A new fuzzy random multi-objective portfolio model with different entropy measures using fuzzy programming based on artificial bee colony algorithm

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.