Three-Way Behavioral Decision Making With Hesitant Fuzzy Information Systems:Survey and Challenges

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.

Bayesian Set Estimation with Alternative Loss Functions: Optimality and Regret Analysis

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.

要他们道歉真的好难——谈“regret”,“sorry”和“apologize”的政治语辞区别

道歉是违背国际法义务的国际法主体对受害方的损害予以精神上的补偿所采取的法律责任形式。《奥本海国际法》指出:"不法行为者方面的正式道歉通常是必要的。"然而,自诩"文明世界"的美国却对其屡屡损害他国及其人民的权利和利益的行为拒不作出道歉。同样,其国民彬彬有礼的日本至今仍迟迟不对其侵略亚洲的历史事实作出诚恳的正式书面道歉。从美国对其他主权国家及人民的侵害并拒绝为之道歉的案例和日本对其侵略史所采取的否定、美化、甚至是颠倒黑白的态度与言行看美国、日本在对待其造成的对他国主权和人民利益受损的问题上难得作出道歉的个中缘由。

分布式在线交替方向乘子法

针对如何对分布式网络采集的数据进行在线学习的问题,提出了一种基于交替方向乘子法(ADMM)的分布式在线学习优化算法——分布式在线交替方向乘子法(DOM)。首先,针对分布式在线学习需要各节点根据新采集的数据来更新本地估计,同时保持网络中所有节点的估计趋于一致这一问题,建立了数学模型并设计DOM算法对其进行求解。其次,针对分布式在线学习问题定义了Regret界,用以表征在线估计的性能;证明了当本地即时损失函数是凸函数时,DOM算法是收敛的,并给出了其收敛速度。最后,通过数值仿真实验结果表明,相比现有的分布式在线梯度下降法(DOGD)和分布式在线自主学习算法(DAOL),所提出的DOM算法具有更快的收敛性能。

Cooperative and Competitive Multi-Agent Systems:From Optimization to Games

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.

分布式在线条件梯度优化算法

针对现有分布式在线优化算法所面临的高维约束难以计算的问题,提出一种分布式在线条件梯度优化算法(Distributed Online Conditional Gradient Optimization Algorithm,DOCG)。首先,通过多个体网络节点间的相互协作进行数据采集,并通过共享采集的信息更新局部估计,同时引入反映环境变化的局部即时损失函数。然后,该算法利用历史梯度信息进行加权平均,提出一种新的梯度估计方案,其用线性优化步骤替代投影步骤,避免了投影运算在高维约束时难以计算的问题。最后,通过分析表征在线估计性能的Regret界,证明了所提DOCG算法的收敛性。利用低秩矩阵填充问题进行仿真验证,结果表明,相比于现有分布式在线梯度下降法(DOGD),所提DOCG算法具有更快的收敛速度。

快速在线分布式对偶平均优化算法

为提高分布式在线优化算法的收敛速度,对底层网络拓扑依次添边,提出一种快速的一阶分布式在线对偶平均优化(FODD)算法。首先,对于分布式在线优化问题,运用添边方法使所选的边与网络模型快速混合,进而建立数学模型并设计FODD算法对其进行优化求解。其次,揭示了网络拓扑和在线分布式对偶平均收敛速度之间的关系,通过提高底层拓扑网络的代数连通度改进了Regret界,将在线分布式对偶平均(ODDA)算法从静态网络拓展到时变网络拓扑上,并证明了FODD算法的收敛性,同时解析地给出了收敛速度。最后的数值仿真表明:和ODDA算法相比,所提出的FODD算法具有更快的收敛速度。

Optimal paths planning in dynamic transportation networks with random link travel times

A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in specific time-dependent networks. A label setting algorithm was designed and tested to find travelers' robust optimal path in a sampled STD network with computation complexity of O(n2+n·m). The validity of the robust approach and the designed algorithm were confirmed in the computational tests. Compared with conventional probability approach, the proposed approach is simple and efficient, and also has a good application prospect in navigation system.

Corrigendum to “Verification of a laboratory-based dilation model for in situ conditions using continuum models” [J Rock Mech Geotech Eng6 (2014) 522e534]

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.

