Deriving priority vector from pairwise comparisons matrix with fuzzy elements

Abstract

This paper deals with the pairwise comparisons matrix with fuzzy elements (FPCM). Fuzzy elements of the FPCM are applied whenever the decision maker is not sure about the value of his/her evaluation of the relative importance of elements in question. We investigate the pairwise comparisons matrices with elements from abelian linearly ordered group (alo-group) over a real interval, introduce the concept of reciprocity and (weak) consistency of FPCMs and derive their properties. Such an approach unifies several approaches known from the literature. Moreover, we propose a new general procedure for deriving the priority vector from the FPCM enabling ranking or rating a given set of alternatives.