Decision-Making Method Based On Hesitant Fuzzy Linguisitic Information And Its Application In Portfolio Selection

Portfolio theory has been a hot topic in the field of finance since its inception,the returns of financial assets exhibit fuzzy and uncertain characteristics due to the random cyclical fluctuations of the financial system itself and the asymmetry of market information.In addition,the Since investors have different risk preferences and it is difficult to be a "rational economic man",the return of financial assets is largely affected by investors’ investment preferences and trading behaviors.Therefore,this research addresses the real-world problem of portfolio selection in finance by combining qualitative analysis of investors with quantitative calculation of portfolio models,and solves the scientific problems of single-person single-criterion,single-person multi-criteria,multi-person multi-criteria,and non-cooperative multi-person multi-criteria portfolio selection based on the quantitative scoring of security returns under different investment decision scenarios obtained by using hesitant fuzzy linguistic decision-making methods,respectively.The main innovative results of the research are as follows.Firstly,the study of portfolio selection based on hesitant fuzzy linguistic single-person single-criterion decision-making model.A comprehensive hesitant fuzzy linguistic portfolio evaluation system is established with the research framework of single investor’s comprehensive evaluation of different security underlying.The quantitative scores about the security underlying are obtained by transforming the natural linguistic evaluation of investors into hesitant fuzzy linguistic evaluation.Further,the return maximizing and risk minimizing hesitant fuzzy linguistic portfolio models are proposed for three types of investors with aggressive,prudent and conservative risk preferences,respectively.Finally,a comparative analysis between the hesitant fuzzy linguistic portfolio strategy and other fuzzy portfolio strategies is conducted through numerical simulation to verify the rationality and effectiveness of the proposed models.Secondly,the study of portfolio selection based on hesitant fuzzy linguistic single-person multi-criteria decision-making model.Based on the comprehensive evaluation of securities,the evaluation of securities is further extended to a multi-criteria decision perspective.In order to better express the psychological changes of investors when facing different degrees of gains and losses,a variable subscript hesitant fuzzy linguistic multi-criteria portfolio evaluation system and a quantitative system are constructed with reference to the cumulative prospect theory,and the quantitative scores of the returns of the securities underlying are obtained under the consideration of different evaluation criteria weights.The hesitant fuzzy linguistic multi-criteria portfolio models are constructed for three types of investors with aggressive,prudent and conservative risk preferences to maximize returns and minimize risks,respectively.Finally,numerical simulations are used to compare and analyze the portfolio strategies of different types of investors and other fuzzy portfolio strategies to verify the rationality and effectiveness of the proposed models and methods.Thirdly,the study of portfolio selection based on hesitant fuzzy linguistic multi-criteria group decision-making model.The selection method of optimal portfolio under multi-criteria decision-making scenario is proposed for an investment committee composed of multiple investors.Considering the influence of investors’ weights and evaluation criteria’ weights on the investment committee’s group decision-making,the final quantitative scores of securities’underlying returns are obtained by constructing an evaluation system and quantification system for multi-criteria group decision-making based on variable subscript hesitant fuzzy linguistic term set.Further,the optimal portfolio strategy under the hesitant fuzzy linguistic multi-criteria group decision-making scenario is obtained by solving the corresponding portfolio model.Finally,numerical simulation is used to compare and analyze the portfolio strategies of investment committees with different investment styles to obtain the effective frontier for different types of investment committees’ portfolios.Fourthly,the study of portfolio selection based on hesitant fuzzy linguistic multi-criteria group decision-making model in the presence of non-cooperative behavior.Based on the original study,the presence of non-cooperative behavior in the group decision-making opinions generated by the investment committee is further considered.In order to reach an effective consensus in group decision-making and to maximize the restoration of each investor’s analytical viewpoint,the research construct a hesitant fuzzy linguistic trust matrix,preference matrix and decision-making matrix based on the non-cooperative variable subscript hesitant fuzzy linguistic multi-criteria group decision-making portfolio evaluation system,detect and correct the non-cooperative behavior in group decision-making by the variable subscript hesitant fuzzy linguistic group decision-making consensus reaching system,obtain the quantitative scores of securities returns of group decision-making that satisfy the consistency level,and then solve the optimal portfolio of hesitant fuzzy linguistic multi-criteria group decision-making with non-cooperative behavior.Finally,numerical simulations are used to compare and analyze the portfolio strategies of investment committees with different investment styles as well as the portfolio strategies before and after reaching consensus in group decision making to verify the feasibility and superiority of the proposed model and method.In general,unlike previous studies on constructing investment portfolios,the decision-making method based on hesitant fuzzy linguistic information takes into account the risk preferences,psychological perceptions,and behavioral changes of investors in the investment decision-making process,and is also more consistent with the terminology used in the decision-making evaluation of actual investment scenarios.By studying the psychological and behavioral factors of investors in the decision-making process,it is possible to integrate investors’ subjective judgments with objective market information,thus realizing the mutual unification of qualitative investor behavior analysis and quantitative portfolio construction methods.In addition,this thesis forms a complete portfolio analysis and evaluation system by the main research lines of single-person single-criterion decision-making,single-person multi-criteria decision-making,multi-criterion group decision-making and multi-criteria group decision-making with non-cooperative behavior.Different investors can match the corresponding investment decision scenarios according to their actual situations,and then choose specific portfolio evaluation methods to get a capital allocation scheme that matches the investors’ personal investment objectives.