A synthesis of fuzzy rule-based system verification

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 V & V We identify two dual lines of thought respectively 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 formerly mentioned 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.c. 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. 1. Introduction The importance of assuring the reliability of knowledge based systems (KBS) need not be emphasized. In that sense it should not come as a surprise that verification of the knowledge base (KB) within a KBS is object of extensive research. Until recently, most of the results have been achieved in the field of classical knowledge based systems [7], [9], [10], [12]-[14], mainly because V & V has received little attention in systems based on non-classical formalisms. Renewed interest in the modeling power of Lotfi Zadeh's fuzzy set theory [29]-[30] and the possibility it provides in reasoning with vague concepts seem to …