<p>The objective of this paper is to present an innovative approach for finding max–min solutions in a ‘two-player zero-sum matrix game with fuzzy goals and fuzzy payoffs’. In this approach, the membership functions for both goals and payoffs are assumed to be linear. A new two-level fuzzy set approach has been developed to address both single and multi-objective matrix game problems involving fuzzy goals and fuzzy payoffs. The decision variables in this method are probabilities, which exhibit distinct characteristics. For the single-objective case, it has been shown that each player’s optimization problem can be framed as a fractional programming problem. This method demonstrates an equivalence between fractional programming and nonlinear crisp goal programming (GP) problems. By applying a novel two-level method, these nonlinear GP problems can be solved effectively. The approach is further extended to address a ‘multi-objective matrix game with fuzzy goals and fuzzy payoffs’. It provides efficiency and suitability for both players by eliminating the need for a defuzzification function to determine the optimal mixed strategies for each player. To demonstrate its applicability, various examples are presented, along with a comprehensive comparative analysis that evaluates the performance, validity and advantages of this approach over existing methods. Additionally, the approach is applied to two real-world problems—a water management problem and a market share problem—to find optimal solutions.</p>