A Gould type integral of fuzzy functions

摘要

In this paper, a new type of integral of a fuzzy-valued function relative to a non-negative set function is proposed as a new useful tool in modeling uncertainties. Various properties of this new type of integral are established concerning the behavior with respect to the fuzzy function or to the set function. Several examples linking our integral with Birkhoff and Lebesgue integrals are provided. Also, problems related to atomicity are addressed. (C) 2017 Elsevier B.V. All rights reserved.