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.