Black Swans,New Nostradamuses,Voodoo decision theories,and the science of decision making in the face of severe uncertainty

The recent global financial crisis, natural disasters, and ongoing debate on global warming and climate change are a stark reminder of the huge challenges that severe uncertainty presents in decision and policy making. My objective in this paper is to look at some of the issues that need to be taken into account in the modeling and analysis of decision problems that are subject to severe uncertainty, paying special attention to some of the misconceptions that are being promulgated in this area. I also examine two diametrically opposed approaches to uncertainty. One, that emphasizes that the difficulties encountered in the modeling, analysis, and solution of decision problems in the face of severe uncertainty are in fact insurmountable, and another that claims to provide, against all odds, a reliable strategy for a successful handling of situations subject to severe uncertainty.     

深度不确定环境下的决策分析方法—–研究现状与展望

复杂、重大的决策活动经常会面临深度不确定的决策环境,其决策难度和风险远超一般不确定环境下的决策。自21世纪以来,对深度不确定环境下决策分析方法的研究已成为决策分析领域新的重要方向之一。对此,首先梳理了该领域的研究现状,总结了深度不确定环境下决策问题的特征和难点,分类阐述了4种主要方法的起源与发展、核心思想、实现步骤和典型应用;然后进行了案例分析;最后展望了该领域未来的研究方向。     

Robust control under worst‐case uncertainty for unknown nonlinear systems using modified reinforcement learning

Reinforcement learning (RL) is an effective method for the design of robust controllers of unknown nonlinear systems. Normal RLs for robust control, such as actor‐critic (AC) algorithms, depend on the estimation accuracy. Uncertainty in the worst case requires a large state‐action space, this causes overestimation and computational problems. In this article, the RL method is modified with the k‐nearest neighbor and the double Q‐learning algorithm. The modified RL does not need the neural estimator as AC and can stabilize the unknown nonlinear system under the worst‐case uncertainty. The convergence property of the proposed RL method is analyzed. The simulations and the experimental results show that our modified RLs are much more robust compared with the classic controllers, such as the proportional‐integral‐derivative, the sliding mode, and the optimal linear quadratic regulator controllers.     

Robust Analysis of Discrete‐Time Lur'e Systems with Slope Restrictions Using Convex Optimization

This paper considers robust stability and robust performance analysis for discrete‐time linear systems subject to nonlinear uncertainty. The uncertainty set is described by memoryless, time‐invariant, sector bounded, and slope restricted nonlinearities. We first give an overview of the absolute stability criterion based on the Lur'e‐Postkinov Lyapunov function, along with a frequency domain condition. Subsequently, we derive sufficient conditions to compute the upper bounds of the worst case H₂ and worst case H∞ performance. For both robust stability testing and robust performance computation, we show that these sufficient conditions can be readily and efficiently determined by performing convex optimization over linear matrix inequalities.     

Data envelopment analysis and robust optimization: A review

This paper reviews the milestone approaches for handling uncertainty in data envelopment analysis (DEA). This paper presents the detailed classifications of robust data envelopment analysis (RDEA). RDEA is appropriate for measuring the efficiencies of decision-making units in the presence of the data and distributional uncertainties. This paper reviews scenario-based and uncertainty set of DEA models. It covers 73 studies from 2008 to 2019. The paper concludes with suggestions about the guidelines for future researches in the field of RDEA.     

不确定性机械系统的最优鲁棒控制设计: 模糊法

针对不确定性机械系统,提出了一种新的最优鲁棒控制方法.本文用模糊法去描述机械系统中的不确定性.机械系统的性能要求是确定的(保证最低要求),同时也是模糊的(成本控制里用到).所提出的控制方法是确定的,而不是基于假设的规则.经过严格的理论证明,控制系统最终可达到理想的性能指标.基于模糊信息,本文设计了一个性能指标(综合成本,包括系统的平均模糊性能和控制成本).通过最小化此性能指标,可解决控制的最优设计问题.这种最优设计方法可得到唯一的解析形式的最优解.总的来说,这种最优鲁棒控制方法较为系统,能够保证确定的系统性能得以实现,同时控制成本最小.最后,本文选了一个机械系统作为例子.     

Robust multi‐response surface optimization: a posterior preference approach

This paper discusses the use of multi‐response surface optimization (MRSO) to select the preferred solutions from among various non‐dominated solutions (NDS). Since MSRO often involves conflicting responses, the decision‐maker's (DM) preference information should be included in the model in order to choose the preferred solutions. In some approaches this information is added to the model after the problem is solved. In contrast, this paper proposes a three‐stage method for solving the problem. In the first stage, a robust approach is used to construct a regression model. In the second phase, non‐dominated solutions are generated by the ε‐constraint approach. The robust solutions obtained in the third phase are NDS that are more likely to be Pareto solutions during consecutive iterations. A simulation study is then presented to show the effective performance of the proposed approach. Finally, a numerical example from the literature is brought in to demonstrate the efficiency and applicability of the proposed methodology.     

