A Novel Mean–Variance-Entropy Portfolio with Two-Parameter Coherent Triangular Intuitionistic Fuzzy Number

There are a lot of fuzzy uncertainties in the real financial market, and fuzzy numbers can well depict this phenomenon. On the one hand, compared with fuzzy numbers (only with membership function), intuitionistic fuzzy numbers (with both membership and non-membership functions) can describe different types of uncertainties more accurately by providing a more comprehensive information description. On the other hand, investors are not entirely rational, and their attitudes are crucial to investment decisions. Based on these facts, we define a new coherent intuitionistic fuzzy number with two parameters, which can describe markets’ fuzzy uncertainties and investors’ attitudes at the same time. Then, we derive specific expressions of its possibilistic mean, possibilistic variance, and possibilistic covariance through rigorous mathematical proofs. In addition, too concentrated allocation of investment weights is not conducive to risk diversification, while entropy can improve portfolio diversity because it does not depend on the normal distribution assumption of security returns. Considering this advantage of entropy, we construct a new mean–variance-entropy portfolio model which incorporates two-parameter coherent intuitionistic fuzzy numbers. Further, we employ the ideal point method to solve this model. Finally, we empirically demonstrate the feasibility and effectiveness of our new model by randomly selecting 20 stocks from the Chinese stock market. The results show that different values of the two parameters can describe the ambiguity of the market and the different attitudes of investors: investors with an optimistic-optimistic attitude tend to achieve higher returns and greater diversification, while optimistic-neutral investors tend to undertake lower risks.