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.

本文建立了线性相关模糊数值函数的演算方法。特别地，当基本模糊数是非对称的时，通过使用表示函数和线性同构来引入导数的定义。我们的定义比导致Fréchet衍生概念的定义更笼统。当基本模糊数是对称的时，使用线性相关模糊数值函数的典范形式引入导数和Riemann积分。分别针对对称和非对称基本模糊数，进一步研究了线性相关模糊数值函数的导数和积分的一些相关性质。