A new ranking method to decision making based on interval fuzzy preference relations

Interval fuzzy preference relations are useful and powerful means for decision makers (DM) to express their uncertainty of preference over criteria in the process of multi-criteria decision making. In this paper, we propose the necessary and sufficient condition for the interval fuzzy preference relation to be consistent and introduce a concise ranking formula for the preference relation. Moreover, some properties of interval weights are discussed in detail. Finally, an illustrative numerical example is furnished to demonstrate the applicability and effectiveness of the calculating method.