模糊多目标半定规划

Fuzzy Multi-Objective Semi-Definition Programming

中文关键词:  模糊多目标半定规划  隶属度函数  最优有效解  最优性条件.

英文关键词:fuzzy multi-objective semi-definite programming  membership function  optimality efficient solution  efficient solution  optimality condition.

中文摘要:

      本文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,将以模糊多目标半定规划转化为一种确定性多目标半定规划,证明了前者最优有效解与后者有效解的一致性,并讨论了二者的最优性条件.最后,通过引入隶属度函数及一系列的转化,给出了一种模糊多目标规划的解法.

英文摘要:

      This paper first applies the 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 is translated to the MSDP. Then we prove that the optimal efficient solution of FMSDP is consistent with the efficient solution of MSDP and present the optimality condition about these programming. At last, we give an algorithm for FMSDP by introducing a new membership function and a series of transformation.