A foundation on semigroups of operators defined on the set of triangular fuzzy numbers and its application to fuzzy fractional evolution equations

In this article, we study the strongly continuous semigroups of fuzzy-valued operators defined on the space of triangular fuzzy numbers. New notions of fuzzy infinitesimal generators and fuzzy resolvent operators of fuzzy semigroups are established in the sense of the generalized Hukuhara difference. A Hille-Yosida-like theorem in the framework of fuzzy metric space is investigated. We demonstrate the efficiency of theoretical results by studying the existence of mild solutions of fuzzy nonlinear fractional evolution equations.