Multiple criteria group decision analysis using a Pythagorean fuzzy programming model for multidimensional analysis of preference based on novel distance measures

Abstract

The preference concerning criteria or alternatives from decision makers (DMs) is a critical element in multicriteria group decision making (MCGDM). The linear programming technique for the multidimensional analysis of preference (LINMAP) is the most influential technique in adjusting the error between the objective assessments on criteria and subjective preferences on alternatives via optimal programming for MCGDM problems. Considering the higher capacity for expressing the uncertainties of human inherent preferences of the Pythagorean fuzzy (PF) sets, this article explores the LINMAP technique for MCGDM problems under the PF scenario. First, we present a novel (squared) Euclidean distance measure for the PF sets since it possesses captivating characteristics of the PF sets and the distance measure. Second, we define the preference degrees over alternatives that are expressed as PF sets and calculate their magnitudes via relative distances, which are used to calculate the consistency and inconsistency indices. Third, the ordered weighted averaging (OWA) operator under the normal distribution is introduced to obtain the weights of DMs to reduce the influence of unfair arguments. Fourth, we construct the biobjective PF-LINMAP model for minimizing both the error extents and the overall distances to the PF positive ideal solution for the minimum error and global optimum. Then, we obtain the optimal criterion weights and ranks of the candidates via relative closeness indices. Finally, we perform our PF-LINMAP method to choose the optimal green supplier, and we implement the sensitivity analysis and comparative analysis with those of the available PF-LINMAP methods to verify the feasibility and superiority of our approach.