Weight determination based on priority preference in multiple attribute decision making with interval numbers

Determining the attribute weights is an important process in multiple attribute decision making. Many methods have been proposed for determining the attribute weights, either by making use of decision makers´ subjective preference judgments, or by utilizing the objective information of the alternatives, i.e., the decision matrix. However, in uncertain decision environment, sometimes, interval numbers are employed to model the multiple attribute decision making problems. The overall values of alternatives are also interval values, which makes it difficult to find strict preference priority relationships between alternatives when the interval overlaps happen. Thus, there exist superiority possibilities between the alternatives when overlapping happens. Under this circumstance, how to determine the attribute weights based on the interval decision matrix and the preference priority relationships with superiority possibility among the alternatives, is a new problem. Therefore, a new programming model is proposed and illustrated by an example in this study.