A synthesis of fuzzy rule-based system verification

Abstract

The verification of fuzzy rule bases for anomalies has received increasing attention these last few years. Many different approaches have been suggested and many are still under investigation. In this paper, we give a synthesis of methods proposed in literature that try to extend the verification of classical rule bases to the case of fuzzy knowledge modeling, without needing a set of representative input. Within this area of fuzzy validation and verification (V&V) we identify two dual lines of thought leading to what is identified as static and dynamic anomaly detection methods. Static anomaly detection essentially tries to use similarity, affinity or matching measures to identify anomalies within a fuzzy rule base. It is assumed that the detection methods can be the same as those used in a non-fuzzy environment, except that the former measures indicate the degree of matching of two fuzzy expressions. Dynamic anomaly detection starts from the basic idea that any anomaly within a knowledge representation formalism, i.e. fuzzy if–then rules, can be identified by performing a dynamic analysis of the knowledge system, even without providing special input to the system. By imposing a constraint on the results of inference for an anomaly not to occur, one creates definitions of the anomalies that can only be verified if the inference process, and thereby the fuzzy inference operator is involved in the analysis. The major outcome of the confrontation between both approaches is that their results, stated in terms of necessary and/or sufficient conditions for anomaly detection within a particular situation, are difficult to reconcile. The duality between approaches seems to have translated into a duality in results. This article addresses precisely this issue by presenting a theoretical framework which enables us to effectively evaluate the results of both static and dynamic verification theories.