Three-way decision(T-WD)theory is about thinking,problem solving,and computing in threes.Behavioral decision making(BDM)focuses on effective,cognitive,and social processes employed by humans for choosing the optimal o...Three-way decision(T-WD)theory is about thinking,problem solving,and computing in threes.Behavioral decision making(BDM)focuses on effective,cognitive,and social processes employed by humans for choosing the optimal object,of which prospect theory and regret theory are two widely used tools.The hesitant fuzzy set(HFS)captures a series of uncertainties when it is difficult to specify precise fuzzy membership grades.Guided by the principles of three-way decisions as thinking in threes and integrating these three topics together,this paper reviews and examines advances in three-way behavioral decision making(TW-BDM)with hesitant fuzzy information systems(HFIS)from the perspective of the past,present,and future.First,we provide a brief historical account of the three topics and present basic formulations.Second,we summarize the latest development trends and examine a number of basic issues,such as one-sidedness of reference points and subjective randomness for result values,and then report the results of a comparative analysis of existing methods.Finally,we point out key challenges and future research directions.展开更多
Decision-theoretic interval estimation requires the use of loss functions that, typically, take into account the size and the coverage of the sets. We here consider the class of monotone loss functions that, under qui...Decision-theoretic interval estimation requires the use of loss functions that, typically, take into account the size and the coverage of the sets. We here consider the class of monotone loss functions that, under quite general conditions, guarantee Bayesian optimality of highest posterior probability sets. We focus on three specific families of monotone losses, namely the linear, the exponential and the rational losses whose difference consists in the way the sizes of the sets are penalized. Within the standard yet important set-up of a normal model we propose: 1) an optimality analysis, to compare the solutions yielded by the alternative classes of losses;2) a regret analysis, to evaluate the additional loss of standard non-optimal intervals of fixed credibility. The article uses an application to a clinical trial as an illustrative example.展开更多
Multi-agent systems can solve scientific issues related to complex systems that are difficult or impossible for a single agent to solve through mutual collaboration and cooperation optimization.In a multi-agent system...Multi-agent systems can solve scientific issues related to complex systems that are difficult or impossible for a single agent to solve through mutual collaboration and cooperation optimization.In a multi-agent system,agents with a certain degree of autonomy generate complex interactions due to the correlation and coordination,which is manifested as cooperative/competitive behavior.This survey focuses on multi-agent cooperative optimization and cooperative/non-cooperative games.Starting from cooperative optimization,the studies on distributed optimization and federated optimization are summarized.The survey mainly focuses on distributed online optimization and its application in privacy protection,and overviews federated optimization from the perspective of privacy protection me-chanisms.Then,cooperative games and non-cooperative games are introduced to expand the cooperative optimization problems from two aspects of minimizing global costs and minimizing individual costs,respectively.Multi-agent cooperative and non-cooperative behaviors are modeled by games from both static and dynamic aspects,according to whether each player can make decisions based on the information of other players.Finally,future directions for cooperative optimization,cooperative/non-cooperative games,and their applications are discussed.展开更多
The authors regret that the photographic image in Fig. 4a of the published article was used in error, and therefore without proper referencing or permission from the originator or copyright holder. The image used in F...The authors regret that the photographic image in Fig. 4a of the published article was used in error, and therefore without proper referencing or permission from the originator or copyright holder. The image used in Fig. 4a of the original manuscript has been previously published by and remains under copyright by the Society for Mining, Metallurgy, and Exploration, Inc. (SME) associated with the following paper.Moalli S, Redmond S, Brox D, Procter P, Jezek D, van der Pouw Kraan M, Blanchet R, Kulka R. TBM Tunneling at the Ashlu Hydro Power Project, Squamish, BC. In: Almeraris G, Mariucci B. editors. Proceedings of Rapid Excavation and Tunnelling 2009. The Society for Mining,Metallurgy, and Exploration, Inc. (SME). 2009. pp. 1208e1217.To correct this error though this Corrigendum, Fig. 4 in this article is replaced with the following set of images. The caption remains unchanged from the original but is included here for convenience and clarity.展开更多
