Optimisation of Thresholds in Probabilistic Rough Sets with Artificial Bee Colony Algorithm

The Probabilistic Rough Sets (PRS) theory determines the certainty of an object's inclusion into a class, resulting in the division of the entire data set into three regions under a concept. These regions, namely the positive, negative and boundary regions, are generated using an evaluation function and threshold values. The threshold optimisation and the construction and interpretation of an evaluation function offer various methods in the background. Even though most of the methods in the PRS follow an iterative strategy, they lack a common framework, usually affecting the comparison and overall performance evaluation among these methods. This proposed work aims to minimise the uncertainty in three regions via optimising the thresholds using the Artificial Bee Colony (ABC) algorithm. The ABC algorithm is adapted to generate a common framework that results in different optimal pairs of thresholds with a minimum number of iterations. By considering the probabilistic information about an equivalence class structure, we compare the results obtained from the proposed approach with the state-of-the-art methods like Information-Theoretic Rough Sets, Game-Theoretic Rough sets and Genetic Algorithm-based optimisation. The results reveal that the proposed algorithm outperforms existing techniques and leads to a superior method for threshold optimisation in the PRS.