Multi-attribute Decision-making Method Of Probabilistic Hesitant Fuzzy And Its Application

In recent years,with the successful application of fuzzy set theory to the field of multi-attribute decision making,a large number of research results have appeared.In multi-attribute decision making,decision makers often hesitate between multiple evaluation values.Probabilistic hesitant fuzzy sets as an extension of fuzzy sets can not only give the decision makers a number of different evaluation results of an attribute,but also provide the probabilistic of these evaluation results.Probabilistic hesitant fuzzy sets effectively solve the inconsistency of expert preferences in complex multi-attribute decision making,which has attracted the attention of more and more scholars at home and abroad.However,as an emerging research direction,the probabilistic hesitation fuzzy set needs to be perfected in theory,and it still needs to be further expanded in application.Based on the collection and compilation of a large amount of literature,this paper systematically studies the probabilistic hesitant fuzzy multi-attribute decision making method and its application based on the hesitant fuzzy set theory.Firstly,the fuzzy set theory and its development are discussed.Based on the review of hesitant fuzzy multi-attribute evaluation theory and method,the multi-attribute decision-making problem under the conditional hesitation fuzzy environment is analyzed.Secondly,in order to solve the uncertainty problem of the uncertainty of probabilistic and fuzzy information,the fuzzy entropy,hesitant entropy,total entropy and overall uncertainty of the probabilistic hesitation fuzzy element is proposed.The multi-attribute decision making model based on probabilistic hesitant fuzzy entropy is established by combining the entropy measure with the TOPSIS method.Furthermore,the correlation coefficient of probabilistic hesitant fuzzy element is studied,and combined with the improved VIKOR method,a probabilistic hesitant fuzzy multi-attribute decision making method based on correlation coefficient is proposed.At the same time,the probabilistic hesitant fuzzy power aggregation operator is studied,and the concept of adjusted probabilistic hesitant fuzzy element is proposed.Based on this,an improved probabilistic hesitant fuzzy distance measure is proposed,and a multi-attribute decision making method based on probabilistic hesitant fuzzy power aggregation operator is formed.Finally,the application of three kinds of probabilistic hesitant fuzzy multi-attribute decision-making methods is demonstrated by the evaluation of telemedicine service quality,and the effectiveness and rationality of the three evaluation models are verified by the comparative analysis method.The research characteristics and innovations of this paper are mainly as follows:(1)For the lack of uncertainty measurement tools for probabilistic hesitant fuzzy information,the fuzzy entropy,hesitant entropy and total entropy,in order to measure the uncertainty of probabilistic hesitant fuzzy element information,are proposed.Multi-attribute decision making model based on probabilistic hesitant fuzzy entropy;(2)In order to solve the problem of the measure of the probabilistic hesitant fuzzy set correlation,the correlation coefficient of the probabilistic hesitant fuzzy set is proposed,and the probabilistic hesitant fuzzy multi-attribute decision making method based on the correlation coefficient is formed;(3)In order to improve the resolution of the probabilistic hesitant fuzzy element distance measure and improve the probabilistic hesitant fuzzy distance measure,a multi-attribute decision making method based on probabilistic hesitant fuzzy power aggregation operator is proposed.The research in this paper not only proposes three effective probabilistic hesitant fuzzy multi-attribute decision-making methods but also expands and deepens the theory and method of probabilistic hesitant fuzzy sets.