On generalized solutions for discontinuous fuzzy differential equations and strong fuzzy Henstock integrals

In this paper, under the notion of strong uniformly AC of fuzzy-number-valued functions, we prove a generalized controlled convergence theorem of strong fuzzy Henstock integral. As the applications of this convergence theorem, we provide sufficient conditions which guarantee the existence of generalized solutions to initial value problems for the fuzzy differential equations by using properties of strong fuzzy Henstock integrals under strong GH-differentiability. In comparison with some previous works, we consider equations whose right-hand side functions are not integrable in the sense of Kaleva on certain intervals and their solutions are not absolute continuous functions.