Measuring criteria weigths by means of dimension

Abstract

Measuring criteria weights in multicriteria decision making is a key issue in order to amalgamate information when reality is being described from several different points of view. In this paper we propose a method for evaluating those weights taking advantage of Dimension Theory, which allows the representation of the set of alternatives within a real space, provided that decision maker preferences satisfy certain consistency conditions. Such a representation allows a first information about possible underlying criteria in decision maker's mind. In particular, we propose to measure the importance of those underlying criteria by means of all possible representations associated to the dimension of the binary preference relations between criteria, each one being understood as a linear order of the set of alternatives.