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Nearness derivatives and fuzzy differentiability

✍ Scribed by Vladimı́ r Janiš

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
81 KB
Volume
108
Category
Article
ISSN
0165-0114

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✦ Synopsis

We introduce a fuzzy di erentiability and a type of generalized derivatives ( -nearness derivatives) based on the notion of nearness operation. Using this type of di erentiability 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 non-di erentiable and even non-continuous functions in terms of the fuzzy theory.

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