Statistical interpretations of three-way decisions

Abstract

In an evaluation based model of three-way decisions, one constructs three regions, namely, the left, middle, and right regions based on an evaluation function and a pair of thresholds. This paper examines statistical interpretations for the construction of three regions. Such interpretations rely on an understanding that the middle region consists of normal or typical instances in a population, while two side regions consist of, abnormal or untypical instances. By using statistical information such as median, mean, percentile, and standard deviation, two interpretations are discussed. One is based on non-numeric values and the other is based on numeric values. For non-numeric values, median and percentile are used to construct three pair-wise disjoint regions. For numeric values, mean and standard deviation are used. The interpretations provide a solid statistical basis of three-way decisions for applications.