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Stochasticity and ambiguity are two aspects of uncertainty in economic problems. In the case of investments in risky assets, this uncertainty is manifested in the uncertainty of future returns. On the contrary, the complexity of the economic phenomenon itself and the ambiguity inherent in human thinking and judgment are characterized by indistinct boundaries. For the same problem, research from different perspectives can often provide us with more comprehensive and systematic information. Currently, the expected value of return or the variance representing risk is still used as a rational investment criterion for both single-stage portfolios and multistage portfolios. However, in general, the greater the expected return of an investor, the greater the risk he should take. Different investors have different requirements for profitability, but regardless of their expected return, they always hope to find a set of portfolios that maximize the probability of achieving the expected rate of return. In this paper, after analyzing the development of portfolio investment theory research, we take fuzzy information processing as the entry point and systematically discuss the theory and methods of fuzzy modeling of portfolio investment decision-making from the perspective of fuzziness around the portfolio investment decision-making process. The results of the empirical analysis show that the existence of basis constraints affects investors’ investment strategies as well as their final returns, but there is a limit to the influence of basis constraints on portfolio performance, and investors can obtain optimal investment returns by selecting a reasonable number of securities to form a portfolio based on the characteristics of different securities.

Application of Algorithms of Constrained Fuzzy Models in Economic Management