In this paper, (gradient) almost Ricci solitons on Finsler measure spaces (M, F, m) are introduced and investigated. We prove that (M, F, m) is a gradient almost Ricci soliton with soliton scalar \(\kappa \) if and only if the infinity-Ricci curvature Ric \(_\infty =\kappa \) on M. Moreover, we give an equivalent characterization of (gradient) almost Ricci solitons for Randers metrics \(F=\alpha +\beta \) , which implies that every Randers (gradient) almost Ricci soliton is of isotropic S \(_{BH}\) -curvature. Based on this and the navigation technique, we further classify Randers almost Ricci solitons (resp., gradient almost Ricci solitons) up to classifications of Randers Einstein metrics F (resp., Riemannian gradient almost Ricci solitons) and the homothetic vector fields of F (resp., solutions of the equation which the weight function f of m satisfies) when F has isotropic S \(_{BH}\) -curvature. As applications, we obtain some rigidity results for compact Randers (gradient) Ricci solitons and construct several Randers gradient Ricci solitons, which are the first nontrivial examples of gradient Ricci solitons in Finsler geometry.
