Probabilistic Hesitant Fuzzy Group Decision Method And Its Application

With the rapid development of human society,the continuous advancement of economic globalization and the rapid development of modern technology,the complexity and uncertainty of practical decision-making issues are increasing.Faced with a large amount of uncertain information in real life,it has become more and more important for decision makers to deal with information more reasonably and effectively and make corresponding decisions.In order to reduce the risk of decision-making and improve the accuracy of decision-making results,on the one hand,a decision-making group is formed to give full play to the collective intelligence,improving the level and quality of decision-making.On the other hand,due to the complexity of decision-making problems and the fuzziness of human thinking,it is difficult to provide accurate information in decision making,so it is necessary to introduce fuzzy sets for objective description.Probabilistic hesitant fuzzy sets,as an extension of fuzzy sets,can better ensure the validity and completeness of decision makers’ evaluation information,which attracts more and more scholars’ attention at home and abroad.Based on the fact that group decision-making can overcome the deficiency of experience and knowledge of single decision-maker,as well as the advantage of probabilistic hesitant fuzzy sets in describing the fuzziness of human thinking,a multi-attribute group decision-making method under probabilistic hesitant fuzzy environment is constructed by improving the traditional multi-attribute decision-making method,which provides a new way to solve the problem of multi-attribute decision-making under probabilistic hesitant fuzzy environment.The purpose of this paper is to deeply study the multi-attribute group decision-making problem using probabilistic hesitant fuzzy information to describe objects.The main research contents include the following four aspects:(1)The multi-attribute group decision-making method based on probabilistic hesitant fuzzy power-weighted average operator is studied.Firstly,by combing the existing operation rules and classical measurement methods of probabilistic hesitant fuzzy elements,aiming at the shortcomings of existing probabilistic hesitant fuzzy distance measures such as weak discrimination ability,the hesitancy degree,incomplete degree and difference measure of probabilistic hesitant fuzzy elements are defined.On this basis,an improved probabilistic hesitant fuzzy distance measure is proposed.Secondly,by combining the power average operator with the improved probabilistic hesitant fuzzy distance measure,the probabilistic hesitant fuzzy power average(PHFPA)operator and the probabilistic hesitant fuzzy power weighted average(PHFPWA)operator are defined,and their properties are studied.Finally,based on the new operator,a new multi-attribute group decision-making method is proposed and applied to the multi-attribute group decision-making problem of evaluation of telemedicine service quality.(2)The probabilistic hesitant fuzzy multi-attribute group decision-making method based on prospect theory is studied.Firstly,in order to measure the reliability of decision-makers’ evaluation information,the credibility of decision-maker in the probabilistic hesitant fuzzy environment is defined.Secondly,the weight of decision-makers is adjusted and the attribute weights are determined based on credibility.Then,the TODIM method based on prospect theory is combined with the probabilistic hesitant fuzzy power weighted average operator,and a probabilistic hesitant fuzzy multi-attribute group decision-making method based on prospect theory is proposed.Finally,the method is applied to the multi-attribute group decision-making problem of selection of pharmaceutical e-commerce.(3)The probabilistic hesitant fuzzy multi-attribute group decision-making method based on cumulative prospect theory is studied.Firstly,in order to measure the level of group consensus,the probabilistic hesitant fuzzy consensus degree is defined,and the group consensus reaching strategy is proposed based on the consensus degree.Secondly,the probabilistic hesitant fuzzy power Heronian mean(PHFPHM)operator and the probabilistic hesitant fuzzy weighted power Heronian mean(PHFWPHM)operator are proposed by combining the Heronian mean operator and the power average operator in the classical category,and the basic properties of the new operators are discussed.Then,under the framework of cumulative prospect theory,a method for calculating cumulative prospect value in probabilistic hesitant fuzzy environment is proposed,and combined with the improved VIKOR method,a probabilistic hesitant fuzzy multi-attribute group decision model based on cumulative prospect theory is constructed.Finally,the model is used in the multi-attribute group decision problem of the government’s purchase of home care services.(4)The multi-attribute group decision-making method based on probabilistic intervalvalued dual hesitant fuzzy is studied.Firstly,based on the concepts of probabilistic hesitant fuzzy sets and interval-valued dual hesitant fuzzy sets,the probabilistic interval-valued dual hesitant fuzzy set is proposed,and its basic operation rules and measurement methods are defined.Secondly,the probabilistic interval-valued dual hesitant fuzzy power Heronian mean(PIDHFPHM)operator,the probabilistic interval-valued dual hesitant fuzzy power geometric Heronian mean(PIDHFPGHM)operator and their weighted forms are defined,and the basic properties of the new operators are discussed.Then,the Co Co So method is introduced into the probabilistic interval-valued dual hesitant fuzzy environment,and the multi-attribute group decision model based on probabilistic interval-valued dual hesitant fuzzy is constructed.Finally,the model is applied to the multi-attribute group decision-making problem of performance evaluation of logistics enterprises.