Research On Probabilistic Hesitant Fuzzy Two-sided Matching Decision-making Methods And Their Applications

Two-sided matching decision-making problems widely exist in daily life,for example,marriage matching between men and women,matching between patients and doctors,matching between personnel and positions,and so on.The research of two-sided matching decision-making problems has important social and theoretical significance.Due to the complexity of the two-sided matching decision-making problems and the ambiguity of human thinking,the two-sided matching decision making problem under fuzzy information has aroused widespread interest among scholars,and a sea of research achievements have been published.However,the two-sided matching subjects sometimes may hesitate among several values,and sometimes the preference information of their stakeholders are also considered.In this case,it is more appropriate to use probabilistic hesitant fuzzy sets to describe preference information of the two-sided matching subjects.However,there is a lack of research on two-sided matching decision problem under probabilistic hesitant fuzzy information.Hence,this thesis intends to study this kind of problem systematically.With respect to the probabilistic hesitant fuzzy two-sided matching decision making problems with aspiration levels on criteria,correlative criteria,and priority levels of criteria,and propose a series of two-sided matching decision-making methods.the feasibility and effectiveness of the proposed methods are demonstrated by the example analysis.The main works are as follows:With respect to the two-sided matching decision problem with the aspiration levels on criteria under the probabilistic hesitant fuzzy information,a new lance distance measure and a lance score function of the probabilistic hesitant fuzzy element are defined.On the basis of this,the criterion utility value matrix of two-sided matching subjects is constructed by using lance score function of the probabilistic hesitant fuzzy element and expected utility function,the regret-rejoice value matrix and perceived value matrix of two-sided matching subjects about the aspiration levels on criteria are constructed according to regret theory.Furthermore,firstly,the weight vector of the criteria is constructed by using new lance distance measure of the probabilistic hesitant fuzzy element and maximal deviation method.and then the comprehensive perceived value matrix and satisfaction matrix of two-sided matching subjects are constructed respectively by using the linear weighted method and the range transformation method,and the optimal matching scheme is obtained by constructing and solving a satisfied and stable matching decision model.Finally,the effectiveness and feasibility of the proposed method are demonstrated based on an example analysis.With respect to the two-sided matching decision-making problem with criteria association under the probabilistic hesitant fuzzy information,a new probabilistic hesitant fuzzy Einstein operation and a probabilistic hesitant fuzzy discrete Einstein Choquet integral operator are defined.On the basis of this,considering the interrelationships between the criteria,the fuzzy measure values of criteria are calculated by using the hybrid entropy and the cross entropy of the probabilistic hesitant fuzzy element,the comprehensive evaluation value matrix of the two-sided matching subjects is constructed by using the probabilistic hesitant fuzzy discrete Einstein Choquet integral operator,and the satisfaction matrix of the two-sided matching subjects is obtained by using mean score function of the probabilistic hesitant fuzzy element,Furthermore,the optimal matching scheme is obtained by constructing and solving a satisfied matching decision model.Finally,the feasibility and the effectiveness of the proposed method are demonstrated based on an example analysis.With respect to the two-sided matching decision problem with the priority levels of criteria under probabilistic hesitant fuzzy information,a probabilistic hesitant fuzzy Einstein scaled prioritized aggregation operator is defined.On the basis of this,considering the priority levels of criteria,the comprehensive evaluation value matrix of two-sided matching subjects is constructed by using the probabilistic hesitant fuzzy Einstein scaled prioritized aggregation operator,the satisfaction of two-sided matching subjects is calculated by constructing a satisfaction function,and the satisfaction matrix is constructed.Furthermore,the optimal matching scheme is obtained by constructing and solving a satisfied matching decision model.Finally,the feasibility and effectiveness of the proposed method are demonstrated based on an example analysis.