Fuzzy Roughness Measurement Model Based on Membership Effect

Rough fuzzy set theory and fuzzy set theory are two commonly used tools in today's uncertain type of information processing. How to construct a fusion method for two kinds of uncertain information systematically has been a focus in both academic and applied fields. By analyzing the characteristics and shortcomings of the current fuzzy roughness sets, this paper puts forward concept of membership effect function and establishes a fuzzy roughness measurement model based on membership effect (denoted by FRM-BME, for short). And then, several necessary and sufficient conditions are given to reflect the value of FRM-BME. Finally, we propose an attribute reduction algorithm based on FRM-BME, and further analyze the characteristics and effectiveness of FRM-BME combined with specific cases. Theoretical analysis and experimental results show that, FRM-BME not only has good structural characteristics and interpretability, but also can simply integrate the fuzzy processing preference into roughness measurement system. To a certain extent, it not only enriches the existing related theories, but also can be widely used in artificial intelligence, resource management and many other fields.