Fuzzy set theory and class inclusion relations in semantic categories

Fuzzy set theory has frequently been suggested to be the appropriate mathematics to model degree of representativeness of exemplars in natural categories. The purpose of the present research was to determine if fuzzy set theory accurately describes how exemplar representativeness values in categories at different levels within a taxonomy are related. The results of three rating studies indicated that (1) two of the most basic operations within fuzzy set theory, containment and union, do not correctly describe the actual representativeness relationships; and (2) the representativeness relationships cannot be described by any simple monotonic function. It is argued that fuzzy set theory, in principle, cannot specify the relationships among representativeness values in different categories, because the theory does not take the attributes of exemplars directly into account.

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