We propose a multi-objective approach for portfolio selection, which allows investors to consider not only return and downside risk criteria but also to include environmental, social and governance (ESG) scores in the investment decision-making process. Owing to the uncertain environment of portfolio selection, the return and ESG score of each asset are considered as independent L-R power fuzzy variables. To make the model more realistic, we take budget, floor ceiling and cardinality constraints into account. In order to select the optimal portfolio along the efficient frontier, we apply the Sortino ratio in a credibilistic environment. The subsequent empirical application uses a data set from Bloomberg’s ESG Data in combination with US Dow Jones Industrial Average data. The experimental results show that the proposed model offers promising results for socially responsible investors seeking ethical and sustainability goals beyond the return-risk trade-off and its ability to beat the benchmark.