Generalized quotient approximation spaces based on fuzzy β-coverings and their applications in feature selection

Quotient space theory provides an effective mechanism for transforming fine-grained problem representations into coarse-grained ones, which is beneficial for knowledge reduction and decision analysis in complex systems. However, classical quotient space models rely heavily on equivalence relations, making them unsuitable for practical scenarios where data exhibit vagueness, uncertainty, and indistinct boundaries. In addition, existing fuzzy rough set-based feature selection methods often suffer from high computational cost, especially in fine-grained information systems. To address these issues, this paper proposes a generalized quotient space framework based on fuzzy neighborhood operators. Within this framework, a fuzzy quotient mapping is constructed, and a quotient fuzzy β-covering approximation space (β-QFCAS) is established. Based on β-QFCAS, a fuzzy β-covering rough set model is developed, and its key properties are systematically investigated. Moreover, a forward feature selection algorithm is designed in the quotient fuzzy β-covering decision space (β-QFCDS) to improve computational efficiency while preserving decision performance. Experimental results demonstrate that the proposed method achieves competitive accuracy, indicating its effectiveness for feature selection in uncertain and complex decision-making environments.