Construction of Interval-Valued Fuzzy Preference Relations Using Ignorance Functions: Interval-Valued Non Dominance Criterion

In this work we present a construction method for interval-valued fuzzy preference relations from a fuzzy preference relation and the representation of the lack of knowledge or ignorance that experts suffer when they define the membership values of the elements of that fuzzy preference relation. We also prove that, with this construction method, we obtain membership intervals for an element which length is equal to the ignorance associated with that element. We then propose a generalization of Orlovsky's non dominance method to solve decision making problems using interval-valued fuzzy preference relations.