Research On The Method And Application Of Multi-attribute Decision Making Based On Two-dimensional Belief Function

In modern decision science,multi-attribute decision-making(MADM)has become an important research field.In real life work,sometimes it is impossible to give a clear decision value because of the decision-making environment or the decision-maker's own academic background and life experience,which causes a lot of uncertainty in the decision-making.Uncertain environment brings many challenges to multi-attribute decision-making,such as the description of uncertain information,the processing of uncertain information,and the choice of decision-making methods under uncertain information.Many theories and methods have been used to solve these problems.Among them,D-S evidence theory has been widely studied and applied in various fields because of its better ability to deal with uncertain information.But D-S evidence theory also has its limitations and deficiencies,such as counter-intuitive results when dealing with highly conflicting data,lack of measurement of data reliability,and so on.Due to the prevalence of uncertain information,unreliable information will have a great impact on decision-making.In 2019,Deng et al.proposed a two-dimensional belief function theory based on evidence theory.It is composed of a pair of ordered basic probability distributions.The latter is a deterministic expression of the former.It not only inherits the advantages of basic probability distribution,but also Experts' evaluation of information reliability has also been added,and a special combination of two-dimensional belief functions has been defined,which extends the classic discounting method of basic probability distribution to a certain extent,and expresses uncertain information more abundantly and flexibly.Part of the conflict of evidence can also be resolved.This article is mainly to expand and supplement the two-dimensional belief function based on the background of evidence theory,as well as the multi-attribute decision-making method and application research based on this.The main innovations of this article are as follows:(1)On the basis of the two-dimensional belief function,an objective reliability evaluation based on the measurement of the divergence of the belief function is added,and it is combined with the reliability evaluation of experts to process uncertain information,and an extended two-dimensional belief function is proposed.And apply it to decision-making processes such as target identification,conflict management,and software production.(2)Based on the intuitive evidence set and the two-dimensional belief function,the intuitive two-dimensional belief function is proposed,which combines the advantages of the intuitive evidence set and the two-dimensional belief function to enhance the ability to describe uncertain information and the reliability of uncertain information assessment ability.Based on the idea of intuitionistic fuzzy sets,the weights of experts and attributes are calculated through intuitionistic fuzzy entropy,and then the weight-average evidence combination method is used to fuse multi-source information.Finally,the proposed method is used in a multi-attribute decision-making method.(3)The weight TOPSIS based on the divergence of the belief function is extended to the two-dimensional belief function environment to solve the problem of failure mode and effect analysis.