Categorizing classes of signals by means of fuzzy gradual rules

This paper presents an approach to the approximate description of univariate real-valued functions in terms of precise or imprecise reference points and interpolation between these points. It is achieved by means of gradual rules which express that the closer the variable to the abscissa of a reference point, the closer the value of the function to the ordinate of this reference point. Gradual rules enable us to specify sophisticated gauges, under the form of connected areas, inside of which the function belonging to the class under consideration should remain. This provides a simple and efficient tool for categorizing signals. This tool can be further improved by making the gauge flexible by means of fuzzy gradual rules. This is illustrated on a benchmark example.