Granular-Ball Fuzzy Set and Its Implement in SVM

Traditional fuzzy set methods, designed around the finest granularity of inputs-individual points and their membership degrees-often struggle with inefficiencies and label noise. To overcome these challenges, we introduce granular-ball computing into the fuzzy set, creating the new granular-ball fuzzy set framework. This approach uses granular-ball inputs rather than single points, significantly reducing the number of entities and minimizing susceptibility to the noise affecting individual sample points. As a result, our framework enhances both efficiency and robustness compared to traditional methods and is applicable across various domains of fuzzy data processing. Furthermore, we apply this framework to fuzzy support vector machines (FSVMs), developing the Granular-ball Fuzzy Support Vector Machine (GBFSVM). Experimental tests on UCI benchmark datasets show that GBFSVM surpasses traditional models in efficiency and robustness.