Thus, X is a fuzzy concept if its denotation, F, is a fuzzy set in its universe of discourse. A fuzzy concept is associated with a membership function which assigns to each point, u, in the universe of discourse of X, the degree to which u is a member of F. Alternatively, it may be defined algorithmically in terms of other fuzzy concepts. Examples of fuzzy concepts are small number, strong evidence and similarity. It should be noted that many concepts associated with fuzzy sets are crisp concepts. An example is the concept of a convex fuzzy set.
Most fuzzy concepts are context-dependent.
The next level is that of f.g-definability, with g standing for granular, and f.g denoting the conjunction of fuzzy and granular. Informally, in the case of a concept which is f.g-granular, the values of attributes are granulated, with a granule being a clump of values which are drawn together by indistinguishability, similarity, proximity or functionality. An example of an f.g-granular concept which is traditionally defined as a crisp concept, is that of statistical independence. In particular, a common misdefinition is to treat a concept as if it were c-definable whereas in fact it is not. The next level is that of PNL-definability, where PNL stands for Precisiated Natural Language.