Ordered weighted utility distance operators and their applications in group decision-making

Abstract

In multiple attribute group decision-making (MAGDM), a consensus exists that the psychological factors of decision makers (DMs) generally influence their choice of optimal alternatives. To quantify well the influence of DMs’ risk attitudes on the group decision-making process, this paper develops a new approach to MAGDM by introducing DMs’ utility functions into the aggregation process. First, the ordered weighted utility distance (OWUD) operator is constructed by introducing DMs’ utility functions into the distance operator. As a novel operator, the OWUD operator not only satisfies both the basic features of distance measures and the desirable properties of aggregation operators, but also has some unique characteristics. Then, the linear risk tolerance (LRT) utility function is further used in the OWUD operator as the basic utility function, and a specific form of the OWUD operator, which is named as the ordered weighted-linear risk tolerance utility distance (OW-LRTUD) operator, is proposed. The OW-LRTUD operator can quantify well the influence of DMs’ risk attitudes on the group decision-making process. It also has an analytically tractable form and includes many well-known distance measures and aggregation operators, and thus can be applied to many different kinds of decision-making problems. Subsequently, to determine the weights of the OW-LRTUD operator, an extension of the maximum Bayesian entropy method is proposed by incorporating the prior known weight information and different risk attitudes of all individual DMs. An approach to MAGDM based on the OW-LRTUD operator and the proposed weight determination method is developed. An application for determining the optimal alternative in the investment selection is provided to show the feasibility, effectiveness and robustness of our approach in practice, and the corresponding sensitive analysis illustrates the influence of DMs’ risk attitudes on the group decision-making process.