Theoretical performance of a multivalued recognition system

A multivalued recognition system was formulated by the authors which has the ability of discriminating the nonoverlapping, and overlapping and no-class ( ambiguous/doubtful) regions and of analyzing the associated uncertainties by providing output decisions in four states, namely, single, first-second, combined, and null choices. The single choices correspond to the nonoverlapping regions, whereas the overlapping regions are reflected by the first-second and combined choices. The null choices reflect the portions outside the pattern classes and/or the portions of the pattern classes uncovered by the training samples. A theoretical analysis of these characteristics and of the performance of the recognition system is provided. It is shown theoretically that with the increase in the size of the training samples, the estimates of the overlapping, nonoverlapping, and no-class regions tend to their actual sizes. All analytical findings have been substantiated with experimental results various situations in one and two-dimensional feature spaces. Bayes decision boundaries are always found to lie within the combined choice region as provided by the multivalued recognition system. The present investigation, in turn, establishes analytically the justification of providing multivalued output decisions in four states for managing uncertainties arising from ambiguous regions