Fuzzy Logic Notesby

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.