Precision devices require surface finish of a few nanometers. The choice of compliant coated abrasive tools used in manufacturing such devices is discussed including a method for selecting a suitable one for a given component using decision-making techniques. Multiple conflicting criteria such as surface roughness and the polishing time influence the selection of appropriate compliant polishing tool. Hence, multi-criteria decision making methods (MCDMs) are implemented to rank the suitability of different polishing processes for a given workpiece geometry. New criteria such as compliance and surface integrity are introduced for such selection. In order to differentiate the level of complexity involved in these MCDMs, a traditional analytical hierarchy process (AHP) and a Fuzzy VIšekriterijumsko KOmpromisno Resenje (multi-criteria optimization and compromise solution, VIKOR) method are chosen. This study illustrates the capability of these two MCDMs as a polishing process selection tool using the linguistic information through a case study. From the decision makers’ inputs, rankings of polishing tools were obtained and compared using these two methods. New factors such as compliance are seen to affect the choice significantly. The approach discussed in this work could be used for developing an intelligent decision-making system for choosing polishing tools with respect to the given conditions. © 2015, Springer-Verlag London.