This study proposes a novel way to deal with uncertainty in a two-person zero-sum matrix game with payoffs expressed as fuzzy rough numbers. Complete and reasonable solutions to these types of games are obtained. In this research we develop two linear programming models with upper and lower approximation intervals of fuzzy rough numbers and handle multi-objective crisp linear programming models by incorporating trapezoidal fuzzy rough numbers as payoffs. To provide each opponent with the optimal strategy and value of the game, the usual simplex approach is applied. Finally, two numerical examples demonstrate the matrix game outcomes using Wolfram Cloud.