Abstract
This paper establishes the calculus for linearly correlated fuzzy number-valued functions. In particular, a definition of derivative is introduced by using representation functions and a linear isomorphism when the basic fuzzy number is non-symmetric. Our definition is more general than that leading to concept of Fréchet derivative. Derivative and Riemann integral are introduced using the canonical form of a linearly correlated fuzzy number-valued function when the basic fuzzy number is symmetric. Some relevant properties of derivatives and integrals of linearly correlated fuzzy number-valued functions are further investigated for symmetric and non-symmetric basic fuzzy number, respectively.
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