Elicitation of membership functions: How far can theory take us?

A taxonomy of interpretations for fuzzy membership functions is given. Depending on each interpretation, the elicitation method and the theory to apply seems to be different. When different interpretations are cast into a measurement-theoretic framework, the difference becomes clearer. However; this raises questions about the validity of the overall measurement-theoretic framework. It is argued that the measurement-theoretic framework imposes an objective account of meaning for fuzzy set theory and implications of this on the practical elicitation of membership functions are commented on.