Spatial strategies in a generalized spatial prisoner’s dilemma

Many strategies, such as tit-for-tat, have been proposed in the iterated prisoner’s dilemma (IPD) in which the prisoner’s dilemma (PD) is carried out repeatedly with two players. A spatial version of the iterated prisoner’s dilemma (SPD) has been studied, where a player at each site plays the IPD game with all the players in the neighborhood. However, the strategies studied in the SPD consider the past actions of a single opponent only. We studied spatial strategies that depend on the configuration of actions taken by all neighbors (as opposed to conventional temporal strategies). Since generosity can be considered as a spatial strategy, we first investigate the generosity required when an action error is involved. We also propose several spatial strategies that outperform many others.This work was presented, in part, at the 9th International Symposium on Artificial Life and Robotics, Oita, Japan, January 28–30, 2004     

Uncertainty evaluation for a Dezert–Smarandache theory-based localization problem

Dezert–Smarandache theory (DSmT) is selected as the fusion method in a decision making system. To compare sensor fusion results, an uncertainty analysis is performed at each level of the decision making system. The supervision is based on the Generalized Aggregated Uncertainty (GAU) measure which is a generalization of Aggregated Uncertainty measure, whereas it is applicable for DSmT results. This measure helps to make decisions on better choice of combinations of sensors or methods of fusion. As an experimental study, localization of an object using cameras’ images is selected. Classic DSmT and hybrid DSmT by using extra knowledge, is applied and then uncertainty evaluation is carried out by the GAU uncertainty measure. The final decision in the presented framework has uncertainty less than each sensor’s measurement. By this method, more accurate and less uncertain results in localizing the object with high conflict sensory data are generated.     

Factor structure for Young’s Internet Addiction Test: A confirmatory study

A number of diagnostic scales have been developed in recent years to assess Internet addiction. To better understand the structure, validity, and reliability of such assessment instruments, Young’s Internet Addiction Test (IAT) was evaluated using a confirmatory approach.Data collected through a survey of 410 Hong Kong university undergraduates was subjected to exploratory factor analysis and data from a hold-out sample was analyzed using confirmatory factor analysis in order to assess the psychometric properties and factor structure of the IAT scale. Three dimensions, namely, “Withdrawal and Social Problems”, “Time Management and Performance”, and “Reality Substitute” were extracted.These dimensions were then correlated with a number of criterion variables, including academic performance, online activities, gender, and Internet usage. The results show that academic performance was negatively correlated with the Internet addiction scores. The degree of Internet addiction was also found to vary across different types of online activity, with people engaged in cyberrelationships and online gambling having higher Internet addiction scores.     

Composition of probabilistic evaluations of preferences: a case of criteria applied to isolated and clustered options

This article applies a transformation into probabilities of preference, to rank papers submitted to the XLI Brazilian Symposium of Operational Research. Some 42 papers were divided into sets according to their main topics of interest and measures for 12 attributes were considered, for each paper separately, and also for sets of papers on the same topic, based on the referees' evaluations. Four alternative forms of composition of the probabilistic preferences are illustrated.     

Interval QFT: a mathematical and computational enhancement of QFT

The paper presents an overview of a mathematical and computational enhancement of Horowitz's QFT design procedure. The enhancement uses methods of interval analysis and is called as interval QFT, or IQFT. IQFT addresses and solves some of the fundamental issues in QFT, concerning selection of design frequencies, selection of controller phases in bound generation, approximation of plant templates with finite plant sets, and generation of plant templates and controller bounds with reliability and to a prescribed accuracy. An example is presented to illustrate the key features of IQFT. Copyright © 2002 John Wiley & Sons, Ltd.     

Robust H∞ control for a class of quasi‐linear uncertain stochastic time‐varying delayed systems

This paper studies the H_∞ control for a class of quasi‐linear uncertain stochastic time‐varying delayed systems. Firstly, by using the linear matrix inequality (LMI) method, a sufficient condition is obtained for the robustly stochastic stability. Secondly, the robust H_∞ state feedback controller is designed, such that the considered system is not only internally stochastically stabilizable but also satisfies the robust H_∞ performance. The desired robust H_∞ controller is obtained via solving some LMIs. Finally, one example is provided to demonstrate the effectiveness of the proposed method.     

A semi-local convergence theorem for a robust revised Newton’s method

It is well known that Newton’s iteration will abort due to the overflow if the derivative of the function at an iterate is singular or almost singular. In this paper, we study a robust revised Newton’s method for solving nonlinear equations, which can be carried out with a starting point with a degenerate derivative at an iterative step. It is proved that the method is convergent under the conditions of the Newton–Kantorovich theorem, which implies a larger convergence domain of the method. We also show that our method inherits the fast convergence of Newton’s method. Numerical experiments are performed to show the robustness of the proposed method in comparison with the standard Newton’s method.     

