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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 2 -- Relating Observations to Fuzzy Sets

For operation of a normal fuzzy expert system only one set of input observations would be necessary. However, to illustrate the fuzzy concepts, lets take an example with 10 observations of energy and protein.


energy = {0., 0., 0., 0., 3.2, 6.1, 10., 3.2, 3.2, 10.}
protein = {0., 3.2, 6.1, 10., 0., 0., 0., 3.1, 3.3, 10.}


The following are the evaluations of theses observations in terms of their membership in the four fuzzy sets we have defined.

  • lowenergy = low[energy] {0.993307, 0.993307, 0.993307, 0.993307, 0.858149, 0.24974, 0.00669285, 0.858149, 0.858149, 0.00669285}

  • lowprotein = low[protein] {0.993307, 0.858149, 0.24974, 0.00669285, 0.993307, 0.993307, 0.993307, 0.869892, 0.845535, 0.00669285}

  • highenergy = high[energy] {0.00669285, 0.00669285, 0.00669285, 0.00669285, 0.141851, 0.75026, 0.993307, 0.141851, 0.141851, 0.993307}

  • highprotein = high[protein] {0.00669285, 0.141851, 0.75026, 0.993307, 0.00669285, 0.00669285, 0.00669285, 0.130108, 0.154465, 0.993307}

Observation 3 for example has an energy value of 0 and a protein value of 6.1 and the following membership on the energy and protein fuzzy sets.

lowenergy[[3]] = 0.993307
lowprotein[[3]] = 0.24974
highenergy[[3]] = 0.00669285
highprotein[[3]] = 0.75026

Note:
All values for membership functions must be between 0 and 1. Also in this example the sum of the contrasting (low and high) fuzzy memberships is 1. This is a common feature of fuzzy systems but is not a requirement.

 

 


Step 1


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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-observe.html