Investigating Decision Making With Game-Theoretic Rough Sets

Abstract

Rough set theory and game theory provide two approaches for analyzing and assisting decision making. Rough set theory provides the ability to make decisions with incomplete and insuffcient information. On the other hand, game theory concerns with decision making where an outcome depends on interaction between two or more decision making criteria. A fundamental challenge in the application of rough sets is how to reduce the uncertain boundary region by configuring the parameters or thresholds defining the region bounds. The game-theoretic rough set (GTRS) model provides a game-theoretic perspective for setting and computing these thresholds. The conventional rough set model in rough set theory is intolerant to classification errors in the positive and negative regions which limit its practical applicability. The probabilistic rough sets allow for some degree of errors in order to include more objects in the positive and negative regions, thereby improving the applicability or generality. A pair of thresholds control the tradeoff between accuracy and generality. The estimation or computation of thresholds is one of the major issues in the probabilistic rough sets. The GTRS model aims to estimate balanced and optimized thresholds when contradictive measures are present. This dissertation further explores di erent aspects of the GTRS model by focusing on two issues of probabilistic rough sets, namely, the determination and interpretation of thresholds, and the application or utilization of decision regions based on the thresholds to assist in decision making. The first issue has two parts, i.e., the determination of thresholds and the interpretation of thresholds. The determination of thresholds is examined by setting up games for trading-off between different criteria employed for evaluating rough sets. The GTRS model aims to provide a tradeoff solution that can be used to obtain cost effective thresholds in the game environment. In particular, we introduce and examine two games including a game for determining a balance between uncertainties of the probabilistic rough set regions and another game for obtaining a tradeoff between the properties of accuracy and generality. The interpretation of thresholds is addressed by exploring the relationship between equilibria or game solutions and the determined thresholds. According to the proposed interpretation, an equilibrium is defined in terms of a pair of thresholds such that no player has any unilateral incentive to change these thresholds within the game. The relationship between different game constructs and the thresholds are also explained. The second issue is the utilization of decision regions to assist and support decision making. In particular, the estimated thresholds with GTRS can be used to obtain the three rough set regions which are utilized in applications for providing decision support in the form of three-way decision rules. We provide an extensive study of two applications, i.e., Web-based medical decision support systems and recommender systems, where the use of GTRS based thresholds can be useful for supporting and assisting in decision making. It is hoped that the research in this dissertation would lead to a better understanding of the GTRS model thereby improving its future usability and applications.