An optimal defuzzification strategy for Pedrycz's identification method

Pedrycz's identification method using the resolution of fuzzy relational equations, is the first method which enables a fuzzy linguistic modelling from the knowledge of crisp observations of a system. The fuzzy relational equation base lends a strong theoretical background to the overall method. The resolution of such equations is based on the minimization of a distance criterion between output fuzzy characterizations and estimated fuzzy characterizations. However, this 'fuzzy' criterion has very different properties when compared with a classical 'crisp' criterion which takes into account the distance between crisp and estimated outputs. The goal of this paper is to increase the link between 'fuzzy' and 'crisp' criterion by using a complementary association between the output fuzzy partition and the defuzzification method presented by Rondeau-Ruelas (1996).