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Abstract: This paper addresses the multi-objective portfolio selection model with fuzzy random returns for investors by studying three criteria: return, risk and liquidity. In addition, securities historical data, experts’ opinions and judgements and investors’ different attitudes are considered in the portfolio selection process, such that the investor’s individual preference is reflected by an optimistic–pessimistic parameter λ. To avoid the difficulty of evaluating a large set of efficient solutions and to ensure the selection of the best solution, a compromise approach-based genetic algorithm has been designed to solve the proposed model. In addition, a numerical example is presented to illustrate the proposed algorithm. [Copyright &y& Elsevier]