Approximation fixpoint theory (AFT) provides an algebraic framework for the\nstudy of fixpoints of operators on bilattices and has found its applications in\ncharacterizing semantics for various classes of logic programs and nonmonotonic\nlanguages. In this paper, we show one more application of this kind: the\nalternating fixpoint operator by Knorr et al. for the study of the well-founded\nsemantics for hybrid MKNF knowledge bases is in fact an approximator of AFT in\ndisguise, which, thanks to the power of abstraction of AFT, characterizes not\nonly the well-founded semantics but also two-valued as well as three-valued\nsemantics for hybrid MKNF knowledge bases. Furthermore, we show an improved\napproximator for these knowledge bases, of which the least stable fixpoint is\ninformation richer than the one formulated from Knorr et al.'s construction.\nThis leads to an improved computation for the well-founded semantics. This work\nis built on an extension of AFT that supports consistent as well as\ninconsistent pairs in the induced product bilattice, to deal with\ninconsistencies that arise in the context of hybrid MKNF knowledge bases. This\npart of the work can be considered generalizing the original AFT from symmetric\napproximators to arbitrary approximators.\n