Interpretative versus prescriptive fuzzy set theory

Both traditional fuzzy set theory and the theory of subjective probabilities postulate their formulas. The former because it does not accept a probabilistic interpretation of grades of membership, the latter because it makes no connection between subjective probabilities and relative frequencies. The interpretational theory of the TEE model ascribes a well-defined meaning to a membership value μ_λ in terms of probabilities which are limits of frequencies. μ _λ is interpreted as the estimate by the subject of the probability that a given object would be assigned the label X in an everyday situation of uncertainty. In contrast to the max-min formulas used in many applications of fuzzy sets, the postulated “summation-to-1” formula of all fuzzy clustering algorithms follows from the interpretative TEE model. This agrees with the author´s view that fuzzy set theory should be defined as a theory which allows partial membership values of an object in a class or cluster, not as a theory which uses specific mathematical operators. The operators must be derived from the well-defined interpretation of partial membership values