On The Validation of Fuzzy Knowledge Bases

Abstract

Roughly speaking, a knowledge base is “potentially inconsistent” or incoherent if there exists a piece of input data which respects integrity constraints and which leads to inconsistency when added to the knowledge base. In the paper we use the framework of possibility theory in order to discuss this problem for fuzzy knowledge bases. More particularly we consider the case where such bases are made of parallel fuzzy rules. There exist several kinds of fuzzy rules: certainty rules, gradual rules, possibility rules. For each kind, the problem of “potential consistency” appears to be different. Only certainty and gradual rules pose serious coherence problems. In each case we caracterize what conditions parallel rules have to satisfy in order to avoid inconsistency problem with input facts. The expression of a fuzzy integrity constraint in terms of impossibility qualification is discussed. The problem of redundancy, which is also of interest for fuzzy knowledge base validation, is briefly addressed for certainty and gradual rules.