Purpose

This paper proposes a fuzzy random multi-objective portfolio model with different entropy measures and designs a hybrid algorithm to solve the proposed model.

Design/methodology/approach

Because random uncertainty and fuzzy uncertainty are often combined in a real-world setting, the security returns are considered as fuzzy random numbers. In the model, the authors also consider the effects of different entropy measures, including Yager's entropy, Shannon's entropy and min-max entropy. During the process of solving the model, the authors use a ranking method to convert the expected return into a crisp number. To find the optimal solution efficiently, a fuzzy programming technique based on artificial bee colony (ABC) algorithm is also proposed.

Findings

(1) The return of optimal portfolio increases while the level of investor risk aversion increases. (2) The difference of the investment weights of the optimal portfolio obtained with Yager's entropy are much smaller than that of the min–max entropy. (3) The performance of the ABC algorithm on solving the proposed model is superior than other intelligent algorithms such as the genetic algorithm, differential evolution and particle swarm optimization.

Originality/value

To the best of the authors' knowledge, no effect has been made to consider a fuzzy random portfolio model with different entropy measures. Thus, the novelty of the research is constructing a fuzzy random multi-objective portfolio model with different entropy measures and designing a hybrid fuzzy programming-ABC algorithm to solve the proposed model.

中文翻译：

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基于人工蜂群算法的基于模糊规划的不同熵测度的模糊随机多目标投资组合模型

目的

本文提出了一种具有不同熵测度的模糊随机多目标投资组合模型，并设计了一种混合算法来求解该模型。

设计/方法/方法

由于随机不确定性和模糊不确定性通常在现实世界中结合使用，因此证券收益被视为模糊随机数。在模型中，作者还考虑了不同熵度量的影响，包括 Yager 熵、Shannon 熵和 min-max 熵。在求解模型的过程中，作者使用排序的方法将期望收益转化为一个清晰的数字。为了有效地找到最优解，还提出了一种基于人工蜂群（ABC）算法的模糊规划技术。

发现

(1) 最优投资组合的回报率随着投资者风险厌恶程度的增加而增加。(2) 用Yager熵得到的最优投资组合的投资权重之差远小于min-max熵。(3) ABC算法对所提模型的求解性能优于遗传算法、差分进化和粒子群优化等其他智能算法。

原创性/价值

据作者所知，考虑具有不同熵测度的模糊随机投资组合模型没有任何效果。因此，该研究的新颖之处在于构建具有不同熵测度的模糊随机多目标投资组合模型，并设计混合模糊规划-ABC算法来求解所提出的模型。