Linguistic Modifiers with Unbalanced Term Sets in Multi-valued Logic

Modeling human knowledge by machines should be as faithful as possible to reality. Therefore, it is imperative to take account of inaccuracies and uncertainties in this knowledge. This problem has been dealt with through different approaches. The most common approaches are fuzzy logic and multi-valued logic. These two logics propose a linguistic term modeling. Generally, problems modeling qualitative aspect use linguistic variables assessed in linguistic terms that are uniformly distributed on the scale. However, in many cases, linguistic information needs to be defined by unbalanced term sets whose terms are not uniformly and/or not symmetrically distributed. In the literature, it is shown that many researchers have dealt with these term sets in the context of fuzzy logic. Thereby, in our work, we introduce a new approach to represent and treat such term sets in the context of multi-valued logic. First, we propose an algorithm that allows representing terms within an unbalanced set. Then, we describe a second algorithm that permits the use of linguistic modifiers within unbalanced multi-sets.