Pythagorean fuzzy preference relations and their applications in group decision‐making systems

In this paper, we introduce a new type of fuzzy preference structure, called Pythagorean fuzzy preference relations (PFPRs), to describe uncertain evaluation information in group decision-making process. Moreover, it allows decision makers to offer effectively handle uncertain information more flexibly than intuitionistic fuzzy preference relations when one compares two alternatives in the process of decision making. Using PFPRs, we propose an approach for group decision making based on group recommendations and consistency matrices. First, the proposed approach constructs the collective consistency matrix, the weight collective preference relations (PRs), and the group collective PR. Then, it construct a consensus relation for each expert and determinate the group consensus degree for all experts. If the group consensus degree is smaller than a predefined threshold value, then it identify the consensus values in each consensus relation which are smaller than the group consensus degree and updates the Pythagorean fuzzy preference values corresponding to the identified consensus values. The above process is continued, until the group consensus degree is larger than or equal to the predefined threshold value. Finally, based on the group collective PR, we calculate the row arithmetic mathematical average values and with respect to that values the various methods are applied for ranking the preference order of the alternatives. Numerical example are provided to illustrate the proposed approach.