Robust optimality analysis of non-degenerate basic feasible solutions in linear programming problems with fuzzy objective coefficients
研究了模糊目标系数线性规划中非退化基本可行解的必然最优性度量的计算方法，利用容差法高效评估解在系数波动下的鲁棒性，并针对多种模糊子集类型提出相应算法。
Abstract The necessarily optimal solution is known as the most reasonable solution to linear programming problems with interval/fuzzy objective function coefficients. As it remains optimal against the certain fluctuations of objective function coefficients, the necessarily optimal solution can be seen as a robust optimal solution. In this paper, we demonstrate that the necessary optimality degree of a non-degenerate basic feasible solution can be obtained easily by utilizing the tolerance approach. The necessary optimality degree evaluates to what extent the solution remains optimal against the fluctuations of objective function coefficients. Several types of fuzzy subsets showing the possible range of the objective function coefficient vector are considered. For each type of fuzzy subset, an efficient calculation method of necessary optimality degree is proposed. Numerical examples are given to illustrate the proposed methods.