On Classifying Mappings Induced by Granular Structures

In this work the subject of granular computing is pursued beyond the content of the previous paper [21]. We study here voting on a decision by granules of training objects, granules of decision rules, granules of granular reflections of training data, and granules of decision rules induced from granular reflections of training data. This approach can be perceived as a direct mapping of the training data on test ones which is induced by granulation of knowledge on the training data. Some encouraging results were already presented in [21], and here the subject is pursued systematically. Granules of knowledge are defined and computed according to a previously used scheme due to Polkowski in the framework of theory of rough inclusions. On the basis of presented results, one is justified in concluding that the presented methods offer a very good quality of classification, comparable fully with best results obtained by other rough set based methods, like templates, adaptive methods, hybrid methods etc.