Calculus of Linear Fuzzy Numerical Functions Based on Non-Increasing Fuzzy Real Numbers

Abstract Fuzzy calculus is the basis of researching fuzzy differential equations. This article mainly investigate the differentiability and integrability of linear fuzzy numerical functions constructed from non-negative and increasing real functions and decreasing fuzzy real numbers. Firstly, we introduced the definitions of limit and continuity on fuzzy numerical functions, which are the cornerstone of researching the differentiation and integration of fuzzy numerical functions. What is more, the concept of differentiability of fuzzy numerical functions is discussed. To be specific, we also introduce some theorems and several examples of solving differential of fuzzy numerical functions. Finally, we proposed the concept and some properties of integrability of linear fuzzy numerical functions. These concepts improve the fuzzy numerical function calculus theory.