Fuzzy Rough Set Models Based on Fuzzy Similarity Relation and Information Granularity in Multi-Source Mixed Information Systems

As a pivotal research method in the field of granular computing (GrC), fuzzy rough sets (FRSs) have garnered significant attention due to their successful overcoming of the limitations of traditional rough sets in handling continuous data. This paper is dedicated to exploring the application potential of FRS models within the framework of multi-source complex information systems, which undoubtedly holds profound research significance. Firstly, a novel multi-source mixed information system (MsMIS), encompassing five distinct data types, is introduced, thereby enriching the dimensions of data processing. Subsequently, a similarity function, designed based on the unique attributes of the data, is utilized to accurately quantify the similarity relations among objects. Building on this foundation, fuzzy T-norm operators are employed to integrate the similarity matrices derived from different data types into a cohesive whole. This integration not only lays a solid foundation for subsequent model construction but also highlights the value of multi-source information fusion in the analysis of the MsMIS. The integrated results are subsequently utilized to develop FRS models. Through rigorous examination from the perspective of information granularity, the rationality of the FRS model is proven, and its mathematical properties are explored. This paper contributes to the theoretical advancement of FRS models in GrC and offers promising prospects for their practical implementation.