Fuzzy product rule with applications

In this paper, we establish the GH-derivative of multiplication of fuzzy functions, the so-called product rule. For the first time, a product rule is constructed while both of the multiplied functions are assumed to be fuzzy without any restriction on the signs of multiplied functions. The rule is extracted based on the MCE-product and its property of distributivity. Then, we propose two important applications of the fuzzy product rule: An integration by parts formula for fuzzy functions and solving a nonlinear fuzzy differential equation. Some illustrative examples are given to verify the theoretical results.