Comparison of Hyperbox Granular Computing Classification Algorithms by Positive Valuation Functions

Granular Computing (GrC) is a computing paradigm derived from the human congiton of the real world, by which different granularity spaces can be converted to each other. For GrC, we have to face two issues, such as the operation between two granules and inclusion relation between two granules. In the paper, we proposed the hyperbox granular computing classification algorithms based on the fuzzy inclusion relation between granules in terms of the different positive valuation functions. The proposed positive valuation functions keep the consistency of the partial order relation between two vectors in the vector space and the partial order relation between two hyperbox granules in the granule space. The fuzzy lattice is constructed by the hyperbox granule set and the fuzzy inclusion relation induced by the proposed positive valuation functions, and used to design the algorithms which realize the transformation from the training set to the sparse granule space. Experimental results on the benchmark data set show superiority of the proposed hyperbox granular computing classification algorithms.