The fuzzy Henstock-Kurzweil delta integral on time scales

Abstract

We investigate properties of the fuzzy Henstock-Kurzweil delta integral (shortly, FHK $\Delta$-integral) on time scales, and obtain two necessary and sufficient conditions for FHK $\Delta$-integrability. The concept of uniformly FHK $\Delta$-integrability is introduced. Under this concept, we obtain a uniformly integrability convergence theorem. Finally, we prove monotone and dominated convergence theorems for the FHK $\Delta$-integral.