In this paper, we consider interval multi-objective linear programming (IMOLP) models which are used to deal with uncertainties of real-world problems. So far, a variety of approaches for obtaining efficient solutions (ESs) of these problems have been developed. In this paper, we propose a new and two generalized methods. In the new method, converting IMOLP into an interval linear programming (ILP) and then obtaining its optimal solutions (OSs), ESs of the IMOLP are determined. This method has several advantages: (i) This method is the only method which obtains a solution box for IMOLP models. (ii) The solving process is not time consuming. (iii) The number of ESs is higher than for other methods. (V) The method is applicable for large-scale problems. Also, we generalize the \(\varepsilon\)-constraint and lexicographic methods which are used for obtaining ESs of the multi-objective linear programming (MOLP) models which do not have any problems such as lengthy and time-consuming and are applicable for large-scale problems. Some examples were solved to show the efficiency of the proposed methods. Finally, by the proposed method, we solve the IMOLP model corresponding to the problem of the facilities and non-return funds in a bank.

中文翻译：

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获得区间多目标线性规划问题的有效解

在本文中，我们考虑了区间多目标线性规划（IMOLP）模型，该模型用于处理实际问题的不确定性。到目前为止，已经开发了用于获得这些问题的有效解决方案（ES）的多种方法。在本文中，我们提出了一种新的和两种广义的方法。在新方法中，将IMOLP转换为区间线性规划（ILP），然后获得其最佳解（OS），确定IMOLP的ES。该方法具有多个优点：（i）该方法是唯一获得IMOLP模型求解盒的方法。（ii）解决过程并不耗时。（iii）ES的数量高于其他方法。（五）该方法适用于大规模问题。此外，我们推广\（\ varepsilon \）-约束和词典方法，用于获得多目标线性规划（MOLP）模型的ES，这些方法没有任何问题，例如冗长和费时，并且适用于大规模问题。解决了一些例子，以证明所提出方法的有效性。最后，通过提出的方法，我们解决了与银行的设施和非归还资金问题相对应的IMOLP模型。