This paper presents a fuzzy multicriteria group decision making approach for effectively considering the degree of confidence of decision makers (DMs) in solving the supplier selection problem. Linguistic variables approximated by fuzzy numbers are used to represent the DM’s subjective assessments so that the uncertainty and imprecision in the selection process are adequately handled in a less cognitively demanding manner. To avoid the complicated and unreliable process of comparing and ranking fuzzy utilities often required in fuzzy multicriteria analysis, the concept of the degree of dominance between alternatives is introduced for calculating an overall performance index for every alternative supplier across all criteria. An example is presented to demonstrate the applicability of the proposed approach for solving the supplier selection problem in real world settings.