Hesitant Fuzzy Decision-making And Game Methods And Applications Based On The Psychological Behavior Of Decision Makers

Due to the complexity and uncertainty of the decision-making environment,it is difficult for decision makers to give complete and accurate evaluation information about alternatives.In some decision-making problems,decision makers are more inclined to express their opinions by the hesitant fuzzy information rather than the real numbers.The hesitant fuzzy set,the hesitant fuzzy linguistic term set and the probabilistic hesitant fuzzy linguistic term set are employed as effective techniques and applied to many decision and game analysis methodologies.The probabilistic hesitant fuzzy linguistic term set,an extension of the hesitant fuzzy linguistic term set,considers the probability part of the linguistic variable,and the possible linguistic variables are allowed to be discontinuous.The purpose of multiple criteria decision making with hesitant fuzzy information is to establish a decision model that comprehensively analyzes and weighs the various alternatives based on the hesitant fuzzy decision-making information of the alternatives,and obtains the optimal alternative or the ranking of alternatives.The basis of game theory is decision analysis,which mainly studies the strategic interaction of multiple stakeholders.When there exists competition among decision-making parties,the players in the game fail to acquire all the accurate payment information of other players.How to solve the matrix game with the hesitant fuzzy payoff information is one of the most pivotal research directions of the uncertainty game theory.This thesis combines behavioral decision-making theory to carry out innovative research on the decision and game methods in the hesitant fuzzy environments:(1)Research on the decision-making methods with the hesitant fuzzy information(1)To deal with the conflict among hesitant fuzzy linguistic information,we propose a decision-making method based on the ER(Evidential Reasoning)algorithm.The ER algorithm is based on the distributed modeling framework and the evidence combination rules of Dempster-Shafer theory,which can effectively copy with the loss of evaluation information and the conflict of evidence.According to the prudent degrees of decision makers,the ?-cut of HFLTS taking the interval value form is proposed.Then,combined with the semantics of linguistic terms,the basic probability distributed model is constructed to assign the corresponding weights to the linguistic terms in the HFLTS,then the decision information is converted into the form of the probabilistic hesitant fuzzy linguistic term set.Finally,the ER algorithm is utilized to aggregate the decision information expressed by the form of the probabilistic hesitant fuzzy linguistic term set,and the alternatives are sorted according to the revised utility function.Compared with the HFL-VIKOR(Hesitant Fuzzy Linguistic Vlse Kriterijumska Optimizacija Ikompromisno Resenje)method,the hesitant fuzzy linguistic evidential reasoning method shows the advantages in the weight distribution of the linguistic term and ignorance information processing.(2)Considering the dynamic characteristics of the decision model,the dynamic reference point method with probabilistic hesitant fuzzy linguistic information based on the regret theory is proposed to deal with the dynamic decision-making problems.In view of the psychological characteristics of decision makers’ regret aversion,we revise the utility function and regret-rejoice function of the regret theory to adapt the probabilistic hesitant fuzzy linguistic decision information.In addition,the definition of probabilistic hesitant fuzzy linguistic time variable and the related operators are proposed to describe and aggregate the dynamic decision information.Finally,in order to maximize the the expectation-level of alternatives at the corresponding time point,the probabilistic hesitant fuzzy linguistic models based on the dynamic reference point method and the modified regret theory are constructed and solved.The probabilistic hesitant fuzzy linguistic dynamic reference point method not only introduces the prospect theory,but also considers the interrelationship in the multi-stage emergency decision making.Compared with other decision-making methods,the proposed method shows strong reliability and rationality.(3)Combining the regret theory and the water-filling algorithm,a thermodynamic decision-making method that simultaneously considers the quantity and quality of probabilistic hesitant fuzzy linguistic decision information is proposed.Some common thermodynamic parameters: energy,exergy,and entropy are introduced into the probabilistic hesitant fuzzy linguistic environment to solve the uncertain multiple criteria decision making by analogy to the quality,validity and imbalance of the probabilistic hesitant fuzzy linguistic information.Through self-comparison and comparison with other probabilistic hesitant fuzzy linguistic decision-making methods,a series of simulation experiments and non-parametric tests are conducted to verify the practicability and effectiveness of the regret theory and the water-filling algorithm in the probabilistic hesitant fuzzy linguistic thermodynamic method and the probabilistic hesitant fuzzy linguistic thermodynamic method.(2)According to the behavioral decision theory,research on the game theory with the hesitant fuzzy information(1)The Ambika method is introduced to solve the matrix game whose payoff values are represented by the hesitant fuzzy sets.Firstly,we investigate the reasonable solution and the solution of the HFMG(Hesitant Fuzzy Matrix Game)and the optimal mixed strategies of the players,which lay the foundation for solving the HFMG problems.In order to reduce the information loss when aggregating the payoff information of the HFMG,the probability part is added to the hesitant fuzzy elements,and the hesitant fuzzy elements are transformed into the hesitant fuzzy elements with probability.According to their preferences,the decision makers select the appropriate position function of the hesitant fuzzy element,and the weight of each hesitant fuzzy element is determined.The value and ambiguity indexes of the hesitant fuzzy element with probability are defined,and the Ambika method of HFMG is presented to obtain players’ optimal mixed strategies in the non-cooperative games.Compared with the dual hesitant matrix game method,the proposed HFMG method not only optimizes the aggregation method of the hesitant fuzzy sets,but also considers decision makers’ risk attitudes,which has certain theoretical significance and practical value.(2)From the perspective of the game between the decision maker and nature,the economic development and environmental protection are regarded as the two parties of the game,and the matrix game method under the hesitant fuzzy linguistic environment is established.According to the semantics of linguistic terms and the attitudes of decision makers,the weights of linguistic terms in the HFLTS are determined,and a new method of aggregating HFLTS is proposed.Combining with the improved prospect theory under the hesitant fuzzy linguistic environment,the constructed hesitant fuzzy linguistic programming model is transformed into a bi-objective nonlinear programming model.According to the defined value index and ambiguity index,the model can be further converted into a linear programming model to obtain the optimal mixed strategy for long-term sustainable economic development.The parameter analysis and comparative analysis illustrate the applicability and effectiveness of the proposed game method.(3)The application of the proposed methods and modelsWe discuss the applications of hesitant fuzzy decision and game methods.This thesis applies the proposed decision-making methods in the hazard level assessment of landslide dams in Wenchuan earthquake,the optimal strategy selection for local governments to respond to COVID-19 and the optimal solution selection in the floods in Tongnan District,Chongqing,respectively.The proposed game methods are applied to the optimal response strategy selection in the terrorism issue and the formulation of the economic development strategy of Sanjiangyuan National Nature Reserve.The above decision and game methods with the hesitant fuzzy information combine the characteristics of uncertain decision information and specific application scenarios,taking into account the influence of behavioral decision-making theory.The proposed methods not only entend uncertain decision-making and game theories and provide beneficial reference and support for further research,but also enrich the ideas and ways to solve practical problems.