Coherence of fuzzy knowledge bases

Checking the coherence of a set of rules is an important step in the validation process of a knowledge base. Roughly speaking, a knowledge base is "potentially inconsistent", what is called "incoherent" here, if there exists a piece of input data which respects integrity constraints and leads to logical inconsistency when added to the knowledge base. This paper is devoted to the case of bases made of parallel fuzzy rules. It is shown that only implication-based rules (gradual rules and certainty rules) are sensitive to coherence problems. However, unlike conjunction-based rules, with which incoherence may be hidden, they allow one to design coherence checking procedures. Necessary and sufficient conditions that a set of parallel certainty (or gradual) rules has to satisfy in order to avoid inconsistency are given.