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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

• 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.

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.

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.

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.

Step 3