Representing and managing unbalanced multi-sets

Abstract

In Knowledge-Based Systems, experts should model human knowledge as faithful as possible to reality. In this way, it is essential to consider knowledge imperfection. Several approaches have dealt with this kind of data. The most known are fuzzy logic and multi-valued logic. These latter propose a linguistic modeling using linguistic terms that are uniformly distributed on a scale. However, in some cases, we need to assess qualitative aspects by means of variables using linguistic term sets which are not uniformly distributed. We have noticed, in the literature, that in the context of fuzzy logic many researchers have dealt with these term sets. However, it is not the case for multi-valued logic. Thereby, in our work, we aim to establish a methodology to represent and manage this kind of data in the context of multi-valued logic. Two aspects are treated. The first one concerns the representation of terms within an unbalanced multi-set. The second deals with the use of symbolic modifiers within such kind of imperfect knowledge.