Feelings influence human beings’decision-making;therefore,incorporation of feeling factors in decision-making is very important.Regret and rejoice are very important emotional feelings that can have a great impact on...Feelings influence human beings’decision-making;therefore,incorporation of feeling factors in decision-making is very important.Regret and rejoice are very important emotional feelings that can have a great impact on decision-making if they are considered together.While regret has received most of the attention in related research,rejoice has been less considered even though it can greatly influence people’s preferences in decision-making.Furthermore,systematically incorporating regret and rejoice in the multicriteria decision-making(MCDM)modeling frameworks for decision-making has received little research attention.In this paper,we introduce a new multiattribute selection procedure that incorporates both regret and rejoice to select the best choice.We utilize the positional advantage operator concept to develop regret and rejoice mathematical equations,and prove them.The proposed MCDM procedure that incorporates these two emotional factors offers a decision-maker the flexibility to trade off some benefits in order to gain a state of psychological satisfaction.More specifically,regret and rejoice are presentedmathematically to enable the decision-maker to determine the values of regret and rejoice,and then make the decision in which the rejoice value is higher than the regret value.To test the performance of this new procedure,we apply it to three numerical examples proposed in previous works.The results are matched with those obtained by other methods such as the regret model,VIKOR,PROMETHEE I,and PROMETHEE II,thereby proving the efficacy of the new procedure.展开更多
In the consensus-reaching process(CRP),the actual utility of decision-makers(DMs)is often influenced by the psychological behavior of regret aversion.However,the influence of regret aversion on DMs’utilities is rarel...In the consensus-reaching process(CRP),the actual utility of decision-makers(DMs)is often influenced by the psychological behavior of regret aversion.However,the influence of regret aversion on DMs’utilities is rarely taken into account in the existing consensus models.The consensus-reaching problem of DMs with regret aversion is explored to maximize their perceived utilities under a limited budget.Firstly,three basic types of perceived utility functions are constructed based on the regret theory to describe the perceived utility of DMs with various preferences.Then,considering the limited budget and individual regret aversion,the maximum perceived utility consensus models based on types of left-skewed,right-skewed,middle-skewed,and heterogeneous utility preferences are proposed to achieve the consensus that maximizes the group perceived utility.After that,an example of land-transfer price negotiation in China is given to illustrate the validity of the proposed models.Finally,the model comparison and the sensitivity analysis are presented to reveal the influence of DMs’regret aversion on the CRP.The results suggest that the DMs’regret aversion will not affect left-skewed and right-skewed groups,but will affect the consensus results of middle-skewed and heterogeneous groups.展开更多
In optimal wind bidding strategy related literatures, it is usually assumed that the full distribution information (for example, the cumulative distribution function or the probability density function) of wind power ...In optimal wind bidding strategy related literatures, it is usually assumed that the full distribution information (for example, the cumulative distribution function or the probability density function) of wind power output is known. In real world applications, however, only very limited distribution information can be obtained. Therefore, the “optimal bidding strategy” obtained based on the hypothetical distribution may be far away from the true optimal one. In this paper, an optimal bidding strategy is obtained based on the minimax regret criterion. The salient feature of the new approach is that it requires only partial information of wind power distribution, for example, the expectation and the support set. Numerical test is then performed and the results suggest that the method established in this paper is effective.展开更多
Critical systems are typically complex systems that are required to perform reliably over a wide range of scenarios, or multistate world. Seldom does a single system exist that performs best for all plausible scenario...Critical systems are typically complex systems that are required to perform reliably over a wide range of scenarios, or multistate world. Seldom does a single system exist that performs best for all plausible scenarios. A robust solution, one that performs relatively well over a wide range of scenarios, is often the preferred choice for reduced risk at an acceptable cost. The alternative with the maximum expected utility may possess vulnerabilities that could be exploited. The best strategy is likely to be a hybrid solution. The von Neumann-Morgenstern Expected Utility Theory (EUT) would never select such a solution because, given its linear functional form, the expected utility of a hybrid solution cannot be greater than that of every constituent alternative. The continuity axiom and the independence axiom are assessed to be unrealistic for the problem of interest. Several well-known decision models are analyzed and demonstrated to be potentially misleading. The linear disappointment model modifies EUT by adding a term proportional to downside risk;however, it does not provide a mathematical basis for determining preferred hybrid solutions. The paper proposes a portfolio allocation model with stochastic optimization as a flexible and transparent method for defining choice problems and determining hybrid solutions for critical systems with desirable properties such as diversification and robustness.展开更多
