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An Example Fuzzy Expert System

Step 1 -- Define Fuzzy Sets

The problem is to generate supplemental feeding recommendations on the basis of the energy and protein levels of current range forage. To do this we need to define fuzzy sets for both the input parameters, energy, and protein levels, and the output, feeding recommendation. For the example, two fuzzy sets are defined for each parameter. One set defining the concept low and another defining the concept high. An advantage of the fuzzy approach is that we don't have to define each possible level. Intermediate levels are accounted for as they can have membership on both the high and low fuzzy sets.

  1. low energy
  2. high energy
  3. low protein
  4. high protein
  5. high feed
  6. low feed

For the example we measure feed, energy, and protein on a 0 to 10 scale (this is just to keep the example simple obviously any scale could have been used). For these sets assume the following membership function for low, i.e. low feed, low energy, and low protein.

low[x_]:= 1- (1/(1+Exp[-((x-5)/1.0)]))

[graph showing membership vs. value]

For these sets assume the following membership function for high

high[x_]:= 1/(1+Exp[-((x-5)/1.0)])

[another graph showing membership vs. value]

What does this mean? If the energy level is 6 then this observation is scored on the low energy fuzzy set as about a .25 and on the high energy fuzzy set as about a .75. Thus this observation is not classed as either high or low energy but is associated to varying degrees with both concepts. This is the key to fuzzy sets.

What can we do with this?




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2011 Dept. of Agricultural & Resource Economics, The University of Arizona
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Last updated September 17, 1999
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