As a foundational analytical tool, the discernibility matrix plays a pivotal role in the systematic reduction of knowledge in rough set-based systems. Recent advancements in rough set theory have witnessed the proliferation of discernibility matrix-based knowledge reduction algorithms, with notable applications in classical, neighborhood, covering, and fuzzy rough set models. However, the quadratic growth of the discernibility matrix’s complexity (relative to domain size) imposes fundamental scalability limits, rendering it inefficient for real-world applications with massive datasets. To address this issue, we introduced a discernibility hashing strategy to limit the growth scale of the discernibility attributes and proposed a feature selection algorithm via discernibility hash based on rough set theory. First, on the premise of keeping the information of the original discernibility matrix unchanged, the method maps the discernibility attribute set of all objects to the storage unit through a hash function and records the number of collisions to construct a discernibility hash. By using this mapping, the two-dimensional matrix space can be reduced to a one-dimensional hash space, which greatly removes invalid and redundant elements. Secondly, based on the discernibility hash, an efficient knowledge reduction algorithm is proposed. The algorithm avoids invalid and redundant element attribute sets to participate in the knowledge reduction process and improves the efficiency of the algorithm. Finally, the experimental results show that the method is superior to the discernibility matrix method in terms of storage space and running time.

As a foundational analytical tool, the discernibility matrix plays a pivotal role in the systematic reduction of knowledge in rough set-based systems. ‌Recent advancements in rough set theory have witnessed the proliferation of discernibility matrix-based knowledge reduction algorithms, with notable applications in classical, neighborhood, covering, and fuzzy rough set models. However, the quadratic growth of the discernibility matrix’s complexity (relative to domain size) imposes fundamental scalability limits, rendering it inefficient for real-world applications with massive datasets. To address this issue, we introduced a discernibility hashing strategy to limit the growth scale of the discernibility attribute sets, and propose a feature selection algorithm via discernibility hash based on rough set theory. First, on the premise of keeping the information of the original discernibility matrix unchanged, the method maps the discernibility attribute set of all objects to the storage unit through a hash function and records the number of collisions to construct a discernibility hash. By using this mapping, the two-dimensional matrix space can be reduced to a one-dimensional hash space, which greatly removes invalid and redundant elements. Secondly, based on the discernibility hash, an efficient knowledge reduction algorithm is proposed. The algorithm avoids invalid and redundant elements attribute sets to participate in the knowledge reduction process, and improves the efficiency of the algorithm. Finally, the experimental results show that the method is superior to the discernibility matrix method in terms of storage space and running time.

Attribute reduction is a fundamental problem in rough set theory that seeks a minimal subset of condition attributes that preserve the discernibility capability of the original decision system. Traditional heuristic methods—greedy forward selection and backward elimination—suffer from two critical deficiencies: the absence of principled attribute-ranking criteria (which leads to over- or under-selection) and the omission of statistical discriminability from the search process. To address these issues, this paper presents MFDRRS, a hybrid framework that integrates three complementary strategies: (1) a Fisher discriminant ratio (FDR) evaluation of the attribute discriminability based on the between- and within-class scatter; (2) FDR-based filtering to select statistically significant candidate attributes; and (3) greedy forward selection guided by the rough-set dependency degree, enhanced with an FDR-driven termination criterion. FDR computation quantifies the discriminative power of individual attributes, thereby facilitating the selection of an optimally discriminative candidate subset. Since the traditional FDR is defined for continuous features, we adapted the continuous-domain FDR to nominal data by proposing a modified Fisher discriminant ratio (MFDR). The MFDR first maps nominal attributes via one-hot encoding and then computes the between-class and within-class scatter matrices. Evaluated on synthetic and real-world UCI datasets against six baselines—classical rough-set greedy forward/backward selection, exhaustive search, MI ranking, MaxRelevance, and JMI—the proposed method achieved more compact reductions with fewer attributes, maintained competitive dependency degrees, and avoided the over-selection characteristic of classical backward elimination.

Attribute reduction is a fundamental problem in rough set theory that seeks a minimal subset of condition attributes preserving the discernibility capability of the original decision system. Traditional heuristic methods—greedy forward selection and backward elimination—suffer from two critical deficiencies: the absence of principled attribute-ranking criteria (which leads to over- or under-selection) and the omission of statistical discriminability from the search process. To address these issues, this paper presents MFDRRS, a hybrid framework that integrates three complementary strategies: (1) Fisher discriminant ratio (FDR) evaluation of attribute discriminability based on between- and within-class scatter; (2) FDR-based filtering to select statistically significant candidate attributes; and (3) greedy forward selection guided by the rough-set dependency degree, enhanced with an FDR-driven termination criterion. FDR computation quantifies the discriminative power of individual attributes, thereby facilitating the selection of an optimally discriminative candidate subset. Since the traditional FDR is defined for continuous features, we adapt the continuous-domain FDR to nominal data by proposing a modified Fisher discriminant ratio (MFDR). The MFDR first maps nominal attributes via one-hot encoding and then computes the between-class and within-class scatter matrices. The subsequent FDR-filtering and rough-set dependency analysis guarantee the optimality of the selected attribute subset. Evaluated on synthetic and real-world UCI datasets against six baselines—classical rough-set greedy forward/backward selection, exhaustive search, MI ranking, MaxRelevance, and JMI—the proposed method achieves more compact reductions with fewer attributes, maintains competitive dependency degrees, and avoids the over-selection characteristic of classical backward elimination.