模糊多目标半定规划的最优性条件

Optimality Condition for Fuzzy Multi-objective Semi-definite Programming

将模糊集理论应用到多目标半定规划中来,提出了有约束的模糊多目标半定规划模型,并首次给出了其最优有效解的定义。通过构造确定的隶属度函数,将以矩阵为决策变量的模糊多目标半定规划转化为一种目标函数的某些分量由约束函数决定的确定性多目标半定规划,并证明了前者最优有效解与后者有效解的一致性。在此基础之上,讨论了二者的最优性条件。

This paper is the first application of fuzzy set theory to multi-objective semi-definite programming （MSDP）, and proposes the fuzzy multi-objective semi-definite programming （FMSDP） model whose optimal efficient solution is defined for the first time, too. By constructing a membership function, the FMSDP in which matrixes are treated as strategy variable is translated to the MSDP whose partial objective functions are bounded by the decision functions. Then we proof that the optimal efficient solution of FMSDP is consistence with the efficient solution of MSDP. On this basis, we present the optimality condition about these programming.