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Fuzzy Logic Control and Hybrid Systems Lecture 3: Fuzzy Membership Function Professor. Dr. Hani Hagras Membership Functions • Determining or finding input/output membership functions is the first step of the fuzzy logic control process where a fuzzy algorithm categorises the information entering a system and assigns values that represent the degree of membership in those categories. • Input membership functions themselves can take any form the designer of the system requires triangles, trapezoids, bell curves or any other shape as long as those shapes accurately represent the distribution of information within the system, and as long as a region of transition exists between adjacent membership functions. Membership Functions •In Rule Based applications of Fuzzy Logic, membership functions are associated with terms that appear in the antecedents or consequents of rules Shapes for Membership (x-a)/b-a) ax b 1 bx c (d-x)/(d-c) cx d 0 otherwise (x-a)/b-a) ax b (c-x)/(c-b) bx c 0 otherwise e(0.5(( x a) / ) ) 2 • Average = a= x = (x1+x2+…xn)/N Where N is the total number of data points • Standard deviation = θ = -3 a 3 Generalised Bell Membership Function A generalised bell membership, can be specified by three parameters {a, b, c} bell (x: a, b, c) = 1/ (1+ (x-c/a)2b) Membership slope = -b/2a c-a c c+a • Due to their simple formulas and computational efficiency, both triangular membership functions and trapezoidal membership functions have been used extensively, especially in real-time implementation • However since the membership functions are composed of straight-line segments, they are not smooth at the switching points specified by the parameters. • The Guassian and the Bell membership function provides smooth and non-linear functions that can be used by the learning systems like Neural Networks. Fuzzy Terminology Support Core -Cut Height Modifiers