Abstract
In this paper, we define strongly fuzzy variational Henstock multiple integral and fuzzy Henstock integral by support functions on n-dimensional fuzzy number space. And we prove these two types of integrals are equivalent. After that, we propose the support-based derivative for strongly fuzzy variational Henstock integral functions and obtain the necessary and sufficient conditions for this differential. By the properties of ACGδ⁎⁎, we use the concepts of inner small variation and singular point covering to derive some characterization theorems of the primitives for strongly fuzzy variational Henstock integral. Finally, the Dominated Convergence Theorem for SFVH integral is obtained in the sense of UACGδ⁎⁎.
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