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Nearness derivatives and fuzzy differentiability. (English) Zbl 0934.26013
Summary: We introduce a fuzzy differentiability and a type of generalized derivatives ($$\alpha$$-nearness derivatives) based on the notion of nearness operation. Using this type of differentiability we show that some basic statements of mathematical analysis remain valid for a wider class of functions. We state generalized versions of Rolle and Lagrange mean value theorems for the case of nondifferentiable and even noncontinuous functions in terms of the fuzzy theory.

##### MSC:
 2.6e+51 Fuzzy real analysis
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