Fuzzy Laplace transform based on the Henstock integral and its applications in discontinuous fuzzy systems

The existing results on the fuzzy Laplace transform and their applications were based on Zaheh's decomposition theorem and were formally characterized by the integrals of real-valued functions directly. That is, the existence of the fuzzy Laplace transform in essence has not been solved. In this article, the fuzzy Laplace transform is incorporated into the framework of the Henstock integral and proposed by use of fuzzy Henstock integrals on infinite intervals. In addition, as a theoretical basis, the existence and the basic properties of the fuzzy Laplace transform are investigated, the convolution of fuzzy-valued functions and real-valued functions is defined, and the convolution theorem of the fuzzy Laplace transform is given. Finally, discontinuous fuzzy initial value problems and two kinds of fuzzy Volterra integral equations are discussed with use of the fuzzy Laplace transform presented in this article. (C) 2018 Elsevier B.V. All rights reserved.