Construction of interval-valued fuzzy preference relations from ignorance functions and fuzzy preference relations. Application to decision making

This paper presents a method to construct an interval-valued fuzzy set from a fuzzy set and the representation of the lack of knowledge or ignorance that experts are subject to when they define the membership values of the elements to that fuzzy set. With this construction method, it is proved that membership intervals of equal length to the ignorance associated to the elements are obtained when the product t-norm and the probabilistic sum t-conorm are used. The construction method is applied to build interval-valued fuzzy preference relations (IVPRs) from given fuzzy preference relations (FRs). Afterwards, a general algorithm to solve decision making problems using IVFRs is proposed. The decision making algorithm implements different selection processes of alternatives where the order used to choose alternatives is a key factor. For this reason, different admissible orders between intervals are analysed. Finally, OWA operators with interval weights are analysed and a method to obtain those weights from real-valued weights is proposed.