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In previous studies, there were few portfolio models involving investors’ psychological states, market ambiguity and entropy. Some entropy can make the model have the effect of diversifying investment, which is very important. This paper mainly studies four kinds of entropy. First, we obtained four definitions of entropy from the literature, and gave the function of fuzzy entropy in different psychological states through strict mathematical proof. Then, we construct a fuzzy portfolio entropy decision model based on the investor’s psychological states, and compared it with the possibilistic mean–variance model. Then we presented a numerical example and compared the five different models established. By comparing the results, we find that: (a) The possibilistic mean–Shannon entropy model solves the problem of the possibility of excessive concentration in the possibilistic mean–variance model, but the dispersion is not enough. Conversely, the possibilistic mean–Yager entropy is over–emphasized due to the definition of its own function, such that it gave an investment pattern of equal weight distribution or approximate average distribution. (b) The results of possibilistic mean–proportional entropy can be said to be the middle status of the portfolios of possibilistic mean–Shannon entropy and possibilistic mean–Yager entropy. This portfolio not only achieves a certain rate of return, but also disperses the risk to some extent. (c) The lines of satisfaction for portfolios derived from different models are approximately U–shaped with the increase in return preference. (d) The possibilistic mean–Shannon entropy model tends to have the highest portfolio satisfaction with the same psychological state of the investor.

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Considering that most studies have taken the investors’ preference for risk into account but ignored the investors’ preference for assets, in this paper, we combine the prospect theory and possibility theory to provide investors with a portfolio strategy that meets investors’ preference for assets. Firstly, a novel reference point is proposed to give investors a comprehensive impression of assets. Secondly, the prospect return rate of assets is quantified as trapezoidal fuzzy number, and its possibilistic mean value and variance are regarded as prospect return and risk and then used to define the fuzzy prospect value. This new definition is presented to denote the score of an asset in investors’ subjective cognition. And then, a prospect asset filtering frame is proposed to help investors select assets according to their preference. When assets are selected, another new definition called prospect consistency coefficient is proposed to measure the deviation of a portfolio strategy from investors’ preference. Some properties of the definition are presented by rigorous mathematical proof. Based on the definition and its properties, a possibilistic model is constructed, which can not only provide investors optimal strategies to make profit and reduce risk as much as possible, but also ensure that the deviation between the strategies and investors’ preference is tolerable. Finally, a numerical example is given to validate the proposed method, and the sensitivity analysis of parameters in prospect value function and prospect consistency constraint is conducted to help investors choose appropriate values according to their preferences. The results show that compared with the general M-V model, our model can not only better satisfy investors’ preference for assets, but also disperse risk effectively.