Research On Uncertain Information Decision Making Method Based On Dempster-Shafer Evidence Theory

Due to the uncertainty of objective things and the complexity of decision-making environment,many practical decision-making problems are difficult to be described in an accurate way,and most of the information obtained by decision makers is presented in the form of imprecision and uncertainty.Therefore,most of the time we need to make decisions in an uncertain information environment.Uncertainty is an important characteristics of the decision making problems.Both the imprecision of information and the fuzziness of perception will produce a certain degree of uncertainty.The existence of uncertainty makes people unable to make decisions directly according to the existing information when facing the practical decision-making problem.Hence,effective processing of uncertain information is the key to solve complex decision-making problems.As an effective inference tool for combining uncertain and inaccurate information,Dempster-Shafer evidence theory has received much attention in many fields.Dempster-Shafer evidence theory provides a powerful and convenient framework for the modeling and representing of uncertain information,and can effectively deal with various types of uncertain information.This paper introduces the Dempster-Shafer evidence theory into the uncertain multi-criteria decision making problem,and uses the evidential reasoning approach to handle the uncertain information contained in the decision making problem.However,Dempster-Shafer evidence theory still has some deficiencies in practical decision-making problems.Therefore,this paper takes evidence theory as the main research content,analyzes and discusses three important problems in evidence theory,and puts forward corresponding solutions.Then,it applies the Dempster-Shafer evidence theory to solve multi-criteria decision making problems under uncertain information environment.The innovative work obtained in this paper is summarized as follows.(1)In order to measure the conflict degree between two bodies of evidence,a new evidential similarity measurement approach based on Tanimoto measurement is proposed to depict the inconsistency between two different bodies of evidence.Then,a novel evidential conflict measurement approach is presented in accordance with the evidential similarity measurement to quantify the conflict degree between two bodies of evidence.Finally,some properties satisfied by the new evidential conflict measure method are analyzed and proved.Numerical examples show that the new evidential conflict measurement approach can achieve accurate conflict measure results in different evidence models,and effectively solve the defects of the existing methods.(2)In order to address the problem of conflict evidence fusion effectively,a new hybrid combination rule based on the weighted sum of the Dempster’s combination rule and the fuzzy combination rule is proposed.The new hybrid combination rule utilizes the conflict size between two bodies of evidence to adjust the weights between two kinds of combination rules to adapt to the evidence combination in different conflict situations.The conflict size between two bodies of evidence is described by the inconsistency between two different bodies of evidence and the conflict coefficient.We utilize the new hybrid combination rule to solve the problem of target recognition,and the experimental results show that the new hybrid combination rule can perform better than the existing combination rules in both low and high conflict situations,and has higher recognition accuracy and faster convergence rate.The new hybrid combination rule not only retains the advantages of Dempster’s combination rule,but also solves the problems existing in Dempster’s combination rule.(3)In the framework of Dempster-Shafer evidence theory,the basic probability assignment of multi-subset focal elements can directly express the uncertain information contained in the proposition.Because of the existence of uncertain information,it is difficult to make decisions directly through the basic probability assignment of propositions.Hence,this paper proposes a new method of decision probability transformation based on belief interval to realize the transition from the belief decision to the probability decision.The new decision probability transformation approach considers the transformation of the basic probability assignment with multi-subset focal elements from the view of the belief interval,and applies the continuous interval argument ordered weighted average operator to quantify the data information contained in the belief interval for each singleton.Then,a method to compute the support degree of the singleton is proposed according to the quantitative data information.Ultimately,the basic probability assignment of multi-subset focal elements is reasonably allocated according to the support degree of the singleton.The comparative results show that the proposed method can obtain accurate decision results and improve the decision accuracy of the decision system in different evidence models.(4)Using Dempster-Shafer evidence theory to solve the problem of multi-criteria decision making under hesitant fuzzy environment,and proposes a new hesitant fuzzy multi-criteria decision making approach with the help of the Dempster-Shafer evidence theory.The new hesitant fuzzy multi-criteria decision making approach takes each decision attribute as a piece of evidence,and the frame of discernment of the evidence consists of a group of alternatives.The utility value of each alternative is determined by calculating the distance between the alternative and the positive ideal solution and the negative ideal solution.The uncertainty of the evaluation information of each alternative is measured by the hesitant fuzzy entropy measurement.Then,the basic probability assignments of the criteria are generated by combining the utility value of each alternative with the uncertain information of the alternative.Moreover,the pairwise comparison matrix of each criterion is constructed by using the score value of the evaluation information of the alternative,and the weight value of each criterion is obtained by solving the pairwise comparison matrix.According to the weight value of each criterion,the basic probability assignment of the criteria is modified,and the final belief value of each alternative is obtained by using the new hybrid combination rule to fuse the modified evidence.Finally,the new decision probability transformation method is utilized to calculate the decision probability of the alternative.Based on this,the optimal alternative is achieved by ranking the alternatives.The effectiveness and advantages of the proposed method are demonstrated by numerical examples and practical application problems.(5)In order to handle the Fermatean fuzzy information effectively,a new Fermatean fuzzy entropy measure is presented to describe the fuzzy degree of Fermatean fuzzy set.Thereafter,a novel Fermatean fuzzy multi-criteria decision-making approach based on Dempster-Shafer evidence theory is developed by combining the Fermatean fuzzy entropy measure and the Dempster-Shafer evidence theory.The proposed method models each Fermatean fuzzy number as a piece of evidence,and the weights of the criteria are determined by the entropy measure of Fermatean fuzzy sets.According to the weight of the criteria,the uncertain information contained in each criterion is transferred to the universe set of each evidence.The new hybrid combination rule is utilized to fuse all the evidence in each alternative to obtain the final evaluation information of the alternative,and then calculate the score value of each alternative.Eventually,the ranking results for all alternatives are obtained according to the score value of each alternative.Based on this,the optimal alternative is determined.The feasibility and effectiveness of the proposed approach are demonstrated through two practical application problems.