###### Abstract  
This paper investigates a fuzzy portfolio selection problem with guaranteed reliability, in which the fuzzy variables are used to capture the uncertain returns of different securities. To effectively handle the fuzziness in a mathematical way, a new expected value operator and variance of fuzzy variables are defined based on the \(m_{\lambda}\) measure that is a linear combination of the possibility measure and necessity measure to balance the pessimism and optimism in the decision-making process. To formulate the reliable portfolio selection problem, we particularly adopt the expected total return and standard variance of the total return to evaluate the reliability of the investment strategies, producing three risk-guaranteed reliable portfolio selection models. To solve the proposed models, an effective genetic algorithm is designed to generate the approximate optimal solution to the considered problem. Finally, the numerical examples are given to show the performance of the proposed models and algorithm. portfolio selection problem; \(m_{\lambda}\) measure; expected value operator; genetic algorithm +
Footnote †: journal:  
0000-0001-5000-6999-4000][PERSON] 0000-0001-5002-3886][PERSON] 0000-0002-3886-2233]M.J.H.M. for the portfolio, and an investment strategy is called a feasible plan if the variance of its random return is not over this threshold. Afterwards, for the stochastic portfolio selection problem, a variety of existing research works focus on improving or extending this type of model to more complex decision environments. For instance, [PERSON] [3] investigated a mean-variance-based portfolio selection problem in a complete market with unbounded random coefficients, which was solved by the stochastic linear-quadratic control theory and the Lagrangian method. [PERSON] et al. [4] explored a continuous-time mean-variance portfolio selection problem with random market parameters and a random time horizon in an incomplete market, which was formulated as a linear constrained stochastic linear quadratic optimal control problem. [PERSON] and [PERSON] [5] considered a multi-period portfolio selection problem with market random uncertainty of asset prices. They formulated the problem as a two-stage stochastic mixed-integer program with recourse and designed a simplification and hybrid solution method to solve the problem of interest. [PERSON] and [PERSON] [6] considered three indexes to model the portfolio selection problem, including the expected value, semivariance and conditional value-at-risk. A hybrid algorithm with a genetic algorithm and a particle swarm optimization algorithm was designed to solve the proposed model. [PERSON] et al. [7] estimated the expected returns by sampling from a multivariate probability model that explicitly incorporated distributional asymmetries to enhance the performance of mean-variance portfolio selection. [PERSON] et al. [8] proposed three multi-period behavioral portfolio selection models under cumulative prospect theory. [PERSON] et al. [9] discussed a mean-variance portfolio selection problem under a constant elasticity of variance model on the basis of backward stochastic Riccati equation. [PERSON] et al. [10] resolved the high-cardinality of mean-variance portfolios through applying the semi-definite relaxation method to a cardinality-constrained optimal tangent portfolio selection model. [PERSON] and [PERSON] [11] investigated a mean-variance portfolio selection problem with regime switching under the constraint of short-selling being prohibited. [PERSON] and [PERSON] [12] further enriched the literature of the mean-variance portfolio selection by considering correlation risk among risky asset returns. [PERSON] [13] proposed a quantile-based risk measure, which is defined using the modified loss distribution according to the decision maker's risk and loss aversion. For other research, interested readers can refer to [PERSON] et al. [14], [PERSON] and [PERSON] [15], [PERSON] et al. [16], [PERSON] [17], etc.