Symbolic Approximate Reasoning with Fuzzy and Multi-valued Knowledge

Knowledge-based systems have nearly become omnipresent in various sectors to facilitate decision-making. Their aim is to get close to human induction. For that, dealing imprecise knowledge is essential since human thinks imprecisely. The principal logics that allow manipulating this kind of knowledge in intelligent systems are fuzzy logic and multi-valued logic. Up to now, according to our knowledge, knowledge-based systems manage separately either fuzzy knowledge or multi-valued knowledge. However, modeling heterogeneous knowledge (fuzzy and multi-valued) in the same inference engine should ensure more flexibility and freedom to the user. In that context, our aim is to allow the use of fuzzy and multi-valued knowledge at once. We propose a new approach to convert fuzzy knowledge into symbolic knowledge by projecting fuzzy inputs over the x-axis that corresponds to the universe of discourse of fuzzy variable. In order to demonstrate its applicability, our proposal is tested within a rule-based system. A numerical example is then provided.