Three-Way Approximate Representation of Rough Fuzzy Multi-granularity Knowledge Spaces via Information Measure
摘要
Three-way approximations of fuzzy sets offer a computationally efficient and conceptually straightforward method for characterizing uncertainty in fuzzy information systems, which has increasingly garnered academic attention. At the core of three-way approximation theory lies the development of objective optimization functions to systematically partition the sample space into three mutually exclusive regions: positive, boundary, and negative domains. While existing methodologies have made progress in traditional approximation analysis, they exhibit limited exploration of how to effectively divide rough fuzzy multi-granularity knowledge spaces into these regions. This paper addresses this research gap by introducing a novel framework for three-way approximate representation of rough fuzzy multi-granularity knowledge spaces. We first propose a fuzzy knowledge granularity measure to quantify the inherent uncertainty of fuzzy concepts. A critical insight is that this uncertainty measure demonstrates a monotonic decay property within hierarchical rough fuzzy approximation spaces. Subsequently, based on the fuzzy knowledge granularity measure, the similarity between different rough fuzzy approximation spaces is defined. Theoretical analysis confirms that the proposed similarity function can be reduced to the information measure under specific conditions. Ultimately, the proposed framework employs a three-way approximation strategy to precisely segment rough fuzzy multi-granularity knowledge spaces into three disjoint regions. This work not only extends the theoretical boundaries of three-way approximation sets by incorporating multi-granularity perspectives but also establishes a systematic methodology for both theoretical refinement and practical applications in uncertain knowledge representation.