Nearness derivatives and fuzzy differentiability. (English) Zbl 0934.26013

Janiš, Vladimír

Fuzzy Sets Syst. 108, No. 1, 99-102 (1999).

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:

26E50

Fuzzy real analysis

Keywords:

nearness derivatives; fuzzy differentiability; Rolle and Lagrange mean value theorems