1. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay1 CS 621 Artificial Intelligence Lecture 9 - 22/08/05 Prof. Pushpak Bhattacharyya Fuzzy Inferencing

2. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay2 22.08.05IIT Bombay2 Example: INVERTED PENDULUM MOTOR θ θ = angular displacement θ` = dθ/dt = angular velocity i = current

3. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay3 22.08.05IIT Bombay3 Rules are of the form If displacement is large, then current is large in the opposite direction. If velocity is small, then current needed is small. Any numerically expressed rule base will be of infinite size. For every θ and θ ` we specify a rule.

4. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay4 22.08.05IIT Bombay4 Fuzzy Rule Base Expressed as a table 0 – region Large Med Small Positive Negative θ θ`

5. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay5 22.08.05IIT Bombay5 The Cell – contents i - value Z-S-M +SZ-S +M+ SZ Z – Zero S – Small M - Med L - Large θ θ` If θ is Z and θ` is +S then i is -S

6. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay6 22.08.05IIT Bombay6 Rules Centre: If θ is z and θ ` is z then i is z. If θ is z and θ ` is +s then i is –s. If θ is z and θ ` is –s then i is +s.

7. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay7 22.08.05IIT Bombay7 Rules (Contd 1) 4) If θ is +s and θ ` is z then i is –s. 5) If θ is –s and θ ` is z then i is +s. 6) If θ is +s and θ ` is –s then i is z.

8. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay8 22.08.05IIT Bombay8 Rules (Contd 2) 7) If θ is –s and θ ` is +s then i is z. 8) If θ is +s and θ ` is +s then i is –M. 9) If θ is –s and θ ` is –s then i is +M.

9. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay9 22.08.05IIT Bombay9 Scenario At every moment 1)θ and θ ` are read by sensors. 2)These numerical values are passed through profiles to get μ – Fuzzification. 3)Rules are computed on the LHS using primitive First order logic operations. 4)Truth values transferred to the RHS (Luk. System). 5)From the μ values in RHS compute the i-value. 5 th step - Computing the target variable - numeric value DEFUZZIFICATION - Centroid Method

10. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay10 22.08.05IIT Bombay10 Fundamentally the operation is FORWARD CHAINING. Unlike precise logic (crisp logic). Many rules apply, potentially all. Corresponds to VERDICT BY MULTIPLE JURY, where each rule is a judge. Forward Chaining

11. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay11 22.08.05IIT Bombay11 Obtain Profiles 1)Profiles of small, medium and large quantities for θ, θ ` and i. 2)Even Zero (z) needs a profile. DOMAIN EXPERTS, EMPIRICAL.

12. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay12 22.08.05IIT Bombay12 Zero - Medium + Medium Alternate Form Of Zero

13. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay13 22.08.05IIT Bombay13 Consider θ = 0.2 degree θ ` = 0.8 degree/sec Work in terms of Units θ = 0.2 unit, θ ` = 0.8 unit

14. 22.08.2005Prof. Pushpak Bhattacharyya, IIT Bombay14 Each of θ and θ ` values can be used to read μ s from all profiles θ