Calculus for fuzzy functions with strongly linearly independent fuzzy coefficients

Abstract This paper establishes a theory of calculus for fuzzy-number-valued functions whose range is embedded in a specific Banach subspace of fuzzy numbers. These spaces are generated by strongly linearly independent (SLI) fuzzy numbers whose operations are induced by an isomorphism with R n . We use the notion of Frechet differentiability and Riemann integrability for these functions and present a fundamental theorem of calculus. Lastly, we develop a theory of fuzzy differential equations and provide an existence and uniqueness theorem.

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