Fuzzy Multi-Objective Semi-Definition Programming

This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming (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.