Solving the linear fractional programming problem in a fuzzy environment: Numerical approach

• A method to compute (α, r) optimal value for fully fuzzy linear fractional programming problem is developed.
• Lower bound of the optimal value is increased when α is increased.
• Upper bound of the optimal value is decreased when α is increased.
• Numerically, the membership function of the optimal value is constructed.
• The method is completely explained through real life problems.

The fuzzy linear fractional programming problem is an important planning tool in different areas such as engineering, business, finance, and economics. In this study, we propose the use of the (α, r) acceptable optimal value for a linear fractional programming problem with fuzzy coefficients and fuzzy decision variables, as well as developing a method for computing them. To obtain acceptable (α, r  ) optimal values, we take an α-cutα-cut on the objective function and r-cutr-cut on the constraints. We then formulate an equivalent bi-objective linear fractional programming problem to calculate the upper and lower bounds of the fully fuzzy LFP problem. Using the upper and lower bounds obtained, we construct the membership functions of the optimal values numerically. We illustrate the proposed procedure using numerical and real life examples.