Determining Three-Way Decision Regions by Combining Gini Objective Functions and GTRS

Game-theoretic rough set model (GTRS) is a recent advancement in determining decision regions by formulating competition or cooperation between multiple measures of decision regions. Different competitions can be formulated with GTRS to gain optimal and balanced decision regions. In three-way decisions, there are some remaining issues where GTRS may be employed to reach a compromise between conflicting measures. When Gini coefficient is used to measure impurity of decision regions, Gini objective functions may be formulated to optimize impurities of multiple decision regions. We aim to examine the problem of minimizing the impurities of immediate and non-commitment decision regions simultaneously. In particular, we consider using GTRS to determine three-way decision regions by finding a solution to Gini objective functions. A compromise solution from various Pareto optimal strategies is obtained with GTRS. The game formulation, Pareto optimal strategies, Nash equilibrium of games, as well as iteration learning mechanism are investigated in detail. An example to demonstrate that compromise decision regions can be obtained by using GTRS to formulate competitions between decision regions is presented.