[9] How are membership values determined?

Date: 15-APR-93

Determination methods break down broadly into the following categories:

1. Subjective evaluation and elicitation

   As fuzzy sets are usually intended to model people's cognitive states,
   they can be determined from either simple or sophisticated elicitation
   procedures. At they very least, subjects simply draw or otherwise specify
   different membership curves appropriate to a given problem. These
   subjects are typcially experts in the problem area. Or they are given a
   more constrained set of possible curves from which they choose. Under
   more complex methods, users can be tested using psychological methods.

2. Ad-hoc forms

   While there is a vast (hugely infinite) array of possible membership
   function forms, most actual fuzzy control operations draw from a very
   small set of different curves, for example simple forms of fuzzy numbers
   (see [7]). This simplifies the problem, for example to choosing just the
   central value and the slope on either side.

3. Converted frequencies or probabilities

   Sometimes information taken in the form of frequency histograms or other
   probability curves are used as the basis to construct a membership
   function. There are a variety of possible conversion methods, each with
   its own mathematical and methodological strengths and weaknesses.
   However, it should always be remembered that membership functions are NOT
   (necessarily) probabilities. See [10] for more information.

4. Physical measurement

   Many applications of fuzzy logic use physical measurement, but almost
   none measure the membership grade directly. Instead, a membership
   function is provided by another method, and then the individual
   membership grades of data are calculated from it (see FUZZIFICATION in [4]).

5. Learning and adaptation

For more information, see:

   Roberts, D.W., "Analysis of Forest Succession with Fuzzy Graph Theory",
   Ecological Modeling, 45:261-274, 1989.

   Turksen, I.B., "Measurement of Fuzziness: Interpretiation of the Axioms
   of Measure", in Proceeding of the Conference on Fuzzy Information and
   Knowledge Representation for Decision Analysis, pages 97-102, IFAC,
   Oxford, 1984.

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