On the Ability of Fuzzy Relations and Fuzzy Implications to Uncover Non-linearity

Given a set of points in some space, each with a label, the problem of finding a separating boundary is an important one. If linear separability holds, then a separating hyperplane can be found with methods such as support vector machines (SVM). However, when the set is non-linearly separable, identifying a boundary is a challenging task. In this paper, a general formulation of naive classifiers based on fuzzy relations and fuzzy implications is proposed. It is established that naive classifiers separate labeled sets of points when appropriate relations and implications are used. Construction techniques for such relations and implications are presented. Graphical illustrations are provided, demonstrating the separating ability of naive classifiers.