基于Bandit反馈的在线分布式镜面下降算法

针对在线分布式优化中一类损失函数梯度信息获取困难的问题,提出一种基于Bandit反馈的在线分布式镜面下降(ODMD-B)算法.首先,推广在线分布式镜面梯度下降(ODMD)算法到免梯度的情形,提出了一种新的仅利用函数值信息来对梯度进行估计的方法即Bandit反馈,其关键在于利用损失函数值信息逼近梯度信息,能有效克服梯度信息难以获取或计算复杂的困难.然后,给出算法的收敛性分析.结果表明算法的收敛速度为O(T),其中T是迭代次数.最后,使用投资组合选择模型进行了数值仿真实验.实验结果表明,ODMD-B算法的收敛速度与已有的ODMD算法的收敛速度接近.对比ODMD算法,本文所提出算法的优点在于仅仅使用了计算花费较小的函数值信息,使其更适用于梯度信息难以获取的优化问题.

Multi-Attribute Selection Procedures Based on Regret and Rejoice for the Decision-Maker

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.

Maximum Group Perceived Utility Consensus Models Considering Regret Aversion

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.

The effects of attributes and buyer regret on overall satisfaction

The current study represents an attempt at exploring product attribute, service attribute evaluation, and buyer regret influence overall satisfaction in the buyer decision context. The data used in the project were collected as part of a large study of buyer regret. The sampling frame consisted of automobile purchases in Taiwan We have collected yield 600 questionnaires, by screening out 44 questionnaires, including those missing value or incomplete answer, and finally a usable sample of 556 questionnaires were utilized in this study. The results reinforce the finding form early research that the concept of buyer regret plays an important role for automobile purchases in the buyer decision. Results show that higher evaluations of service and product attributes lead to less buyer regret, and lower buyer regret will likely to increase overall satisfaction. Specifically, the finding indicates that buyer regret mediates the effects of the attributes on overall satisfactions. Implications for marketing theory and practitioners are discussed, and possible directions for future research are sketched.

Wind Power Bidding Strategy Based on the Minimax Regret Criterion with Limited Distribution Information

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.

基于Bandit反馈的分布式在线对偶平均算法

为解决梯度信息难以获取的分布式在线优化问题,提出了一种基于Bandit反馈的分布式在线对偶平均(DODA-B)算法。首先,该算法对原始梯度信息反馈进行了改进,提出了一种新的梯度估计,即Bandit反馈,利用函数值信息去近似原损失函数的梯度信息,克服了求解复杂函数梯度存在的计算量大等问题。然后,给出了该算法的收敛性分析,结果表明,Regret界的收敛速度为O(Tmax{k,1-k}),其中T是最大迭代次数。最后,利用传感器网络的一个特例进行了数值模拟计算,计算结果表明,所提算法的收敛速度与现有的分布式在线对偶平均(DODA)算法的收敛速度接近。与DODA算法相比,所提出算法的优点在于只考虑了函数值信息,使其更适用于梯度信息获取困难的实际问题。

Optimization of Critical Systems for Robustness in a Multistate World

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.

Stability of Generalized Minimax Regret Equilibria with Scalar Set Payoff

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.

The Influence Factors on Regret Emotion Responsibility and Perceived Control

When people realize or imagine that ＂if you have not taken the same choices as before, the result will be better＂, which kind of experience is called a regret emotion. The purpose of this study is to prove the relationship between regret emotions and a sense of responsibility and control. The results show that the individual＇s sense of responsibility and regret that there is a positive correlation and there is a negative correlation between the control and regret, which is not match the previous part of the study so as to be further explored. At the same time, we found that the regret tendencies in the personality can be explained as some of the regret experiencing in the specific situation. When people realize or imagine that ＂if the choice is not the same as before that things are getting better now＂, they will feel regret.

切换网络下加速分布式在线加权对偶平均算法

研究了切换网络下加速分布式在线加权对偶平均算法,提出了A-DOWDA算法。首先利用加权因子对对偶变量进行加权,其次在有向切换网络是周期强连通,且对应的邻接矩阵是随机的而非双随机的条件下,加速了算法的收敛速率,最后通过数值实验验证了算法的可行性。

Minimum Regret Climate Policy with Act-Then-Learn Decision-A New Model Framework under Long-Term Uncertainties

The technology investment strategy under uncertainty is the key subject. However, the expected utility maximization often employed as the decision process fails to consider the high risk with low probability cases. On the other hand, the existing min-max regret strategy tends to be dominated by the ＂worst assumption＂ regardless of its probability. This research proposes a new framework by formulating the regret by the Minkowski＇s generalized distance. The authors then apply the formulation to the IAM （integrated assessment model） MARIA. This study focuses on the uncertainties of CCS （carbon capture and storage） costs and the global warming damages. This formulation is then extended to the multi-stage decision frame, known as ATL （act-then-learn） method. The simulation results suggest that the substantial changes in CCS and nuclear deployment strategies depending on the future uncertainty scenarios. The results also suggest that the minimum regret strategy favors the capital accumulation in the early stage.