Fuzzy Support Vector Classification Machine Using Possibility Inequality Measures

This paper proposes a novel fuzzy support vector algorithm for pattern classification by using the possibility inequality measure. We first introduce the concepts of fuzzy hyperplane and fuzzy linear separability. Then, the proposed approach seeks a fuzzy hyperplane that satisfies the possibility inequality conditions and best separates the positive class from the negative class with the widest margin in the feature space. Further, the decision function is also based on the possibility inequality measure and indicates the membership degree of these individuals in a given category. This integration preserves the benefits of fuzzy set theory and SVM theory, where the fuzzy hyperplane provides the SVM with effective means for capturing the approximate, imprecise nature of the real world. On the other hand, the SVM provides the advantage to minimize the structural risk and effectively generalize the unseen data.