Determining Attribute Weights Based on Heterogeneous Discriminating Power and Solution Reliability in Evidential Reasoning Approach

In multiple attribute decision analysis (MADA), the determination of attribute weights by using discriminating power (DCP) has become an important research topic. However, the reliability of a solution, which is an important factor in improving decision quality, has not been considered in existing studies on determining attribute weights with DCP. To address this, a method is proposed to objectively determine attribute weights with belief distributions (BDs) by considering three types of heterogeneous DCP (HDCP) and high solution reliability. The three types of HDCP in BDs are constructed to generate three sets of attribute weights in terms of entropy, deviation maximization and criteria importance through intercriteria correlation. The difference of belief degrees on grades and variation of the ordered preference intensity of grades are simultaneously considered in the HDCP. Three rules are proposed based on the majority principle to deal with possible conflicts among the three sets of attribute weights. By incorporating the three rules as constraints, a mixed-integer optimization model with the aim of maximizing the solution reliability is constructed to generate an integrated set of attribute weights. The maximum solution reliability will guarantee that the generated solution is satisfactory for the decision maker. Based on the integrated set of attribute weights, a pair of optimization models is further constructed on the condition that the solution reliability is the largest to determine the minimal and maximal expected utilities of the given alternatives, which will be further applied to generate a solution to the MADA problem. A strategic project selection problem is investigated using the proposed method to verify its applicability and validity.