Abstract: In order to make the comprehensive evaluation factor value of each scheme contain more evaluation information,a three-factor decision algorithm is designed.For each evaluation attribute,the comprehensive weights of other evaluation experts are calculated in turn according to the scores of authoritative evaluation experts.According to the evaluation information given by the evaluation experts with different comprehensive weights,the true function value,the virtual function value and the distance calculation formulas of two weighted probabilistic hesitant fuzzy elements are given respectively.Based on the calculation results of truth-value function and virtual-value function,entropy method is used to obtain the objective weights of evaluation attributes.On the evaluation attributes with different comprehensive weights,the comprehensive evaluation factor values of each scheme are obtained by using the truth function values,virtual function values and distance calculation results,and the schemes are ranked according to the comprehensive evaluation factor values.The feasibility of the decision algorithm is verified by a numerical example.

Key words: weighted probabilistic hesitant fuzzy set, weighted probabilistic hesitant fuzzy element, authoritative decision-making expert, entropy method