THEORETICAL PERFORMANCE OF A MULTIVALUED RECOGNITION SYSTEM

A multivalued recognition system was formulated by the authors which h as the ability of discriminating the nonoverlapping, and overlapping a nd no-class (i.e., ambiguous/doubtful) regions and of analyzing the as sociated uncertainties by providing output decisions in four states, n amely, single, firstsecond, combined, and null choices. The single cho ices correspond to the nonoverlapping regions, whereas the overlapping regions are reflected by the first-second and combined choices. The n ull choices reflect the portions outside the pattern classes and/or th e portions of the pattern classes uncovered by the training samples. A theoretical analysis of these characteristics and of the performance of the recognition system has been provided in the present article. It has been shown theoretically that with the increase in the size of th e training samples, the estimates of the overlapping, nonoverlapping, and no-class regions tend to their actual sizes. All analytical findin gs have been substantiated with experimental results various situation s in one- and two-dimensional feature spaces. Bayes decision boundarie s are always found to lie within the combined choice region as provide d by the multivalued recognition system. The present investigation, in turn, establishes analytically the justification of providing multiva lued output decisions in four states for managing uncertainties arisin g from ambiguous regions.