Incomplete interval fuzzy preference relations and their applications

This paper investigates incomplete interval fuzzy preference relations. An additive consistency property of fuzzy preference relations proposed by Herrera-Viedma et al. (2004) is first extended to a more general case. This property is then generalized to interval fuzzy preference relations (IFPRs) based on additive transitivity. Subsequently, we examine how to characterize additive consistent IFPR. Using these new characterizations, we propose a method to construct an additive consistent IFPR from an acceptable incomplete IFPR comprising n-1 preference data and an estimation algorithm for an acceptable incomplete IFPR with more known elements. Numerical examples are provided to illustrate the effectiveness and practicality of the proposed solution procedure.