In this paper, we first introduce the notion and model of generalized minimax regret equilibria with scalar set payoffs. After that, we study its general stability theorem under the conditions that the existence theor...In this paper, we first introduce the notion and model of generalized minimax regret equilibria with scalar set payoffs. After that, we study its general stability theorem under the conditions that the existence theorem of generalized minimax regret equilibrium point with scalar set payoffs holds. In other words, when the scalar set payoffs functions and feasible constraint mappings are slightly disturbed, by using Fort theorem and continuity results of set-valued mapping optimal value functions, we obtain a general stability theorem for generalized minimax regret equilibria with scalar set payoffs. At the same time, an example is given to illustrate our result.展开更多
基金supported in part by the National Natural Science Foundation of China(12271146,12161036,61866011,11961025,61976120)the Natural Science Key Foundation of Jiangsu Education Department(21KJA510004)Discovery Grant from Natural Science and Engineering Research Council of Canada(NSERC)。
文摘Three-way decision(T-WD)theory is about thinking,problem solving,and computing in threes.Behavioral decision making(BDM)focuses on effective,cognitive,and social processes employed by humans for choosing the optimal object,of which prospect theory and regret theory are two widely used tools.The hesitant fuzzy set(HFS)captures a series of uncertainties when it is difficult to specify precise fuzzy membership grades.Guided by the principles of three-way decisions as thinking in threes and integrating these three topics together,this paper reviews and examines advances in three-way behavioral decision making(TW-BDM)with hesitant fuzzy information systems(HFIS)from the perspective of the past,present,and future.First,we provide a brief historical account of the three topics and present basic formulations.Second,we summarize the latest development trends and examine a number of basic issues,such as one-sidedness of reference points and subjective randomness for result values,and then report the results of a comparative analysis of existing methods.Finally,we point out key challenges and future research directions.
文摘Decision-theoretic interval estimation requires the use of loss functions that, typically, take into account the size and the coverage of the sets. We here consider the class of monotone loss functions that, under quite general conditions, guarantee Bayesian optimality of highest posterior probability sets. We focus on three specific families of monotone losses, namely the linear, the exponential and the rational losses whose difference consists in the way the sizes of the sets are penalized. Within the standard yet important set-up of a normal model we propose: 1) an optimality analysis, to compare the solutions yielded by the alternative classes of losses;2) a regret analysis, to evaluate the additional loss of standard non-optimal intervals of fixed credibility. The article uses an application to a clinical trial as an illustrative example.
基金supported in part by the National Natural Science Foundation of China(Basic Science Center Program:61988101)the Sino-German Center for Research Promotion(M-0066)+2 种基金the International(Regional)Cooperation and Exchange Project(61720106008)the Programme of Introducing Talents of Discipline to Universities(the 111 Project)(B17017)the Program of Shanghai Academic Research Leader(20XD1401300).
文摘Multi-agent systems can solve scientific issues related to complex systems that are difficult or impossible for a single agent to solve through mutual collaboration and cooperation optimization.In a multi-agent system,agents with a certain degree of autonomy generate complex interactions due to the correlation and coordination,which is manifested as cooperative/competitive behavior.This survey focuses on multi-agent cooperative optimization and cooperative/non-cooperative games.Starting from cooperative optimization,the studies on distributed optimization and federated optimization are summarized.The survey mainly focuses on distributed online optimization and its application in privacy protection,and overviews federated optimization from the perspective of privacy protection me-chanisms.Then,cooperative games and non-cooperative games are introduced to expand the cooperative optimization problems from two aspects of minimizing global costs and minimizing individual costs,respectively.Multi-agent cooperative and non-cooperative behaviors are modeled by games from both static and dynamic aspects,according to whether each player can make decisions based on the information of other players.Finally,future directions for cooperative optimization,cooperative/non-cooperative games,and their applications are discussed.
文摘The authors regret that the photographic image in Fig. 4a of the published article was used in error, and therefore without proper referencing or permission from the originator or copyright holder. The image used in Fig. 4a of the original manuscript has been previously published by and remains under copyright by the Society for Mining, Metallurgy, and Exploration, Inc. (SME) associated with the following paper.Moalli S, Redmond S, Brox D, Procter P, Jezek D, van der Pouw Kraan M, Blanchet R, Kulka R. TBM Tunneling at the Ashlu Hydro Power Project, Squamish, BC. In: Almeraris G, Mariucci B. editors. Proceedings of Rapid Excavation and Tunnelling 2009. The Society for Mining,Metallurgy, and Exploration, Inc. (SME). 2009. pp. 1208e1217.To correct this error though this Corrigendum, Fig. 4 in this article is replaced with the following set of images. The caption remains unchanged from the original but is included here for convenience and clarity.
基金This research was funded by the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University,through the Research Funding Program(Grant No.FRP-1440-31).
