Download presentation

Presentation is loading. Please wait.

Published bySincere Cockroft Modified over 3 years ago

1
Learning from Examples Adriano Cruz ©2004 NCE/UFRJ e IM/UFRJ

2
@2001 Adriano Cruz NCE e IM - UFRJ Reference n L. Wang, J. Mendel, Generating Fuzzy Rules by Learning from Examples, IEEE Transactions on Systems, Man and Cybernetics, vol 22, no.6, november 1992

3
@2001 Adriano Cruz NCE e IM - UFRJ Information sources n Information used for most real-world control and signal processing problems can be classified into two kinds: –Numerical obtained form sensor, etc –Linguistic information obtained from human experts

4
@2001 Adriano Cruz NCE e IM - UFRJ Current situation n Solutions are heuristic in nature n Combine standard control processing methods and expert systems n Weakpoints: –Problem dependent –No commom framework

5
@2001 Adriano Cruz NCE e IM - UFRJ Problems n Linguistic rules may be incomplete due to loss when humans express their knowedge n Input-output data pairs because past experience may not cover all situations

6
@2001 Adriano Cruz NCE e IM - UFRJ Generating fuzzy rules n Consider a two input-one output problem as an example n So data is available as input-output pairs as n (x 1 (1),x 2 (1) ;y (1) ), (x 1 (2),x 2 (2) ;y (2) ), … n F(x 1,x 2 ) -> y

7
@2001 Adriano Cruz NCE e IM - UFRJ Step 1 n Divide the input and output space into fuzzy regions n Assign to each region a membership function n Similar to creating fuzzy sets over a universe of discourse

8
@2001 Adriano Cruz NCE e IM - UFRJ Step1 x1 B1B2CES1S2 x2 CEB1S1S2S3B2B3 X (2) 1 X (1) 1 X (1) 2 X (2) 2

9
@2001 Adriano Cruz NCE e IM - UFRJ Step1 y B1B2CES1S2 y (1) y (2)

10
@2001 Adriano Cruz NCE e IM - UFRJ Step2 n Generate fuzzy rules from given data pairs n First determine the degrees of each given x 1 (i),x 2 (i) and y (i) in different regions n Second assign a given x 1 (i),x 2 (i) and y (i) to the regions with maximum degree n Finally, obtain one rule from one pair of input data

11
@2001 Adriano Cruz NCE e IM - UFRJ Step2 n (x 1 (1), x2 (1); y (1) )= [0.8 in B1, 0.7 in S1; 0.9 in CE] = Rule 1 n If x1 is B1 and x2 is S1 then y is CE n (x 1 (2), x2 (2); y (2) )= [0.6 in B1, 1.0 in CE; 0.7 in B1] = Rule 1 n If x1 is B1 and x2 is CE then y is B1 = Rule 2

12
@2001 Adriano Cruz NCE e IM - UFRJ Step3 n Assign a degree to each rule n It is high probable that there will be some conflicting rules, i.e., rules that have the same antecedent but different consequents n The degree is calculated as n D(rule)=m A (x 1 )m B (x 2 )m C (z)

13
@2001 Adriano Cruz NCE e IM - UFRJ Step3 n D(rule)=m A (x 1 )m B (x 2 )m C (z) n Rule 1 = 0.8 * 0.7 * 0.9 = 0.504 n Rule 2 = 0.6 * 1.0 * 0.7 = 0.42

14
@2001 Adriano Cruz NCE e IM - UFRJ Step4 n Create a combined fuzzy rule n If there is more than on rule in one box of the fuzzy rule base, use the rule that has maximum degree.

15
@2001 Adriano Cruz NCE e IM - UFRJ Step5 n Determine a Mapping based on the combined Fuzzy Rule Base. n Combine the antecedents of ith fuzzy rule: m O i = m I1 i (x 1 )m I2 i (x 2 ) (product operator) n m CE 1 =m B1 (x 1 )m S1 (x 2 )

16
@2001 Adriano Cruz NCE e IM - UFRJ Step5 n Use the following centroid defuzzification method n y i represents the center value of the region O i (the smallest abs value among all values with membership equals to 1) n K is the number of fuzzy rules combined

Similar presentations

OK

Fuzzy Expert Systems. Lecture Outline What is fuzzy thinking? What is fuzzy thinking? Fuzzy sets Fuzzy sets Linguistic variables and hedges Linguistic.

Fuzzy Expert Systems. Lecture Outline What is fuzzy thinking? What is fuzzy thinking? Fuzzy sets Fuzzy sets Linguistic variables and hedges Linguistic.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on dc power supply Ppt on email etiquettes presentation skills Free download ppt on work energy and power Download ppt on web designing Ppt on object-oriented concepts interview questions Ppt on project management tools Ppt on management by objectives ppt Ppt on our changing earth for class 7 What does appt only meant Ppt on game theory five nights