Tolerance rough sets for pattern classification using multiple grey single-layer perceptrons

Tolerance rough sets (TRSs) can operate effectively on continuous attributes for pattern classification. The formulation of a similarity measure plays an important role for TRSs. The existence of certain relationships between any two patterns motivated us to use grey relational analysis (GRA) to implement a similarity measure on the basis of grey single-layer perceptrons (GSLPs). Additive and nonadditive GSLPs can perform additive and nonadditive versions of GRA, respectively. This paper contributes to use a one-class-in-one-network structure to construct the additive/nonadditive GSLP-based TRS for pattern classification by devoting each GSLP to one class. A GSLP-based tolerance class for each pattern can be generated by measuring the similarity for the output from the network. To yield a high classification performance of the proposed TRS-based classifier, a genetic-algorithm-based learning algorithm was designed to determine parameter specifications of the proposed classifier. Experimental results demonstrate that the test results of the proposed nonadditive classifier are better than, or comparable to, those of other known rough-set-based classification methods.