This paper discusses a new algorithm for generating the Pareto frontier for bi-level multi-objective rough nonlinear programming problem (BL-MRNPP). In this algorithm, the uncertainty exists in constraints which are modeled as a rough set. Initially, BL-MRNPP is transformed into four deterministic models. The weighted method and the Karush-Kuhn-Tucker optimality condition are combined to obtain the Pareto front of each model. The nature of the problem solutions is characterized according to newly proposed definitions. The location of efficient solutions depending on the lower/upper approximation set is discussed. The aim of the proposed solution procedure for the BL-MRNPP is to avoid solving four problems. A numerical example is solved to indicate the applicability of the proposed algorithm.

本文讨论了一种为双层多目标粗糙非线性规划问题 (BL-MRNPP) 生成帕累托前沿的新算法。在该算法中，不确定性存在于建模为粗糙集的约束中。最初，BL-MRNPP 被转换为四个确定性模型。加权法和Karush-Kuhn-Tucker最优条件相结合，得到每个模型的Pareto前沿。问题解决方案的性质根据新提出的定义进行表征。讨论了取决于下/上近似集的有效解决方案的位置。BL-MRNPP 所提议的求解过程的目的是避免求解四个问题。一个数值例子被解决，以表明所提出的算法的适用性。