Abstarct: There are many optimization problems, in which ratios of the objective functions give betterinsightratherthantheirabsolutevalues. Also,thereareproblemsthatratiosofthe objectives should be optimized, inherently. One of the efficient tools commonly used for handling these types of problems is linear-fractional programming. However, in real-world problems, due to imperfect and inaccurate information, precise models are unavailable. One of the efficient methods for dealing with imprecise and ambiguous values is using fuzzy numbers instead of crisp ones. Therefore, the concept of fuzzy linear-fractional programming has arisen. In recent decades, many researchers have made a lot of efforts for developing new efficient methods for solving such problems. In this thesis, first, we describe fuzzy programming. Then we investigate the fuzzy linear-fractional programming. Furthermore, we express two new methods for solving fuzzy linear-fractional programming problems, considering the trapezoidal fuzzy numbers. The first method, presented for solving the fuzzy linear-fractional programming problems with inequality constraints, solves the problem using the lexicographic method after converting it to a multi-objective linear programming problem. In the second method, fuzzy linear-fractional programming problems with inequality constraints are solved by assuming auxiliary variables for converting inequality constraints to equality ones. Finally, we compare the efficiency and performance of the proposed methods with others by solving some problems