This paper discusses a class of uncertain optimization problems, in which unknown parameters are modeled by fuzzy intervals. The membership functions of the fuzzy intervals are interpreted as possibility distributions for the values of the uncertain parameters. It is shown how the known concepts of robustness and light robustness, for the traditional interval uncertainty representation of the parameters, can be generalized to choose solutions that optimize against plausible parameter realizations under the assumed model of uncertainty in the possibilistic setting. Furthermore, these solutions can be computed efficiently for a wide class of problems, in particular for linear programming problems with fuzzy parameters in constraints and objective function. Thus the problems under consideration are not much computationally harder than their deterministic counterparts. In this paper a theoretical framework is presented and results of some computational tests are shown.

本文讨论了一类不确定优化问题，其中未知参数通过模糊区间建模。模糊区间的隶属函数被解释为不确定参数值的可能性分布。展示了对于参数的传统区间不确定性表示的稳健性和光稳健性的已知概念如何可以被推广以选择在可能性设置中的假定不确定性模型下针对似是而非的参数实现进行优化的解决方案。此外，这些解决方案可以针对多种问题高效计算，特别是对于约束和目标函数中具有模糊参数的线性规划问题。因此，所考虑的问题在计算上并不比确定性问题难多少。在本文中，提出了一个理论框架，并展示了一些计算测试的结果。