Two Approximation Models of Fuzzy Weight Vector from a Comparison Matrix

Abstract

In this study, our uncertain judgment on multiple items is denoted as a fuzzy weight vector. Its membership function is estimated from more than one interval weight vector. The interval weight vector is obtained from a crisp/interval comparison matrix by Interval Analytic Hierarchy Process (AHP). We redefine it as a closure of the crisp weight vectors which approximate the comparison matrix. The intuitively given comparison matrix is often imperfect so that there could be various approaches to approximate it. We propose two of them: upper and lower approximation models. The former is based on weight possibility and the weight vector with it includes the comparison matrix. The latter is based on comparison possibility and the comparison matrix with it includes the weight vector.