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 space of fuzzy numbers. These spaces are generated by strongly linearly independent (SLI) fuzzy numbers whose operations are induced by an isomorphism with Rn. We use the notion of Fréchet 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.