Robust Optimization by Fuzzy Linear Programming

提出了一种用必要性度量来表示决策者对稳健约束的偏好的方法，并证明了具有一般必要性度量的模糊线性规划问题在不损失线性度的情况下得到了很好的解。研究了两层线性规划问题的稳健优化和多目标问题的稳健有效解。此外，文中还指出，分次劣知集的近似计算相当容易。然后，用类似于模糊线性规划问题的方法来处理具有分次不确定集的线性规划问题。最后，在给定部分两两偏好信息的情况下，提出了区间有序回归方法。我们研究了区间有序回归方法的推广。

A method for representation of the decision maker's preference on robust constraints by a necessity measure is proposed and it is shown that fuzzy linear programming problems with general necessity measures are solved without great loss of linearity. Robust optimization in two level linear programming problems and robust efficient solutions in multiple objective problems are investigated. Moreover, it is shown that approximate calculations of graded ill-known sets are rather easy. Then the linear programming problems with graded ill-known sets can be treated in a similar way to fuzzy linear programming problems. Finally, we proposed interval ordinal regression method when a part of pairwise preference information is given. We investigated the generalizations of the interval ordinal regression method.