Game theoretic approach to shadowed sets: A three-way tradeoff perspective

Three-way approximations can be constructed by shadowed sets based on a pair of thresholds. The determination and interpretation of the thresholds is one of the key issues for applying three-way approximations. We apply a principle of tradeoff with games in order to determine the thresholds of three-way approximations in the shadowed set context. The changes of the elevation and reduction errors with the alteration of thresholds are examined and analyzed. The proposed game-theoretic shadowed sets (GTSS) aim to determine the thresholds of three-way approximations according to a principle of tradeoff with games. GTSS employ game theoretic approaches to formulate games between the elevation and reduction errors. A repetition learning mechanism is adopted to gradually reach balanced threshold pairs by repeatedly formulating games and finding the equilibria between the errors. The shadowed set based three-way approximations defined by the resulting thresholds represent a tradeoff between the elevation and reduction errors. Feasibility study and effectiveness analysis of GTSS is conducted with an experimental data set. (C) 2018 Elsevier Inc. All rights reserved.