SUM NORMAL OPTIMIZATION OF FUZZY MEMBERSHIP FUNCTIONS

DAN SIMON
2002 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
Given a. fuzzy logic system, how can we determine the membership functions that will result in the best performance? H we constrain the membership functions to a certain shape (e.g., t riangles or trapezoids) then each membership function can be parameteri'l:ed by a small number of variables and the membership optimization problem can be reduced to a parameter optimization problem. This is the approach that is typically taken, hut it results in membership functions that are not (in general) sum
more » ... normal. That is, the resulting membership function values do not add up to one at each point in the domain. This optimization approach is modified in this paper so that the resulting membership functions are sum normal. Sum normality is desirable not only for its intuitive app eal but also for computational reasons in the real time implementation of fuzzy logic systems. The sum normal constraint is applied in t his paper to both gradient descent optimization and Kalman filter optimization of fuzzy membership fu nctions. The methods are illustrated on a fuzzy automotive cruise controller.
doi:10.1142/s0218488502001533 fatcat:zrgle47en5glta6ihifk4ep5sa