1. S. Mandayam/ ANN/ECE Dept./Rowan University Artificial Neural Networks ECE.09.454/ECE.09.560 Fall 2008 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/fall08/ann/ Lecture 9 November 3, 2008

2. 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

3. 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 http://www.cs.berkeley.edu/People/Faculty/Homepages/zadeh. html http://www.cs.berkeley.edu/People/Faculty/Homepages/zadeh. html Bart Kosko http://sipi.usc.edu/~kosko/ http://sipi.usc.edu/~kosko/

4. 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)

5. 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

6. 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

7. 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

8. S. Mandayam/ ANN/ECE Dept./Rowan University Fuzzy I/O Map (contd.) 0% 100% 70% 20% Air Temp. in Fahrenheit cool right 50 60 68 70 80 centroid Motor Speed in RPM 10 47 0% 100% 70% 20% IF x THEN y summed sets 68 degrees: 20% cool 70% right Motor speed: 20% slow 70% medium

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

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

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