Abstract: In the face of some complex multiple-attribute decision-making problems, the decision maker prefers to give linguistic evaluation information such as good, medium, bad, et al, and therefore linguistic multiple-attribute decision-making problem occurs. Linguistic multiple-attribute decision-making problem can be seen everywhere in real life, and has attracted considerable attention from domestic and overseas experts and scholars in recent years. However, so far the linguistic multiple-attribute decision-making methods are mostly based on expected utility theory, and do not consider the influence relationships among indexes. To overcome these defects, a new linguistic multiple-attribute decision-making method that combines the regret theory, Decision Making Trial and Evaluation Laboratory (DEMATEL) is proposed, in which the decision maker’s regret aversion behavior and the influence relationships among indexes are considered. Firstly, a linguistic regret-rejoice function is defined on the base of the regret theory and the computational formula of perceived utility value is given. Secondly, the index weights based on linguistic DEMATEL are calculated through analyzing the influence relationships among indexes, and the index weights based on water-filling theory are calculated through a programming model that is constructed by the maximum total capacity of index, then the comprehensive perceived utility value is obtained, through which we can rank the alternatives. Finally, two examples are used to illustrate the feasibility and validity of the proposed method. The results show that this method is more practical and reliable as it considers the decision maker’s psychological behavior and the influence relationships among indexes. This paper expands the study of the traditional linguistic multiple-attribute decision-making method, and provides an important reference and guidance for solving linguistic multiple-attribute decision-making problem.

Key words: multiple attribute decision making, regret theory, decision making trial and evaluation laboratory, perceived utility, water-filling theory