Multi-objective 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 multi-objective 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 multi-objective linear plus linear fractional programming problem transformed into a multi-objective nonlinear programming problem. Applying the linear approximation method, the nonlinear objectives are converted into linear. In order to solve the multi-objective 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 real-life 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.

中文翻译：

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线性和线性分数规划问题的多目标和的优化：模糊非线性规划方法

多目标线性加线性分数规划问题是一种用于解决不同环境中的问题的新兴工具，例如生产计划，财务和公司计划以及医疗保健和医院计划，近年来吸引了许多研究人员。本文提出了一种通过非线性隶属度函数求解多目标线性加线性分数规划问题的Pareto最优解的方法。所提出的方法通过非线性隶属函数为每个目标定义一个模糊目标。利用非线性隶属函数，将多目标线性加线性分数规划问题转化为一个多目标非线性规划问题。应用线性逼近方法，将非线性目标转换为线性。为了解决多目标线性规划问题，通过最小化负偏差变量建立了模糊目标规划模型。通过数值示例和实际应用问题说明了所提出的过程。此外，将其与现有方法进行比较。最后，利用欧氏距离函数证明了该方法的有效性。