FL-GrCCA: A granular computing classification algorithm based on fuzzy lattices

Defining a relation between granules and computing ever-changing granules are two important issues in granular computing. In view of this, this work proposes a partial order relation and lattice computing, respectively, for dealing with the aforementioned issues. A fuzzy lattice granular computing classification algorithm, or FL-GrCCA for short, is proposed here in the framework of fuzzy lattices. Algorithm FL-GrCCA computes a fuzzy inclusion relation between granules by using an inclusion measure function based on both a nonlinear positive valuation function, namely arctan, and an isomorphic mapping between lattices. Changeable classification granules are computed with a dilation operator using, conditionally, both the fuzzy inclusion relation between two granules and the size of a dilated granule. We compare the performance of FL-GrCCA with the performance of popular classification algorithms, including support vector machines (SVMs) and the fuzzy lattice reasoning (FLR) classifier, for a number of two-class problems and multi-class problems. Our computational experiments showed that FL-GrCCA can both speed up training and achieve comparable generalization performance.