Attribute Reduction of Type-2 Fuzzy Information Systems Based on \(\sigma \) Self-information

Type-2 fuzzy information systems (TFISs-2), one interesting form of complex data, are extensions of fuzzy information systems. Uncertainty measurement and attribute reduction of TFISs-2 are key issues when describing and analyzing complex fuzzy data. However, existing researches mainly focus on the traditional fuzzy data, and seldom consider type-2 fuzzy data. This paper focuses on finding an effective indicator to measure the uncertainty of TFISs-2, and carries out the research of attribute reduction based on this indicator. Firstly, the weighted membership distance and the weighted membership similarity are defined, which are used to describe the relation between two objects in TIFSs-2, and \(\sigma \) $\sigma$ similarity relations are introduced. Secondly, a fuzzy neighborhood structure is defined based on \(\sigma \) $\sigma$ similarity relations. The classical rough set model is extended on TFISs-2, and the definitions of upper and lower approximation, accuracy and roughness are given. Then, a novel indicator called \(\sigma \) $\sigma$ self-information is used to describe the uncertainty of TFISs-2, and a heuristic greedy selection attribute reduction algorithm is proposed. Finally, the experimental results show that the constructed uncertainty measurement indicator is suitable for TFISs-2, and the proposed attribute reduction method is effective. This study is beneficial to promote the understanding of complex fuzzy data, and contributes to the data analysis and processing of TFISs-2.