Abstract
The membership function of a fuzzy set is the cornerstone upon which fuzzy set theory has evolved. The question of where these membership functions come from or how they are derived must be answered. Expert systems commonly deal with fuzzy sets and must use valid membership functions. This paper puts forth a method for constructing a membership function for the fuzzy sets that expert systems deal with. The function may be found by querying the appropriate group and using fuzzy statistics. The concept of a group is defined in this context, as well as a measure of goodness for a membership function. The commonality and differences between membership function for a fuzzy set and probabilistic functions are shown. The systematic methodology presented will facilitate effective use of expert systems.
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