An analytical formulation of the influence of membership functions shape

This paper presents a study of the defuzzification method given by Rondeau et al. (1996) when it is used in a Mamdani-like fuzzy model. This defuzzification strategy has been developed to strictly respect the fuzzy partition of the output variable. The model so-derived has interesting properties since the input and output membership functions shape directly control the interpolation between rules. This result enables a systematic choice of the input and output membership functions shape.