Application in Group Decision Making

Distance measure and intuitionistic fuzzy TOPSIS method based on the centroid coordinate representation *

In real life, people often need to aggregate some multi criteria fuzzy information and then make reasonable and effective decisions. The distance measure in intuitionistic fuzzy set (IFS) space is an important tool to deal with multi criteria information fuzzy decision making problems. Motivated by these reasons, an intuitionistic fuzzy TOPSIS multi criteria decision-making method is proposed based on distance measure represented by centroid coordinates. Firstly, some existing distance measures in IFS space are summarized, and some of existing shortcomings are discussed. Secondly, the concept of hesitation factor is proposed by using the centroid coordinate representation of hesitation region, and then a new distance measure between two intuitionistic fuzzy numbers is defined. It is proved that the distance measure satisfies the traditional distance axioms. Then, an intuitionistic fuzzy TOPSIS method based on the proposed distance measure is developed. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method. Also, the superiority and advantages of the method are shown via comparative analysis and discussion.

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

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.