关键词: 证据推理方法, TODIM, 信念分布, 分布式偏好关系

Abstract: Belief distributions and distributed preference relations as two types of information description in the evidential reasoning method have been widely applied to complex decision making problems. Due to the complexity of decision making problems and limited cognitive capability of decision makers, the existing decision making methods are not enough to satisfy the requirement for information description and preference characterization for decision makers in complex decision making situations. It is necessary to develop a new decision making method that can be used to cope with heterogeneous decision making problems including belief distributions and distributed preference relations. To solve this problem, some researchers proposed a heterogeneous evidential reasoning decision making method. This method applies an indirect transformation way of heterogeneous information to transform belief distributions to distributed preference relations. However, in the transformation process, there are two drawbacks. One is that the process is irreversible. The other is that the process will result in the information distortion and loss. To overcome these drawbacks, this paper proposes a heterogeneous evidential reasoning decision making method based on an acronym in Portuguese for Interactive and Multicriteria Decision Making (TODIM) to solve the heterogeneous decision making problem with belief distributions and distributed preference relations.
The definitions of belief distributions and distributed preference relations are first introduced as the basic concepts in this paper. The interval utility of belief distribution and the interval score of distributed preference relation are also introduced. Then, the distance measure between belief distributions with the consideration of utility variance is introduced. By referring to the distance measure between belief distributions, the distance measure between distributed preference relations is defined and then the related coefficient of distributed preference relations is also defined to develop the matching coefficient of distributed preference relations. The matching coefficient of distributed preference relations is used to characterize the matching degree between the difference of belief distributions and the distributed preference relations transformed from belief distributions. The properties of the matching coefficient are analyzed and verified. The next step is to calculate attribute weights. After analyzing the existing studies of determining attribute weights, the existing methods have been divided into three categories, which are subjective methods, objective methods and hybrid methods. Different methods have their different advantages and disadvantages. By using distance measure of belief distributions and the matching coefficient of distributed preference relations, the hybrid method of determining attribute weights is proposed in the context of heterogeneous decision information. After that, a heterogeneous multiple attribute decision making problem is modelled by using belief distributions and distributed preference relations simultaneously. TODIM method is then introduced to aggregate the heterogeneous decision making information. Hereinto, the individual dominance degrees of two alternatives with belief distributions and distributed preference relations are defined respectively to generate the overall dominance degree of each alternative. The higher the overall dominance degree of each alternative is, the better the alternative will be. By considering the loss aversion of decision makers, a parameter is designed in TODIM method to portray the loss aversion. When the decision maker has different risk attitude, the parameter will have the different values. According to the idea of alternative reliability, three situations where the decision maker may have the three different risk attitudes are considered to construct two optimization models to determine the rational parameter of TODIM method. Then, a heterogeneous decision making solution will be generated. The process of the heterogeneous evidential reasoning decision making method is further demonstrated.
The proposed method is applied to solve the problem with selecting appropriate members for the aerospace research and development team in an academy of aerospace technology to verify its effectiveness and applicability. The decision matrix including belief distributions on two attributes and distributed preference relations on four attributes is constructed. By using the proposed method, the overall dominance degree of each alternative is calculated to select four members to build a new aerospace research and development team. In the future study, the proposed method will be applied to solve multiple attribute group decision making problems with heterogeneous information.

Key words: evidential reasoning method, TODIM, belief distributions, distributed preference relation