The aim of this paper is to introduce the notions of fuzzy upper and lower s-limits sets. Properties and basic relationships among fuzzy upper s-limit set, fuzzy lower s-limit set, fuzzy semi-continuity are investigated. Possible applications to quantum physics and computer graphics are touched upon. We speculate that s-convergence and s-properties may be relavant to the physics of fractal and cantorian spacetime. (c) 2005 Elsevier Ltd. All rights reserved.