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A mathematical model for solving fuzzy integer linear programming problems with fully rough intervals

机译：以完全粗略的间隔解决模糊整数线性编程问题的数学模型

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A suggested algorithm to solve triangular fuzzy rough integer linear programming (TFRILP) problems with a-level is introduced in this paper in order to find rough value optimal solutions and decision rough integer variables, where all parameters and decision variables in the constraints and the objective function are triangular fuzzy rough numbers. In real-life situations, the parameters of a linear programming problem model may not be defined precisely, because of the current market globalization and some other uncontrollable factors. In order to solve this problem, a proper methodology is adopted to solve the TFRILP problems by the slice-sum method with the branch-and-bound technique, through which two fuzzy integers linear programming (FILP) problems with triangular fuzzy interval coefficients and variables were constructed. One of these problems is an FILP problem, where all of its coefficients are the upper approximation interval and represent rather satisfactory solutions; the other is an FILP problem, where all of its coefficients are the lower approximation interval and represent completely satisfactory solutions. Moreover, a-level at a - 0.5 is adopted to find some other rough value optimal solutions and decision rough integer variables. Integer programming is used, since a lot of the linear programming problems require that the decision variables be integers. In addition, the motivation behind this study is to enable the decision makers to make the right decision considering the proposed solutions, while dealing with the uncertain and imprecise data. A flowchart is also provided to illustrate the problem-solving steps. Finally, two numerical examples are given to clarify the obtained results.
机译：在本文中引入了解决三角形模糊粗糙整数线性编程（TFRILP）问题的建议算法，以查找粗糙度最佳解决方案和决策粗糙整数变量，其中限制和目标中的所有参数和决策变量功能是三角形模糊粗糙的数字。在现实生活中，由于当前的市场全球化和其他一些无法控制的因素，因此可能无法正常定义线性编程问题模型的参数。为了解决这个问题，采用了一种适当的方法来解决与分支和绑定技术的切片和方法解决TFRILP问题，通过该方法，三角形模糊间隔系数和变量的两个模糊整数线性编程（Filp）问题。被建成了。其中一个问题是一个FILP问题，其中所有系数都是上近似间隔，并且代表了相当令人满意的解决方案;另一个是一个文件，其中所有系数都是较低的近似间隔，并且表示完全令人满意的解决方案。此外，采用A-0.5的A级来找到一些其他粗糙度最佳解决方案和决策粗糙整数变量。使用整数编程，因为许多线性编程问题要求决策变量是整数。此外，本研究背后的动机是使决策者能够考虑拟议的解决方案，同时处理不确定和不精确的数据。还提供流程图以说明解决问题的步骤。最后，给出了两个数值例子来澄清所得结果。

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