Several Statistical Decision Methods Based On Fuzzy Data Information

Decision process is widely existed in human activities,and the expression of decision information and decision method are the important parts of decision making.Many experts have studied the fuzzy information decision making in depth,but the research on fuzzy information is not comprehensive enough.In this paper,several types of fuzzy information are applied to construct judgment matrix,TODIM method,VIKOR method and regret theory.Firstly,the research background of this paper is introduced,and then the research progress of the methods and theories studied in this paper is summarized.Finally,the structure of this paper is introduced.The second chapter,this chapter introduces the relevant theories in this paper,including the Pythagorean fuzzy set,the interval Pythagorean fuzzy set,the uncertain language information,the correlation properties and algorithms of the interval binary semantic information.Finally,the statistical decision method based on regret theory is introduced.The third chapter,the aim of this part is to conduct the consistency analysis for Pythagorean fuzzy judgement matrix.First,a consistency index to measure multiplicative consistency of Pythagorean fuzzy judgement matrix is presented.Then,for the non-consistent PFPR,an iteration algorithm is put forward to adjust it to achieve acceptable consistent.On this basis,the synthetic ordering value of Pythagorean fuzzy judgment matrix is calculated.Finally,an illustrative example is provided to test and verify the effectiveness and applicability of the proposed method.The fourth chapter,aiming at the group decision problem whose attribute information is interval-value Pythagorean fuzzy set and the attribute weight and expert weight are unknown,combined with information entropy theory,an interval-value Pythagorean fuzzy VIKOR statistical decision making method is proposed.Firstly,a new interval-value Pythagorean fuzzy distance measure is defined,and its properties are discussed.Secondly,based on the distance measure,the interval-value Pythagorean fuzzy relative distance index is presented and entropy model are constructed to determine the weights of experts and attributes.Then an interval-value Pythagorean fuzzy VIKOR statistical decision making method is proposed.Finally,the feasibility and effectiveness of the proposed new method are illustrated by the enterprise production plan selection case.The fifth chapter,aiming at the problem of statistical decision making for evaluating information interval-value Pythagorean fuzzy uncertain linguistic sets,a TODIM statistical decision making method based on interval-value Pythagorean fuzzy uncertain linguistic sets and regret theory improvements was proposed.Firstly,the new definition of the scoring function,the accurate function and the distance of interval-value Pythagorean fuzzy uncertain linguistic sets are given,and the ordered weighted operator of interval-value Pythagorean fuzzy uncertain linguistic variable is given.Secondly,a non-linear model is constructed to solve attribute weights.Then combined with regret theory,a TODIM statistical decision making method based on interval-value Pythagorean fuzzy uncertain linguistic sets was proposed.Finally,the improved TODIM method is used to select a suitable open-air emergency shelter for the city,and the effectiveness of the method is verified.The sixth chapter,Aiming at the statistical decision making problem with the evaluation information as interval binary semantic information,this paper proposes an interval binary semantic statistical decision making method based on regret theory,which can effectively consider the kind of decision makers in the decision process.Risk aversion,and there are psychological differences between regret and rejoice.First of all,this paper introduces some basic concepts about interval binary linguistic information and gives the definition of interval binary linguistic mean and variance.Aiming at the statistical decision making problem in which the decision matrix elements are unknown to the weight of the interval binary semantic variable,the variance of the interval binary linguistic is used to determine the optimal attribute weight by constructing the optimization model,and a interval based on regret theory is proposed.Meta-semantic statistical decision making method.Finally,the method is applied to the choice of enterprise design scheme.The results and comparative analysis show that the method has certain feasibility and effectiveness.At last,it summarizes and forecasts the whole paper.