In many real-world problems, one may encounter uncertainty in the input data. The fuzzy set theory fits well to handle such situations. However, it is not always possible to determine with full satisfaction the membership and non-membership degrees associated with an element of the fuzzy set. The intuitionistic fuzzy sets play a key role in dealing with the hesitation factor along-with the uncertainity involved in the problem and hence, provides more flexibility in the decision-making process. In this article, we introduce a new ordering on the set of intuitionistic fuzzy numbers and propose a simple approach for solving the fully intuitionistic fuzzy linear programming problems with mixed constraints and unrestricted variables where the parameters and decision variables of the problem are represented by intuitionistic fuzzy numbers. The proposed method converts the problem into a crisp non-linear programming problem and further finds the intuitionistic fuzzy optimal solution to the problem. Some of the key significance of the proposed study are also pointed out along-with the limitations of the existing studies. The approach is illustrated step-by-step with the help of a numerical example and further, a production planning problem is also demonstrated to show the applicability of the study in practical situations. Finally, the efficiency of the proposed algorithm is analyzed with the existing studies based on various computational parameters.

中文翻译：

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一种求解具有不受限制决策变量的完全直觉模糊线性规划问题的新方法

在许多实际问题中，可能会遇到输入数据的不确定性。模糊集理论非常适合处理这种情况。然而，并不总是能够完全满意地确定与模糊集合元素相关联的隶属度和非隶属度。直觉模糊集在处理犹豫因素以及问题中涉及的不确定性方面起着关键作用，因此在决策过程中提供了更大的灵活性。在本文中，我们介绍了直觉模糊数集的新排序，并提出了一种简单的方法来解决具有混合约束和无限制变量的完全直觉模糊线性规划问题，其中问题的参数和决策变量由直觉模糊数表示。数字。所提出的方法将问题转化为一个清晰的非线性规划问题，并进一步找到问题的直觉模糊最优解。还指出了拟议研究的一些关键意义以及现有研究的局限性。该方法在数值示例的帮助下逐步说明，此外，还演示了一个生产计划问题，以显示该研究在实际情况中的适用性。最后，基于各种计算参数的现有研究分析了所提出算法的效率。还指出了拟议研究的一些关键意义以及现有研究的局限性。该方法在数值示例的帮助下逐步说明，此外，还演示了一个生产计划问题，以显示该研究在实际情况中的适用性。最后，基于各种计算参数的现有研究分析了所提出算法的效率。还指出了拟议研究的一些关键意义以及现有研究的局限性。该方法在数值示例的帮助下逐步说明，此外，还演示了一个生产计划问题，以显示该研究在实际情况中的适用性。最后，基于各种计算参数的现有研究分析了所提出算法的效率。