In this paper, we present a fuzzy multiple criteria decision making (FMCDM) model known as fuzzy balancing and ranking. In contrast to other MCDM models, our proposed model does not require the weights of decision making criteria. First, we appraise the performance of alternatives against criteria via linguistic variables which are expressed as triangular fuzzy numbers. The foregoing model obtains the alternative rankings through a four-stage process. Second, an outranking matrix is derived indicating that the frequency with which one alternative is superior to all other alternatives based on each criterion. Third, the outranking matrix is triangularised to obtain an implicit pre-ordering or provisional order of alternatives. Fourth, the provisional order of alternatives is subjected to various screening and balancing operations that require sequential application of a balancing principle to the so-called advantages–disadvantages table that combines the criteria with the pair-wise comparisons of alternatives. Additionally, to demonstrate the procedural implementation of the proposed model and its effectiveness, we apply it on a case study regarding the problem of supplier selection.