Conditional value‐at‐risk beyond finance: a survey

A large number of problems involve making decisions in an uncertain environment and, hence, with unknown outcomes. Optimization models aimed at controlling the trade‐off between risk and return in finance have been widely studied since the seminal work by Markowitz in 1952. In financial applications, shortfall or quantile risk measures are receiving ever‐increasing attention. Conditional value‐at‐risk (CVaR) is arguably the most popular of such measures. In the last decades, optimization models aimed at controlling risk have been applied to several application domains different from financial optimization. This survey provides an overview of the main contributions where CVaR is incorporated into an optimization approach and applied to a context different from financial engineering. The literature is classified following an application‐oriented perspective. The applications cover classical areas studied in operational research—such as supply chain management, scheduling, and networks—and less classical areas such as energy and medicine. For each area, concise paper excerpts are provided that convey the main ideas of the problems studied, and analyze how the CVaR has been used to cope with different sources of uncertainty. Finally, some open research directions are outlined.     

A Decision Procedure for a Sublanguage of Set Theory Involving Monotone, Additive, and Multiplicative Functions, I: The Two-Level Case

2LS is a decidable many-sorted set-theoretic language involving one sort for elements and one sort for sets of elements. In this paper we extend 2LS with constructs for expressing monotonicity, additivity, and multiplicativity properties of set-to-set functions. We call the resulting language 2LSmf. We prove that 2LSmf is decidable by reducing the problem of determining the satisfiability of its sentences to the problem of determining the satisfiability of sentences of 2LS. Furthermore, we prove that the language 2LSmf is stably infinite with respect to the sort of elements. Therefore, by using a many-sorted version of the Nelson–Oppen combination method, 2LSmf can be combined with other languages modeling the sort of elements.     

Geometrically non-linear behavior of structural systems with random material property: An asymptotic spectral stochastic approach

An asymptotic spectral stochastic approach is presented for computing the statistics of the equilibrium path in the post-bifurcation regime for structural systems with random material properties. The approach combines numerical implementation of Koiter’s asymptotic theory with a stochastic Galerkin scheme and collocation in stochastic space to quantify uncertainties in the parametric representation of the load–displacement relationship, specifically in the form of uncertain post-buckling slope, post-buckling curvature, and a family of stochastic displacement fields. Using the proposed method, post-buckling response statistics for two plane frames are obtained and shown to be in close agreement with those obtained from Monte Carlo simulation, provided a fine enough spectral representation is used to model the variability in the random dimension.     

Approximation schemes for a class of subset selection problems

In this paper we develop an easily applicable algorithmic technique/tool for developing approximation schemes for certain types of combinatorial optimization problems. Special cases that are covered by our result show up in many places in the literature. For every such special case, a particular rounding trick has been implemented in a slightly different way, with slightly different arguments, and with slightly different worst case estimations. Usually, the rounding procedure depended on certain upper or lower bounds on the optimal objective value that have to be justified in a separate argument. Our easily applied result unifies many of these results, and sometimes it even leads to a simpler proof.     

Identification of time‐varying OE models in presence of non‐Gaussian noise: Application to pneumatic servo drives

Intensive research in the field of mathematical modeling of pneumatic servo drives has shown that their mathematical models are nonlinear in which many important details cannot be included in the model. Owing the influence of the combination of heat coefficient, unknown discharge coefficient, and change of temperature, it was supposed that parameters of the pneumatic cylinder are random (stochastic parameters). On the other side, it has been well known that the nonlinear model can be approximated by a linear model with time‐varying parameters. Due to the aforementioned reasons, it can be assumed that the pneumatic cylinder model is a linear stochastic model with variable parameters. In practical conditions, in measurements, there are rare, inconsistent observations with the largest part of population of observations (outliers). Therefore, synthesis of robust algorithms is of primary interest. In this paper, the robust recursive algorithm for output error models with time‐varying parameters is proposed. The convergence property of the proposed robust algorithm is analyzed using the methodology of an associated ordinary differential equation system. Because ad hoc selection of model orders leads to overparameterization or parsimony problem, the robust Akaike's criterion is proposed to overcome these problems. By determining the least favorable probability density for a given class of probability distribution represents a base for design of the robust version of Akaike's criterion. The behavior of the proposed robust identification algorithm is considered through intensive simulations that demonstrate the superiority of the robust algorithm in relation to the linear algorithms (derived under an assumption that the stochastic disturbance has a Gaussian distribution). The good practical values of the proposed robust algorithm to identification of the pneumatic cylinder are illustrated by experimental results. Copyright © 2016 John Wiley & Sons, Ltd.     

To the 70th anniversary of academician V. S. Mikhalevich academician V. S. Mikhalevich as a scientist and science organizer

The article is devoted to the 70th birthday of Academician V. S. Mikhalevich and presents a survey of his fruitful activity as scientist and science organizer. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 77–100, January–February, 2000.