The choice of suitable robots in manufacturing, to improve product quality and to increase productivity, isa complicated decision due to the increase in robot manufacturersand configurations. In this article, a novelapproach is proposed to choose among alternatives, differentlyassessed by decision makers on different criteria, to make the final evaluation for decision-making. Theapproach is based on the ELLIPSOID algorithm for systems oflinear inequalities. Most of the ranking methods depend onintegration that becomes complicated for nonlinear membershipfunctions, which is the case in robot selection. Themethod simply uses the membership function or itsderivative. It takes the decision maker’ s attitude in ranking. It effectively ranks fuzzy numbers and their images, preservingsymmetry. It is a simple recursive algebraic formulathat can be easily programmed. The performance ofthe algorithm is compared with the performance of someexisting methods through several numerical examples toillustrate its advantages in ranking, and a robot selectionproblem is solved.