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)