Research On Portfolio Selection Model Based On Several Types Of Hesitant Fuzzy Sets

The fuzzy theory is useful in describing uncertain information and it has been applied successfully in portfolio selection.Specifically,the hesitant fuzzy set,which use a set of values to describe membership degree,is an important extension of the fuzzy theory.However,the research on portfolio selection under hesitant fuzzy environment is still at an early stage.Therefore,to help investors find optimal portfolios,we focus on the portfolio selection models based on the hesitant fuzzy set,probabilistic hesitant fuzzy set,and dual hesitant fuzzy set.The contributions are as follows.(1)The hesitant fuzzy element is used as the objective reference point of prospect value function in the existing hesitant fuzzy portfolio selection model based on prospect theory.However,investors may give their reference points objectively and certainly based on their satisfaction degrees,in this case the hesitant fuzzy element may be not useful.Therefore,we define a novel prospect value function using an interval as the reference point and discuss its properties.The theoretical result shows that the novel function is superior in calculation efficiency.Based on the novel function,we build a new hesitant fuzzy portfolio selection model and use a case study to illustrate the effectiveness of the model.(2)Since the downside risk is more consistent with investors’ risk intuitions,we extend the semi-variance to the hesitant fuzzy environment.We define a hesitant semi-variance and discuss its properties in theory.Moreover,a score-hesitant-semi-variance portfolio selection model is built.In the model,a parameter is used to describe the risk preferences of investors.Then,a case study shows that the model can not only meet the needs of investors with different risk preferences,but also has better returns than the score-deviation portfolio selection model.(3)Since the probabilistic hesitant fuzzy set includes the importance degrees of the elements,some researchers have proposed the hesitant VaR.However,it is mainly used in decision-making models instead of portfolio selection models.Therefore,we propose a probabilistic hesitant fuzzy portfolio selection model based on the hesitant VaR and safety level of score.Some examples are used to illustrate the effectiveness of the model and the necessity of the safety level of score.Then,we use a case study to show that the model is not only consistent with market rules,but can also diversify risks.(4)The dual hesitant fuzzy set is an important extension of the hesitant fuzzy set.However,the research on portfolio selection based on dual hesitant fuzzy set still need to be improved.Therefore,we extend the traditional mean-variance portfolio selection model to the dual hesitant fuzzy environment and build a score-deviation dual hesitant fuzzy portfolio selection model with investors’ information preferences and risk appetites.In the model,we use a parameter to show the different importance of membership degrees and non-membership degrees,which can represent investors’ information preferences.Then,we not only analyze the model in theory,but also use a case study to show the feasibility of the model.In conclusion,in this paper,the variance,semi-variance and value at risk are extended to hesitant fuzzy environment,probabilistic hesitant fuzzy environment and dual hesitant fuzzy environment.On this basis,we build some corresponding portfolio selection models.In the models,we use the prospect theory and some parameters to describe investors’ psychological behaviors,information preferences and risk appetites.Moreover,the theoretical analysis and case study are conduct to show the reasonability of the models.The result of this paper can not only enrich the research on hesitant fuzzy portfolio selection,but also help investors make decisions in practical.