Abstract
Multiobjective linear plus linear fractional programming problem is an emerging tool for solving problems in different environments such as production planning, financial and corporate planning and healthcare and hospital planning which has attracted many researchers in recent years. This paper presents a method to find a Pareto optimal solution for the multiobjective linear plus linear fractional programming problem through nonlinear membership function. The proposed approach defines a fuzzy goal for each objective through a nonlinear membership function. By means of nonlinear membership function, the multiobjective linear plus linear fractional programming problem transformed into a multiobjective nonlinear programming problem. Applying the linear approximation method, the nonlinear objectives are converted into linear. In order to solve the multiobjective linear programming problem, the fuzzy goal programming model is formulated by minimizing the negative deviational variables. The proposed procedure is illustrated through numerical examples and a reallife application problem. Further, it is compared with the existing methods. Finally, the Euclidean distance function has been used to prove the efficiency of the proposed method.
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Abbreviations
 LPP:

Linear programming problem
 LPLFPP:

Linear plus linear fractional programming problem
 MOLPLFPP:

Multiobjective linear plus linear fractional programming problem
 FMONLFPP:

Fuzzy multiobjective nonlinear fractional programming problem
 FMOLPP:

Fuzzy multiobjective linear programming problem
 FMOLFPP:

Fuzzy multiobjective linear fractional programming problem
 MOLPP:

Multiobjective linear programming problem
 FFLFPP:

Fully fuzzy linear fractional programming problem
 MOFPP:

Multiobjective fractional programming problem
 MOMIFCSTP:

Multiobjective multiitem fixedcharge solid transportation problem
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Veeramani, C., Sharanya, S. & Ebrahimnejad, A. Optimization for multiobjective sum of linear and linear fractional programming problem: fuzzy nonlinear programming approach. Math Sci (2020). https://doi.org/10.1007/s4009602000333w
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Keywords
 Goal programming
 Linear programming problem
 Multiobjective nonlinear programming problem
 Multiobjective linear plus linear fractional programming problem