Fuzzy Rough Attribute Reduction Based on Fuzzy Implication Granularity Information

Fuzzy rough set model is a powerful tool for handling attribute reduction tasks for complex data. While the fuzzy rough set model commonly employs fuzzy information entropy to measure attribute uncertainty, utilizing fuzzy conditional information entropy for measuring attribute relationships presents a drawback due to its lack of monotonicity, impacting attribute reduction results. Furthermore, entropy computations involve numerous logarithmic function computations, resulting in a significant computational burden. Moreover, the results obtained from logarithmic functions are unbounded. To address these problems, this paper presents the concept of Fuzzy Implication Granularity Information (FIGI) for measuring attribute information. Additionally, we introduce several related generalizations, such as fuzzy conditional implication granularity information, fuzzy mutual implication granularity information, and fuzzy joint implication granularity information, aiming to measure the relationships between attributes. Notably, the introduced fuzzy conditional implication granularity information to measure the relationship between attributes demonstrates the desirable property of monotonicity. Crucially, all the metrics proposed in this paper are bounded, ensuring that computed values within the range of 0 to 1. Finally, we propose a forward greedy attribute reduction algorithm based on the monotonic fuzzy conditional implication granularity information (MFIGI), and the performance of our MFIGI algorithm was compared against six different attribute reduction algorithms using three classifiers across 15 different datasets, the experimental results demonstrate the excellence of our MFIGI algorithm.