Affiliations: Department of Computer Science, University of Regina, Regina, Saskatchewan S4S 0A2, Canada. {deng200x, yyao}@cs.uregina.ca
Note: [] This work is partially supported by a discovery grant from NSERC Canada. This paper is an extended version of a conference paper [2] published in RSKT 2012. The authors thank reviewers for their constructive comments. Address for correspondence: Department of Computer Science, University of Regina, Regina, Saskatchewan, S4S 0A2, Canada
Abstract: In situations where available information or evidence is incomplete or uncertain, probabilistic two-way decisions/classifications with a single threshold on probabilities for making either an acceptance or a rejection decision may be inappropriate. With the introduction of a third non-commitment option, probabilistic three-way decisions use a pair of thresholds and provide an effective and practical decision-making strategy. This paper presents a multifaceted analysis of probabilistic three-way decisions. By identifying an inadequacy of two-way decisions with respect to controlling the levels of various decision errors, we examine the motivations and advantages of three-way decisions. We present a general framework for computing the required thresholds of a three-way decision model as an optimization problem. We investigate two special cases, one is a decision-theoretic rough set model and the other is an information-theoretic rough set model. Finally, we propose a heuristic algorithm for finding the required thresholds.
