The Study On Multiple Attributive Matching Decision Methods Based On Evidence Theory

The decision-making problem of two-sided matching widely exists in the economic life. It is related to numerous application fields, for example the two-way choice problem of students and colleges, the supply and demand of knowledge and technology, financial supplies and the need for economic growth, the buyers and sellers in group purchase and so on. The method for matching decision-making is to get the objective that satisfies every agent of both groups, according to the mutual evaluation information. However, as we all know,the information gained by one agent from the other agent is often uncertain, unknown, or even dynamic. Already existing methods are mainly limited to solve the matching decision-making problem based on the evaluation information that is single attributive, static and certain.Recently, scholars have started to study the matching decision-making problems with multi-attribute and uncertain information, but there are two disadvantages in them. One is hard to solve the matching decision-making problems with unknown and uncertain information. The other is hard to solve the matching decision-making problems with dynamic information based on sequential characteristic. These disadvantages seriously affect their popularization and application. In contrast to uncertain rational methods such as the certain factors method and subjective Bayes method, evidence theory is good at dealing with aggregation problems of dynamic or unknown information. Therefore, evidence theory is introduced into the field of multiple attributive matching decision-making in this article.The research contents and methods are as follows:(1) The improvement of evidence theoryTo suppress the counterintuitive results generated from the combination of conflicting precise evidences, a new method for combining evidence optimally is proposed with related theoretical proofs. On this basis, a grouping method for combining evidence is proposed to take the advantages of sequence fusion and batch fusion. Finally,numerical examples are provided to demonstrate the advantages of the proposed new method such as less computation, better stability and higher precision.To suppress the counterintuitive results generated from the combination of conflicting interval-valued evidences, a modified evidence combination approach is proposed. An optimization model of pignistic probability distance is built from the global perspective to provide the relative importance weights for weighting evidence such that the weighted evidence can be reasonably combined with the Dempster rule of combination. Finally,numerical examples show the efficiency and rationality of the proposed approach.(2) Evidence fusion methods of multi-attribute matching decision-making with uncertain information.To solve the matching decision-making problem with uncertain preference ordinals, first, the description of evidence fusion is given. Then, the ordinal scores of the evaluation of both matching agents are taken as evidences, and the fusion degrees of two-sided ordinal scores are got by evidence combining. Furthermore, an optimization model is developed to obtain two-sided matching scheme. Finally, the methods’feasibility and validity are proved through illustrative examples.To solve multi-attribute matching decision-making problem with uncertain information, first, the concept of rank belief degrees and related theoretical proofs are presented. Then, belief degrees evaluation information with multiple format data is transformed into rank belief degrees information. On this basis, rank belief degrees information is taken as evidence and fusion degrees of two-sided matching are computed by fusing evidence. Furthermore, a matching result is obtained by an optimization model based on fusion degrees. Finally, numerical examples show the proposed approach is feasible and valid.(3) Evidence fusion methods of dynamic multi-attribute matching decision-making with uncertain information.In order to solve dynamic multi-attribute matching decision-making problem with uncertain preference ordinals, first, the related description of uncertain ordinal scores is presented. Then, the ordinal scores of the horizontal evaluation and vertical evaluation in both matching agents are taken as evidence, and the fusion degrees of two-sided matching are got by evidence combining. Furthermore, an optimization model is developed to obtain two-sided matching scheme. Finally, numerical examples show the proposed approach is feasible and valid.In order to solve dynamic multi-attribute matching decision-making problem with uncertain information, first, the comprehensive evaluation value of each attribute at all times is calculated. Then, the evaluation value is transformed into rank belief degrees information. On this basis, rank belief degrees information is taken as evidence and fusion degrees of two-sided matching are computed by fusing evidence. Furthermore, a two-sided matching result is obtained by an optimization model based on fusion degrees. Finally, numerical examples show the feasibility and validity of the proposed approach.