Research On Group Decision-Making Method Of Interval-Valued Probabilistic Hesitant Fuzzy Preference Relations

In recent years,a large number of research findings have emerged since the successful application of preference relation theory to the field of group decisionmaking.In the process of group decision-making,the preference matrix given by decision-makers is often difficult to meet the consistency,so that the opinions of decision-making experts cannot reach a consensus.Probabilistic hesitant preference relations can give different evaluation results for preference degree of decision makers among alternatives,and provide the probabilities corresponding to these evaluation results.Among them,additive consistency and multiplicative consistency are essential studies of probabilistic hesitant fuzzy preference relations.As an emerging research direction,the study of interval-valued probabilistic hesitant fuzzy sets has attracted more and more attention from scholars at home and abroad.However,additive consistency and multiplicative consistency were hardly extended to the study of interval-valued probability hesitation fuzzy preference relationships.By collecting and compilating a large amount of literature,this paper systematically studies the group decision-making method and its application of interval-valued probabilistic hesitant fuzzy preference relations based on fuzzy theory.Firstly,on the basis of probability hesitant fuzzy preference relations and intervalvalued probabilistic hesitant fuzzy sets,the interval-valued probabilistic hesitant fuzzy preference relations are defined.Secondly,in order to solve the additive inconsistency of the interval-valued probabilistic hesitant fuzzy preference relations,an additive consistency index of interval-valued probabilistic hesitant fuzzy preference relations is proposed.And combined with the group consensus analysis,a group decision-making method with an additive consistent interval-valued probabilistic hesitant fuzzy preference relations are developed.Furthermore,through proposing the multiplicative consistency index of the interval-valued probabilistic hesitant fuzzy preference relations,a multiplicative consistent interval-valued probabilistic hesitant fuzzy preference relations are established,and the corresponding group decision-making method is developed.Moreover,the intervalvalued probabilistic hesitant fuzzy incomplete preference relations are also studied,and the missing preference information is proposed to be completed by additive consistency analysis and multiplicative consistency analysis,and a group decisionmaking method based on interval-valued probabilistic hesitant fuzzy incomplete preference relations is developed.Finally,the application of the two kinds of intervalvalued probabilistic hesitant fuzzy preference relations for group decision-making method is demonstrated by the evaluation of network public opinion emergencies,and the validity and rationality of the two evaluation models are verified by the comparative analysis method.The research characteristics and innovations of this paper are mainly as follows:(1)For the definition and characteristics of interval-valued probabilistic hesitant fuzzy preference relations have not been studied deeply,the definition and related operation rules of the interval-valued probabilistic hesitant preference relations are proposed,as well as the definition and judgement theorems of weak consistency,additive consistency,and multiplicative consistency.(2)To address the lack of additive consistency,multiplicative consistency and group consensus measurement tools for interval-valued probabilistic hesitant fuzzy preference relations,a new consistency index and group consensus index are proposed by combining distance formula and rank correlation coefficient,which can measure the degree of consistency and group consensus of preference matrix in two dimensions of distance and order.(3)In order to adapt to the complexity of the decision-making environment,the interval-valued probabilistic hesitant fuzzy incomplete preference relations is defined,and additive consistency and multiplicative consistency are applied to construct a model to obtain the missing preference relations,and the group decision-making methods of intervalvalued probabilistic hesitant fuzzy incomplete preference relations is proposed.