The fuzzy Henstock–Kurzweil delta integral on time scales

Abstract

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