Interval evaluation by AHP with rough set concept

Abstract

In AHP, there exists the problem of pair-wise consistency where evaluations by pair-wise comparison are presented with crisp value. We propose the interval AHP model with interval data reflecting Rough Set concept. The proposed models are formulated for analyzing interval data with two concepts (necessity and possibility). According to necessity and possibility concepts, we obtain upper and lower evaluation models, respectively. Furthermore, even if crisp data in AHP are given, it is illustrated that crisp data should be transformed into interval data by using the transitive law. Numerical examples are shown to illustrate the interval AHP models reflecting the uncertainty of evaluations in nature.