The research and comparison of multi-objective portfolio based on intuitionistic fuzzy optimization

In this study, to deal with assets more realistically, we discuss the fuzzy multi-objective portfolio problem with a new vision of intuitionistic fuzzy sets. Essentially, considering security returns described as fuzzy variables, the corresponding mean-variance-skewness-entropy portfolio model is presented by using the degrees of acceptance and rejection as the objective functions. The main concern of this work is to transform the intuitionistic fuzzy multi-objective model into a single-objective model by three types of different methods. In addition to the intuitionistic fuzzy "min-max" operator method, this paper proposes the method of "max-min" operator from another novel aspect, as well as applies Compromise Programming (CP) and Nadir Compromise Programming (NCP). Besides, we consider three types of objective functions respectively, including p-norm, geometric mean, and extreme deviation. Then, inspired by Monte Carlo simulations, we design a new algorithm to solve the proposed model efficiently. Finally, some experiments are conducted in detail by using the data of Shanghai Stock Exchange (SSE) to illustrate our developed models. Several portfolio performance evaluation techniques are used to evaluate the performance of these models, and then give the comparison analysis among these models, which also indicates the superiority of the models we proposed in some respects.