Decision making with an interval-valued fuzzy preference relation and admissible orders

In this paper we analyze under which conditions we must use interval-valued fuzzy relations in decision making problems. We propose an algorithm to select the best alternative from a set of solutions which have been calculated with the nondominance algorithm using intervals and different linear orders among them. Based on the study made by Orlovsky in his work about nondominance, we study a characterization of weak transitive and 0.5-transitive interval-valued fuzzy relations, as well as the conditions under which transitivity is preserved by some operators on those relations. Next, we study the case of interval-valued reciprocal relations. In particular, we describe the preservation of reciprocity by different operators and analyze the transitivity properties for these interval-valued reciprocal relations. Finally, we propose to use, in the nondominance algorithm, linear interval orders generated by means of operators which preserve transitivity.

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