In this paper, we deal with two-person zero-sum games with fuzzy payoffs and fuzzy goals. We have presented two models for studying two-person zero-sum matrix games with fuzzy payoffs and fuzzy goals. We assume that each player has a fuzzy goal for each of the payoffs. We obtained that the fuzzy relation approach and the max-min solution are equivalent. (C) 2010 Elsevier Ltd. All rights reserved.