Analyzing discretizations of continuous attributes given a monotonic discrimination function

This article addresses the problem of analyzing existing discretizations of continuous attributes with regard to their redundancy and minimality properties. The research was inspired by the increasing number of heuristic algorithms created for generating the discretizations using various methodologies, and apparent lack of any direct techniques for examining the solutions obtained as far as their basic properties, e.g., the redundancy, are concerned. The proposed method of analysis fills this gap by providing a test for redundancy and enabling for a controlled reduction of the discretization's size within specified limits. Rough set theory techniques are used as the basic tools in this method. Exemplary results of discretization analyses for some known real-life data sets are presented for illustration.