Preorder Information Based Attributes' Weights Learning in Multi-attribute Decision Making

Choquet integral, as an adequate aggregation operator, extends the weighted mean operator by considering interactions among attributes. Choquet integral has been widely used in many real multi-attribute decision making. Weights (fuzzy measures) of attribute sets directly affect the decision results in multi-attribute decision making. In this paper, we aim to propose an objective method based on granular computing for determining the weights of the attribute sets. To address this issue, we first analyze the implied preorder relations under four evaluation forms and construct the corresponding preorder granular structures. Then, we define fuzzy measure of an attribute set by the similarity degree between a special preorder pairs. Finally, we employ two numerical examples for illustrating the feasibility and effectiveness of the proposed method. It is deserved to point out that the weight of each attribute subset can be learned from a given data set by the proposed method, not but be given subjectively by the decision maker. This idea provides a new perspective for multi-attribute decision making.