Four fuzzy supervised classification methods for discriminating classes of non-convex shape

Our work deals with modelling and optimising industrial processes such as metal cutting with high-speed machining. In this field we have chosen to use fuzzy supervised classification methods in order to design a diagnosis system or a process-monitoring module. The problem, we currently meet, concerns the shape of the classes, we generally obtain. These shapes are often nonconvex and non-separable by a hyperplane. For these reasons, we focus on fuzzy supervised classification methods in order to discriminate these classes. The choice of a method is not obvious and we perform a comparative study. The two classical methods tested were the fuzzy K-nearest-neighbours method and a method based on distributed fuzzy rules. Furthermore, we propose two adaptations of the fuzzy pattern matching algorithm called fuzzy pattern matching with exponential function and fuzzy pattern matching multidensity. After some refresher on supervised classification, the four tested methods are detailed and compared according to the following criteria: quality of the discrimination, computation time and ability to decide. The response of each classifier is illustrated by membership level curves and the quality of diagnosis is studied by the introduction of membership and ambiguity rejects.