Determining attribute weights for multiple attribute decision analysis with discriminating power in belief distributions

Attribute weight assignment plays an important role in multiple attribute decision analysis (MADA). When the performances of alternatives on each attribute are expressed by distributions instead of single values, how to use the differences among the performances to obtain attribute weights is an interesting but difficult issue. To address this issue, in this paper, we propose a method for obtaining attribute weights from discriminating power in belief distributions. With the consideration of the differences among the utilities of all assessment grades used to profile belief distributions, the dissimilarity based discriminating power, the standard deviation based discriminating power and the Gini's mean difference based discriminating power of the performances of all alternatives on each attribute are constructed to determine three sets of respective weights of attributes. They are convexly combined using three coefficients to generate integrated weights of attributes. To relieve the burden on a decision maker to provide precise values for the three coefficients, they are allowed to change between 0 and 1, as long as their sum is equal to 1. Under such constraints on the three coefficients, an optimization model is constructed to determine the minimum and maximum expected utilities of each alternative. From the expected utilities, all alternatives are then compared using Hurwicz rule with the provided optimism degree interval to generate solutions to MADA problems. The transitivity of the comparison outcomes among three alternatives under a given optimism degree interval is theoretically analyzed to guarantee the rationality of the outcomes. A focal form selection problem is investigated to demonstrate the applicability and validity of the proposed method.