Abstract: The effective mean-semi-deviation portfolio model is used for the analysis of the investment portfolio with financing in this paper. First, the gain obtained by the mean-semi-deviation model with financing and the risks of the goal are described in a fuzzy way by constructing the linear membership functions μmax(x) and μmin(x), which are widely used. Then, based on fuzzy decision theory, variable μ is introduced to transform the biobjective model with financing under fuzzy environment into a linear portfolio selection model with financing. This model not only greatly simplifies the computation, but also clearly describes the subjective investment willingness of the investors. Finally, an example is presented to illustrate the applicability and effectiveness of the proposed model.

Key words: the mean-semi-deviation portfolio model, membership function；fuzzy decision；financing