Fuzzy Least Squares Support Vector Machine with Fuzzy Hyperplane

This study uses fuzzy set theory for least squares support vector machines (LS-SVM) and proposes a novel formulation that is called a fuzzy hyperplane based least squares support vector machine (FH-LS-SVM). The two key characteristics of the proposed FH-LS-SVM are that it assigns fuzzy membership degrees to every data vector according to the importance and the parameters for the hyperplane, such as the elements of normal vector and the bias term, are fuzzified variables. The proposed fuzzy hyperplane efficiently captures the ambiguous nature of real-world classification tasks by representing vagueness in the observed data set using fuzzy variables. The fuzzy hyperplane for the proposed FH-LS-SVM model significantly decreases the effect of noise. Noise increases the ambiguity (spread) of the fuzzy hyperplane but the center of a fuzzy hyperplane is not affected by noise. The experimental results for benchmark data sets and real-world classification tasks show that the proposed FH-LS-SVM model retains the advantages of a LS-SVM which is a simple, fast and highly generalized model, and increases fault tolerance and robustness by using fuzzy set theory.