In this paper, a concept of fuzzy semientropy is proposed to quantify the downside uncertainty. Several properties of fuzzy semientropy are identified and interpreted. By quantifying the downside risk with the use of semientropy, two mean-semi-entropy portfolio selection models are formulated, and a fuzzy simulation-based genetic algorithm is designed to solve the models to optimality. We carry out comparative analyses among the fuzzy mean-entropy models and the fuzzy mean-semi-entropy models and demonstrate that the mean-semi-entropy models can significantly improve the dispersion of investment. Several illustrative examples using stock dataset from the real-world financial market (China Shanghai Stock Exchange) also show the effectiveness of the models.
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