Research On Decision-making Methods And Applications Based On Three Types Of Probabilistic Linguistic Information

As the expanded forms of the emerging decision-making instruments that present decision-making information in a quantitative and qualitative way,the emergence of probabilistic linguistic term set,probabilistic uncertain linguistic term set and dual probabilistic linguistic term set is striking.Based on the perspective of enriching uncertain decision-making theories,this paper makes the following innovative research on the decision-making theories and methods of these three types of probabilistic linguistic information.(1)The analytic hierarchy process(AHP)is extended to the probabilistic linguistic environment to improve the modeling ability of AHP in various decision-making problems.Firstly,the probabilistic linguistic comparison matrix(PLCM)is redefined,and a new consistency index is proposed.Then,a new method for testing and improving the consistency of the PLCMs is proposed.Secondly,the individual PLCMs are integrated into a collective PLCM,and the priority of the collective PLCM is determined.Thirdly,the priority is determined by combining priority and decision-making matrix,and the feasibility and effectiveness of the proposed theory are proven by comparing the performance evaluation of Xiong'an new district and the comparison of decision results.(2)Two different types of incomplete probabilistic linguistic preference relations(IPLPRs)are introduced.Firstly,based on the different linguistic scales selected by the decision makers,the IPLPRs are divided into two categories: the additive preference relationship and the multiplication preference relationship.Then,the corresponding repair algorithms are proposed for different types of IPLPRs.Secondly,according to the transition function,the obtained complete preference relationship is converted into a unified form in order to realize the integration of information.Thirdly,it examines and enhances the consistency of the uniform form preference relationship,determines the ordering of the schemes,and shows the feasibility and effectiveness of the decision-making method by evaluating the performance of the new four major inventions in China.(3)The probabilistic uncertain linguistic preference relation(PULPR)and the normalized PULPR are constructed.Firstly,the definitions of the distance measure and the similarity measure are defined.Then two different consensus processes are introduced: one is the consensus process based on the distance measure between individual PULPRs and the group PULPR;the other is the consensus based on the similarity among individual PULPRs.Secondly,the selection process is determined based on the proposed possibility degree.Thirdly,two different algorithms are proposed to solve the group decision-making problem of the virtual reality industry selection cooperative company,and verify the effectiveness of the two algorithms.(4)The probabilistic uncertain multiplicative linguistic preference relations(PUMLPRs)and the incomplete probabilistic uncertain multiplicative linguistic preference relations(IPUMLPRs)are given.Firstly,based on the elemental composition of the PUMLPRs,the IPUMLPRs are repaired in two aspects: repairing the uncertain multiplicative linguistic variables and repairing the corresponding probabilities.Then,the consistency of the PUMLPRs is studied.Secondly,based on the newly proposed possibility formula,the management method of network public opinion is evaluated to determine the optimal mode.(5)From the perspective of cognitive certainty and uncertainty,the dual probabilistic linguistic term sets(DPLTSs)are proposed.Firstly,the dual probabilistic linguistic correlation coefficient is given.Then,based on the difference in the degree of importance between the research objectives,the entropy of the DPLTSs is defined to calculate the integrated weight vector.Secondly,the weighted dual probabilistic linguistic correlation coefficient is proposed as the benchmark for selecting artificial intelligence projects.Thirdly,the dual probabilistic linguistic closeness coefficient is defined to determine program sequencing and comparative analysis.(6)The dual probabilistic multiplicative linguistic term sets(DPMLTSs)are proposed.Firstly,the comparability between the DPMLTSs is defined.Then,the dual probabilistic multiplicative linguistic preference relations(DPMLPRs)are proposed.Secondly,the comparability between the DPMLPRs is defined,and the consensus of the group DPMLPR is studied.Thirdly,based on the definition of comparability,an extended grey correlation analysis method,an extended TODIM method,and an extended VIKOR method are proposed.Finally,these similarities and differences between the three methods are compared through a case of selecting a cloud enterprise partner.