Sensitivity analysis of fuzzy rule-based classification systems by means of the Lipschitz condition

Abstract

The fuzzy rule-based classifier can be taken as a function that assigns to a point from the feature space a class, or a class with an association degree. Under this assumption, the robustness of fuzzy rule-based classifiers is investigated by means of the Lipschitz condition. The Lipschitz continuity of fuzzy sets, fuzzy rules and whole fuzzy rule-based classifiers is examined for multi-polar outputs, extended multi-polar outputs and outputs in the form of a class. Related performance of a fuzzy rule-based classifier is also discussed. All studied concepts are shown on an exemplar fuzzy rule-based classifier.