Fuzzy lattice neural network (FLNN): a hybrid model for learning

This paper proposes two hierarchical schemes for learning, one for clustering and the other for classification problems. Both schemes can be implemented on a fuzzy lattice neural network (FLNN) architecture, to be introduced herein. The corresponding two learning models draw on adaptive resonance theory (ART) and min-max neurocomputing principles but their application domain is a mathematical lattice. Therefore they can handle more general types of data in addition to N-dimensional vectors. The FLNN neural model stems from a cross-fertilization of lattice theory and fuzzy set theory. Hence a novel theoretical foundation is introduced in this paper, that is the framework of fuzzy lattices or FL-framework, based on the concepts fuzzy lattice and inclusion measure. Sufficient conditions for the existence of an inclusion measure in a mathematical lattice are shown. The performance of the two FLNN schemes, that is for clustering and for classification, compares quite well with other methods and it is demonstrated by examples on various data sets including several benchmark data sets.