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In financial markets, the presence of background risk may affect investors’ investments. This article develops a fuzzy portfolio selection model with background risk, based on the definitions of the possibilistic return and possibilistic risk. For the returns of assets obey LR-type possibility distribution, we propose a specific portfolio selection model with background risk. Then, a numerical study is carried out by using the data concerning some stocks. Based on the data, we obtain the efficient frontier of the possibilistic portfolio with background risk, and compare it with the efficient frontier of the portfolio without background risk. Finally, we conclude that the background risk can better reflect the investment risk of the real economy environment which make the investors choose a more suitable portfolio to them. [ABSTRACT FROM AUTHOR]