Summary: By analogy with Feller’s general probabilistic scheme used in the construction of many classical convergent sequences of linear operators, in this paper, we consider a Feller-kind scheme based on the possibilistic integral, for the construction of convergent sequences of nonlinear operators. In particular, in the discrete case, all the so-called max-product Bernstein-type operators and their qualitative convergence properties are recovered. Also, discrete nonperiodic nonlinear possibilistic convergent operators of Picard type, Gauss-Weierstrass type and Poisson-Cauchy type are studied and the possibility of introduction of discrete periodic(trigonometric) nonlinear possibilistic operators of de la Vallée-Poussin type, of Fejér type and of Jackson type is mentioned as future directions of research.