Learning Decision Rules from Similarity Based Rough Approximations

Decision rules induced from lower approximations of decision classes are certain in the sense of covering the objects which certainly belong to the corresponding decision classes. The definition of rough approximations is originally based on an indiscernibility relation in the set of objects. The indiscernibility relation requiring strict equality of attribute values for the objects being compared is often restrictive in practical applications. This is why, we are proposing to use a more natural similarity relation to define rough approximation of decision classes. The only requirement imposed on this relation is reflexivity. The similarity relation is being derived from data. Decision rules induced from lower approximations of decision classes based on similarity are not only certain but robust in the sense of covering objects which belong to the corresponding decision classes and are not similar to objects from outside. The approach is illustrated by a simple example and it is validated on a set of benchmark examples.

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