A game-theoretic sequential three-way decision using probabilistic rough sets and multiple levels of granularity

Abstract The sequential three-way decision accepts additional information at each level and makes more accurate definite decisions with less uncertainty. This process can also be extended to two-way classification with the finer-grained information level. However, both the decision process cost and decision result cost of the model must be considered for optimal performance. The proposed model adapts the game-theoretic approach to deal with the trade-off between the decision process cost and the decision result cost, and thereby balance the number of levels of the model. The time complexity, information level, and feature importance contribute to the process cost while evaluation metrics stand for the result cost. The model starts with reliable initial results by using the most significant features at the first level itself and follows an objective function-based method to determine threshold pairs at each level, which avoids relying on domain experts. Furthermore, if the process cost outweighs the result cost, the number of levels is adjusted accordingly. Using the experimental datasets, instances are classified at each level at the optimal threshold pairs; therefore the trisection is obtained with the highest precision/recall value. The obtained results prove that the proposed model outperforms existing models in terms of precision, recall, and time complexity with balanced decision costs. In summary, the proposed model is cost-efficient, interpretable, termination-aware, and result-oriented, ensuring effective and practical decision-making.