文摘Feelings influence human beings’decision-making;therefore,incorporation of feeling factors in decision-making is very important.Regret and rejoice are very important emotional feelings that can have a great impact on decision-making if they are considered together.While regret has received most of the attention in related research,rejoice has been less considered even though it can greatly influence people’s preferences in decision-making.Furthermore,systematically incorporating regret and rejoice in the multicriteria decision-making(MCDM)modeling frameworks for decision-making has received little research attention.In this paper,we introduce a new multiattribute selection procedure that incorporates both regret and rejoice to select the best choice.We utilize the positional advantage operator concept to develop regret and rejoice mathematical equations,and prove them.The proposed MCDM procedure that incorporates these two emotional factors offers a decision-maker the flexibility to trade off some benefits in order to gain a state of psychological satisfaction.More specifically,regret and rejoice are presentedmathematically to enable the decision-maker to determine the values of regret and rejoice,and then make the decision in which the rejoice value is higher than the regret value.To test the performance of this new procedure,we apply it to three numerical examples proposed in previous works.The results are matched with those obtained by other methods such as the regret model,VIKOR,PROMETHEE I,and PROMETHEE II,thereby proving the efficacy of the new procedure.
基金National Natural Science Foundation of China(No.71901058)Fundamental Research Funds for the Central Universities,China(No.2232018H-07)。
文摘In the consensus-reaching process(CRP),the actual utility of decision-makers(DMs)is often influenced by the psychological behavior of regret aversion.However,the influence of regret aversion on DMs’utilities is rarely taken into account in the existing consensus models.The consensus-reaching problem of DMs with regret aversion is explored to maximize their perceived utilities under a limited budget.Firstly,three basic types of perceived utility functions are constructed based on the regret theory to describe the perceived utility of DMs with various preferences.Then,considering the limited budget and individual regret aversion,the maximum perceived utility consensus models based on types of left-skewed,right-skewed,middle-skewed,and heterogeneous utility preferences are proposed to achieve the consensus that maximizes the group perceived utility.After that,an example of land-transfer price negotiation in China is given to illustrate the validity of the proposed models.Finally,the model comparison and the sensitivity analysis are presented to reveal the influence of DMs’regret aversion on the CRP.The results suggest that the DMs’regret aversion will not affect left-skewed and right-skewed groups,but will affect the consensus results of middle-skewed and heterogeneous groups.
文摘In optimal wind bidding strategy related literatures, it is usually assumed that the full distribution information (for example, the cumulative distribution function or the probability density function) of wind power output is known. In real world applications, however, only very limited distribution information can be obtained. Therefore, the “optimal bidding strategy” obtained based on the hypothetical distribution may be far away from the true optimal one. In this paper, an optimal bidding strategy is obtained based on the minimax regret criterion. The salient feature of the new approach is that it requires only partial information of wind power distribution, for example, the expectation and the support set. Numerical test is then performed and the results suggest that the method established in this paper is effective.
文摘Critical systems are typically complex systems that are required to perform reliably over a wide range of scenarios, or multistate world. Seldom does a single system exist that performs best for all plausible scenarios. A robust solution, one that performs relatively well over a wide range of scenarios, is often the preferred choice for reduced risk at an acceptable cost. The alternative with the maximum expected utility may possess vulnerabilities that could be exploited. The best strategy is likely to be a hybrid solution. The von Neumann-Morgenstern Expected Utility Theory (EUT) would never select such a solution because, given its linear functional form, the expected utility of a hybrid solution cannot be greater than that of every constituent alternative. The continuity axiom and the independence axiom are assessed to be unrealistic for the problem of interest. Several well-known decision models are analyzed and demonstrated to be potentially misleading. The linear disappointment model modifies EUT by adding a term proportional to downside risk;however, it does not provide a mathematical basis for determining preferred hybrid solutions. The paper proposes a portfolio allocation model with stochastic optimization as a flexible and transparent method for defining choice problems and determining hybrid solutions for critical systems with desirable properties such as diversification and robustness.
文摘In this paper, we first introduce the notion and model of generalized minimax regret equilibria with scalar set payoffs. After that, we study its general stability theorem under the conditions that the existence theorem of generalized minimax regret equilibrium point with scalar set payoffs holds. In other words, when the scalar set payoffs functions and feasible constraint mappings are slightly disturbed, by using Fort theorem and continuity results of set-valued mapping optimal value functions, we obtain a general stability theorem for generalized minimax regret equilibria with scalar set payoffs. At the same time, an example is given to illustrate our result.