A bipolar three-way decision model and its application in analyzing incomplete data

Abstract

The theory of three-way decision has contributed to data science in many topics, such as three-way classification, three-way clustering, and three-way feature selection. Most three-way decision models are formulated based on evaluation functions that commonly consider two opposite aspects of positive and negative, alliance and conflict, etc. This idea coincides with the concept of bipolarity, which studies the two opposite poles of positive and negative. However, the connections between bipolarity and three-way decision models have not been well investigated, despite the fact that they share many common features. Therefore, this work explores their relationships and proposes a new bipolar three-way decision model. Firstly, we examine the connections between the polarity theory, including the concepts of unipolarity and bipolarity, and decision models, including the two-way and three-way decision models. The examination suggests a lack of a three-way decision model corresponding to certain types of bipolarity. Thus, secondly, we propose a new bipolar three-way decision model 3WD-(ep,en)2, which considers a pair of a positive evaluation function ep and a negative evaluation function en and applies a pair of thresholds on each function. Finally, we illustrate the usefulness and effectiveness of 3WD-(ep,en)2 in data science through its application in analyzing incomplete data. In particular, we present a computational formulation based on similarity classes and a conceptual formulation based on a conjunctive description language. The two formulations together provide a multi-view understanding of the approach.