Belief Structure-Based Pythagorean Fuzzy LINMAP for Multi-Attribute Group Decision-Making with Spatial Information

Pythagorean fuzzy sets have higher performance in expressing uncertainty information in multi-attribute group decision-making (MAGDM). The linear programming technique for multidimensional analysis of preference (LINMAP) is a prototypical compromising model that adjusts the deviation between objective assessments and subjective preferences on decision alternatives. However, the disadvantages of Pythagorean fuzzy sets in conflict measure and LINMAP model in inconsistent decision information structure have not been solved yet. To solve the problems that incomplete decision information in Pythagorean fuzzy set and inconsistent evaluation structure in LINMAP, the spatial measures and Dempster-Shafer evidence theory are introduced. A new spatial structure conflict measure is thus presented, and the belief structure of Dempster-Shafer evidence theory is used to provide a unified decision-making framework for LINMAP inconsistent evaluation structure. Firstly, a novel spatial distance measurement method is developed. Secondly, comprehensive closeness is introduced to measure individual order consistency and inconsistency between subjective preference and objective evaluation. Thirdly, we define the objective basic probability assignment and subjective basic probability assignment based on Dempster-Shafer belief structure to develop the bi-objective LINMAP of Pythagorean fuzzy sets and add the deviance between individual goodness of fit and poorness of fit is introduced as constraints to obtain the optimal attribution weights. Then, the final order of decision alternatives can be obtained by the fusion rules of Dempster-Shafer. Finally, we verify that the proposed method can improve the alternative discrimination in the case of unstable order, and the result of alternative order total biased of the proposed method is reduced by at least 80% compared with the comparative method.