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For more information about this area, please contact:

Russ Tronstad
Extension Economist

Phone: (520) 621-2425
Email: tronstad@ag.arizona.edu

 

 

An Example Fuzzy Expert System

Step 4 -- Inference

Now we want to relate the observations to the rules. We are interested in what degree an observation has membership in the fuzzy set associated with each rule. The following memberships need to be evaluated.
  • Rule 1 -- lowenergy and lowprotein
  • Rule 2 -- lowenergy and highprotein
  • Rule 3 -- highenergy and lowprotein
  • Rule 4 -- highenergy and highprotein

For logical "and" operations using fuzzy sets the resulting membership functions are defined as the minimum of the values of the memberships on the component sets. If the rule has "or" operations the maximum of the memberships would be used.

For our example data.

  • Rule 1 -- {0.993307, 0.858149, 0.24974, 0.00669285, 0.858149, 0.24974, 0.00669285, 0.858149, 0.845535, 0.00669285}
  • Rule 2 -- {0.00669285, 0.141851, 0.75026, 0.993307, 0.00669285, 0.00669285, 0.00669285, 0.130108, 0.154465, 0.00669285}
  • Rule 3 -- {0.00669285, 0.00669285, 0.00669285, 0.00669285, 0.141851, 0.75026, 0.993307, 0.141851, 0.141851, 0.00669285}
  • Rule 4 -- {0.00669285, 0.00669285, 0.00669285, 0.00669285, 0.00669285, 0.00669285, 0.00669285, 0.130108, 0.141851, 0.993307}

Further these memberships can be used to define a fuzzy set for the outcomes of the rules. Specifically, the membership of an observation on the rules fuzzy set becomes the maximum membership of the outcomes fuzzy set. For example the low energy low protein maximum membership value for observation 3 is .24974, applying this as a maximum to the high feed fuzzy set results in the following.

[graph showing score rule 1 vs. feed level]

The low energy high protein maximum membership value for observation 3 is .75026, applying this as a maximum to the high feed fuzzy set results in the following.

[graph showing score rule 2 vs. feed level]

The high energy low protein maximum membership value for observation 3 is .00669285, applying this as a maximum to the low feed fuzzy set results in the following.

[graph showing score rule 3 vs. feed level]

The high energy high protein maximum membership value for observation 3 is .00669285, applying this as a maximum to the low feed fuzzy set results in the following.

[graph showing score rule 4 vs. feed level]

 

 

 


Step 3


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2011 Dept. of Agricultural & Resource Economics, The University of Arizona
Send comments or questions to arecweb@ag.arizona.edu

Last updated September 17, 1999
Document located at http://ag.arizona.edu/arec/fuzzy/ex-infer.html