Abstract
In this paper, we introduce extension of the fuzzy type theory (FTT) by subtypes. This demand arises in situations when, for example, it is useful to distinguish rational and real numbers, where the set of rational numbers is a subset of the reals. In the original FTT, this causes a problem because we cannot assign rational numbers a special type. The solution is to introduce special types for both of them and declare that the former is a subtype of the latter. The resulting fuzzy type theory is denoted by sFTT. When constructing the frame for sFTT we must realize that, though all the considered functions are total, if we take them as functions between subsets then they become partial.
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