Multi-criteria Based Three-Way Classifications with Game-Theoretic Rough Sets

摘要

Three-way classifications divide the universe of objects into three regions based on a given concept. Rough sets and its extensions provide effective ways to construct three-way classifications. When multiple criteria are involved to determine three-way classifications, the problem of determining three-way regions can be formulated as a typical multi-criteria decision making (MCDM) problem. In this paper, we use game-theoretic rough set model (GTRS) to solve and address the multi-criteria based three-way classifications constructed in the context of rough sets. GTRS implement competitive games amongst multiple criteria in order to obtain a compromise between criteria by finding an equilibrium of the games. Applying GTRS in MCDM consists of three stages, namely, competitive game formulation, repetition learning process, and decision making based on equilibria. The advantage of applying GTRS is twofold. GTRS do not require the predefined weights for criteria or compound decision objectives. GTRS are inherently suitable for a competitive environment in which the involved criteria maximize their own benefits and the payoff of each criterion is influenced by other's strategies.