Fuzzy Logic Notes by Dr. Ashraf Abdelbar American University in Cairo

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Presentation transcript:

Fuzzy Logic Notes by Dr. Ashraf Abdelbar American University in Cairo to accompany chapter 2 of Jang, Sun & Mizutani

Fuzzy Sets Notation for specifying a fuzzy set. Terminology: support, core, normality, crossover point, fuzzy singleton, alpha-cut, convexity, fuzzy number, width, symmetry, open-left and open-right Set operations: union, intersection, complement, Cartesian product.

Membership Functions Triangular, trapezoid, Gaussian, Cauchy, bell, sigmoid, closed & assymetric Two-Dimension MF’s. Cylindrical extension. Projection. Composite & non-composite 2-D MF’s.

Fuzzy Complement Two axioms Involution axiom Stronger requirement Sugeno’s complement. Yager’s complement.

T-norms & S-norms Four T-norm & S-norm operations. Relations between them. Duality Principle. Parametrized norms: e.g. S & S.