Determining thresholds in three-way decisions with chi-square statistic

Abstract

In an evaluation function based three-way decisions model, a pair of thresholds divides a universal set into three regions called a trisection or tri-partition of the universe: a region consists of objects whose values are at or above one threshold, a region of objects whose values are at or below the other threshold, and a region of objects whose values are between the two thresholds. An optimization based method for determining the pair of thresholds is to minimize or maximize an objective function that quantifies the quality, cost, or benefit of a trisection. In this paper, we use the chi-square statistic to interpret and establish an objective function in the context of classification. The maximization of the chi-square statistic searches for a strong correlation between the trisection and the classification.