Modelling a linguistic variable as a hierarchical family of partitions induced by an indistinguishability operator

Abstract

This work shows a method to obtain a hierarchy of partitions on the universe [0,1] in such a way that each of them is compatible with a refinement of Lukasiewicz indistinguishability operator. The classes of the partition at a given level present a relation of antonymy between them. Moreover, the partition at a certain level can be seen as the refinement of a previous level by means of a class of linguistic modifiers. Due to this fact, they seem appropriate for modeling linguistic labels of a linguistic variable. The associated indistinguishability operators show the increasing granularity when the number of classes rises up.