S. Mandayam/ ANN/ECE Dept./Rowan University Artificial Neural Networks ECE.09.454/ECE.09.560 Fall 2008 Shreekanth Mandayam ECE Department Rowan University.

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S. Mandayam/ ANN/ECE Dept./Rowan University Artificial Neural Networks ECE /ECE Fall 2008 Shreekanth Mandayam ECE Department Rowan University Lecture 9 November 3, 2008

S. Mandayam/ ANN/ECE Dept./Rowan UniversityPlan Fuzzy Logic and Application to Neural Nets Fuzzy Set Theory Fuzzy I/O Map Fuzzy Inference System Fuzzy Neural Nets Fuzzy-MLP Fuzzy-RBF Functional equivalence with RBF Final Project Discussion Lab Activity

S. Mandayam/ ANN/ECE Dept./Rowan University Fuzzy Logic Fuzzy logic or fuzzy set theory is a formal system for representing and reasoning with imprecise information Pioneers Lotfi Zadeh html html Bart Kosko

S. Mandayam/ ANN/ECE Dept./Rowan University Fuzzy Sets: Membership Functions 0 1 x  (x) 0 1 x 0 1 x Triangular Gaussian Crisp (Not Fuzzy)

S. Mandayam/ ANN/ECE Dept./Rowan University Fuzzy Inference System Fuzzifier Inference Procedure Fuzzy Rule Base Defuzzifier Inputs Outputs (crisp) (fuzzy) (crisp) Fuzzy Rule Base Rule i: IF x 1 is A i1 AND x 2 is A i2 …………………… x m is A im THEN y 1 is B i1 AND y 2 is B i2 …………………… y n is B in

S. Mandayam/ ANN/ECE Dept./Rowan University Application Example Fuzzy Controller for an Air-Conditioner Inputs Outputs (Temperature Settings)(Fan Motor Speed) ColdStop CoolSlow RightMedium WarmFast HotBlast Rules IFCoolTHENSlow RightMedium WarmFast

S. Mandayam/ ANN/ECE Dept./Rowan University Input (x): Air Temp. Output (y): Motor Speed cool rightwarm hot cold stop slow medium fast blast IF cool THEN slow IF right THEN medium IF warm THEN fast Function x  y Fuzzy I/O Map

S. Mandayam/ ANN/ECE Dept./Rowan University Fuzzy I/O Map (contd.) 0% 100% 70% 20% Air Temp. in Fahrenheit cool right centroid Motor Speed in RPM % 100% 70% 20% IF x THEN y summed sets 68 degrees: 20% cool 70% right Motor speed: 20% slow 70% medium

S. Mandayam/ ANN/ECE Dept./Rowan University Functional Equivalence between Fuzzy Systems and RBF

S. Mandayam/ ANN/ECE Dept./Rowan University Lab 3: RBF Neural Nets /fall08/ann/lab3.htmlhttp://engineering.rowan.edu/~shreek /fall08/ann/lab3.html

S. Mandayam/ ANN/ECE Dept./Rowan UniversitySummary