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===Naive model of the meaning of evaluative linguistic expressions===

According to this model, the meaning of an evaluative
expression <math>\mathcal{A} </math> is identified with a simple fuzzy set
<math> A: U\to L </math> where <math> U </math> is a ''universe'' and <math> L </math> is a
set of truth values (usually the interval [0, 1] of real numbers). The universe is
not specified, but quite often it is a set of real numbers. Shapes of fuzzy sets are 
often simplified to triangles. In applications, they can be further modified, usually in arbitrary way.

A standard example of this model is depicted in  <figref>TriangularFSets.gif</figref> where the triangular fuzzy sets characterize certain typical values for "very small", "small", "medium", "big", and "very big" which thus determine the corresponding
''categories''. The used natural-language expressions are only labels of these categories because the depicted triangular fuzzy sets ''cannot'' represent their linguistic meaning. This can be easily seen when considering, for example, 0, which is clearly a ''small number''. According to the model in  <figref>TriangularFSets.gif</figref>, however, 0 is ''very small'', but ''not small'' at all. This contradicts the linguistic meaning of the considered evaluative expressions. 

[[Image:Intenze-Sm-Me-Bi.gif|thumb|500px|right|F3| Scheme of intensions of basic evaluative expressions ''extremely small, very small, small, medium'' and ''big''. ]]