Decision Expansion And Application Of Probabilistic Interval-valued Intuitionistic Hesitant Fuzzy Information

Decision-making evaluation is ubiquitous in human daily life,however,due to the rapid increase in the breadth and complexity of various information flows in modern society,the uncertainty of evaluation information makes decision-making more and more complex,it is difficult for decision makers to make correct judgments,leading to large errors in results.Faced with a large number of uncertain decision evaluation information,how to effectively deal with information and make objective evaluation is particularly important.Decision-makers began to use fuzzy comprehensive evaluation methods to make decisions.In order to ensure the relative validity and completeness of the evaluation information,and to solve the inconsistent preferences of decision-makers' preferences in complex decision-making problems,this paper extends on the probabilistic interval value intuitionistic hesitation fuzzy set to better avoid the uncertainty and evaluation information in the evaluation process.Moreover,as the form of fuzzy set in the current emerging environment,the improvement of its theoretical knowledge and application are also of positive significance.The extended results of this paper are applied to the comprehensive evaluation of poverty governance performance,and relatively ideal simulation results have been obtained.The specific research contents are summarized as follows:(1)Based on the relevant theoretical knowledge of probability interval valued intuitionistic hesitation fuzzy sets(PIVIHFSs)and existing ensemble operators,the probabilistic interval-valued intuitionistic hesitancy module(PIVIHFOWA)and the probabilistic interval-valued intuitionistic hesitancy module and ordered weighted geometry(PIVIHFOWG)operators are proposed,the theoretical system of PIVIHFSS is extended and the foundation of the method is established.(2)Combining the advantages of probability interval-valued intuitionistic hesitant fuzzy sets(PIVIHFSs)and Maclaurin(MSM)operator,PIVIHFMSM operator and PIVIHFWMSM operator are proposed,and the properties and special cases of these two kinds of operators are discussed.A comprehensive evaluation method based on PIVIHFWMSM operator is proposed.The method is applied to the performance evaluation of poverty alleviation governance in poor areas.The advantages and disadvantages of the evaluated towns are sorted,and the towns with the best effect of poverty governance are selected.Through comparative analysis,it proves the flexibility and effectiveness of the newly propose method.Under the premise of ensuring the relative integrity of evaluation information,this method takes into account the correlation between indicators,and enables decision makers to select appropriate parameters for decision-making evaluation based on their own experience and risk preference and other subjective attitudes.It has stronger applicability and operability.(3)We proposed the European weighted distance measure formula of PIVIHFSs,on an basis of existing probabilistic hesitancy and set distance measure,which improves the theoretical system of PIVIHFSs,and can be widely used in the field of decision-making,providing theoretical support for the following research on statistical decision-making methods.(4)PIVIHFSs are extended to classical statistical decision-making methods,and PIVIHFS-TOPSIS,PIVIHFS-VIKOR and PIVIHFS-TODIM methods are proposed.All three methods are implemented under the new formula of PIVIHFSs distance measure.Three new evaluation methods are used to measure the effect of poverty alleviation in a certain poverty-stricken area,and the results are compared and analyzed to show the usefulness of our methods.The sensitivity of each parameter involved in each evaluation method is analyzed,and the results were observed,which showed that our method is stable and reliable.The application of these methods and the comparison of the ranking results show that their advantages are more prominent.The method of PIVIHFS-TOPSIS is more simple and easy to understand,more suitable for actual promotion and application.The PIVIHFS-VIKOR method can comprehensively consider the two factors of group utility and individual regret to make decisions,and get a compromise solution,which makes the evaluation result more reasonable.Considering the reinforcement of different mechanisms,it is applied to the performance evaluation to prove the robustness and feasibility of this method.The results of PIVIHFS-TODIM can contain more evaluation information by pair comparison of the evaluation objects.At the same time,the correlation between the evaluation indicators and the dependence of decision-makers and the psychology of loss avoidance are fully considered.The feasibility and robustness of the method are also proved in the subsequent simulation applications.The three methods proposed provide new ideas and new choices for dealing with decision-making evaluation problems.The research in this article provides ideas for the comprehensive evaluation of uncertain information,and expands the existing methods so that they can be applied more effectively and accurately in political,economic,environmental,cultural and other fields,such as poverty management.The research,the selection of preventive mechanisms such as infectious diseases,the evaluation of teaching and the evaluation of environmental governance capabilities and other practical issues.