Abstract: For multi-attribute decision-making problems with decision information as picture fuzzy, this paper firstly defines the assignment of the degree of refusal membership with parameters based on the limitations of existing picture fuzzy distances. It also proposes a picture fuzzy distance that reflects decision-makers’ risk preferences by combining consistency concepts. Through a numerical example, the new picture fuzzy distance is compared and analyzed with existing picture fuzzy distances to verify its superiority. Secondly, for attribute weights, this paper adopts the combination weighting method of game theory to combine the objective weights determined by entropy weighting with the subjective weights given by decision-makers. On this basis, the new picture fuzzy distance is extended to evaluation based on distance from average solution (EDAS) method, and the weighted sum of positive and negative distances between each scheme and the average scheme is calculated using the new distance, resulting in comprehensive scores. Finally, numerical examples are used to verify the applicability and effectiveness of the proposed decision-making method. Sensitivity and comparative analysis results show that decision-makers can adjust the parameter values according to their risk preferences to meet different decision-making needs. The method is more general and flexible compared to other existing decision-making methods, and the ranking results are more reasonable. 

Key words: picture fuzzy set, picture fuzzy distance, combination weighting method of game theory, evaluation based on distance from average solution(EDAS) method, multi-attribute decision making