Multiple Attribute Decision Making Based on Preference Orderings and Interval Numbers

This paper focuses on the multiple attribute decision making problems with the attribute values being preference orderings and interval numbers evaluations. For the attributes with preference orderings evaluations, the fuzzy preference relation between the alternatives are calculated and the their rankings values are further normalized by measuring their relative distances to the ideal point; For the attributes with interval number evaluations, by calculating the relative distances between the interval evaluations and their negative ideal point, interval evaluations are normalized into single point ones. The decision matrix is thus normalized, based on which a mathematical programming model is set up to figure out the attribute weights with the overall values of the alternatives being the goals. Therefore, the overall values of the alternatives are obtained, and therefore the alternatives are ranked. An example is used to illustrate the proposed approach, which is suitable for extensive applications in the end.