Sequential Decision Theory Research Articles

Intuitionistic Fuzzy Sequential Three-Way Decision Model in Incomplete Information Systems

As an effective method for uncertain knowledge discovery and decision-making, the three-way decisions model has attracted extensive attention from scholars. However, in practice, the existing sequential three-way decision model often faces challenges due to factors such as missing data and unbalanced attribute granularity. To address these issues, we propose an intuitionistic fuzzy sequential three-way decision (IFSTWD) model, which introduces several significant contributions: (1) New intuitionistic fuzzy similarity relations. By integrating possibility theory, our model defines similarity and dissimilarity in incomplete information systems, establishing new intuitionistic fuzzy similarity relations and their cut relations. (2) Granulation method innovation. We propose a density neighborhood-based granulation method to partition decision attributes and introduce a novel criterion for evaluating attribute importance. (3) Enhanced decision process. By incorporating sequential three-way decision theory and developing a multi-level granularity structure, our model replaces the traditional equivalent relation in the decision-theoretic rough sets model, thus advancing the model’s applicability and effectiveness. The practical utility of our model is demonstrated through an example analysis of “Chinese + vocational skills” talent competency and validated through simulation experiments on the UCI dataset, showing superior performance compared to existing methods.

Sequential 3WD-based local optimal scale selection in dynamic multi-scale decision information systems

The multi-scale decision information system (MDIS) is a typical granular computing model. In the research of MDIS, uncertainty is an important factor in making decision analysis, and the selection of optimal scale is a core problem. Therefore, the uncertainty of decision is an important factor in the scale selection. With the rapid increase of data size, the amount of feature information will increase greatly, and the uncertainty of the system will become more and more complex, which makes the optimal scale selection more difficult. The purpose of this study is to investigate the updating law of the local optimal scale under the condition of the dynamic increase of objects. The criterion of scale selection is to keep the uncertainty of the system unchanged. Firstly, the updating law of uncertainty for the decision class in a decision information system under the case of object increment is explored. Secondly, the definition of local optimal scale which keeps the uncertainty of decision classes is given by the sequential three-way decision theory, and the updating law of optimal scale is given by using the updating mechanism of the uncertainty of decision classes. Finally, experiments are conducted to verify the correctness and effectiveness of the proposed method in the calculation of local optimal scale by comparing the algorithms for adding multiple objects directly and adding objects one by one.

Homeostatic Agent for General Environment

Abstract One of the essential aspect in biological agents is dynamic stability. This aspect, called homeostasis, is widely discussed in ethology, neuroscience and during the early stages of artificial intelligence. Ashby’s homeostats are general-purpose learning machines for stabilizing essential variables of the agent in the face of general environments. However, despite their generality, the original homeostats couldn’t be scaled because they searched their parameters randomly. In this paper, first we re-define the objective of homeostats as the maximization of a multi-step survival probability from the view point of sequential decision theory and probabilistic theory. Then we show that this optimization problem can be treated by using reinforcement learning algorithms with special agent architectures and theoretically-derived intrinsic reward functions. Finally we empirically demonstrate that agents with our architecture automatically learn to survive in a given environment, including environments with visual stimuli. Our survival agents can learn to eat food, avoid poison and stabilize essential variables through theoretically-derived single intrinsic reward formulations.

Nonlinear Sequential Bayesian Analysis-Based Decision Making for End-Point Detection of Chemical Mechanical Planarization (CMP) Processes

Chemical mechanical planarization (CMP) process has been widely used in the semiconductor manufacturing industry for realizing highly polished (surface roughness Ra ~1 nm ) and planar [WIWNU ~ 1%, thickness variation standard deviation ~3 nm] surfaces of an in-process wafer. In CMP, accurate and timely decisions for end-point detection (EPD) are extremely important to enable the process to effectively respond to demand variations and disruptions. In this paper, we apply nonlinear sequential Bayesian analysis and decision theory to establish a quantitative relationship that connects the features (inputs) extracted from on-line wireless vibration sensor signals with the process performance measures, such as material removal (outputs) for EPD in copper CMP process. A case study with actual CMP data is provided to demonstrate the effectiveness of the present approach. Note to practitioners. The semiconductor industry widely uses CMP process for realizing highly polished planar surfaces on inter-level dielectrics and metallic interconnects in the fabrication of integrated circuits. Accurate and timely detection of the end-point (EPD) of the CMP process is critical to prevent over-polishing or under-polishing of wafer surfaces, and thus meet the wafer yield requirements under growing demands on wafer density and performance. An EPD system uses information from in-process sensors and/or inspection instruments to facilitate decisions on when to stop the polishing process, and adjust process settings for optimal performance. However, the issue of developing cost-effective sensors, and addressing the uncertainty in the sensor information remains a challenge. We have developed an EPD system based on deriving and sequentially updating a cost-function using the uncertain information from wireless MEMS vibration sensors mounted on a CMP apparatus. Decisions on EPD are made based on optimizing the updated cost function at every time-step. Our experimental investigations suggest that the sensor information can be effectively used for implementing EPD, and it can minimize the costs of over-polishing and under-polishing of wafers during CMP process. As part of future work, we are investigating the robustness of the EPD system to different forms of uncertainty in the sensor information, and much wider configurations of sensors and CMP setups.

A Bayesian sequential procedure for determining the optimal number of interrogatory examples for concept-learning

The purpose of this paper is to derive optimal rules for sequential decision-making in intelligent tutoring systems. In a sequential mastery test, the decision is to classify a student as a master, a nonmaster, or to continue testing and administering another item. The framework of Bayesian sequential decision theory is used; that is, optimal rules are obtained by minimizing the posterior expected losses associated with all possible decision rules at each stage of testing and using techniques of backward induction. The main advantage of this approach is that costs of testing can be taken explicitly into account. The sequential testing procedure is demonstrated for determining the optimal number of interrogatory examples for concept-learning in the Minnesota adaptive instructional system. The paper concludes with an empirical example in which, for given maximum number of interrogatory examples for concept-learning in medicine, the appropriate action is indicated at each stage of testing for different number-correct score.

Sequential Decision Analysis of the Traditional Deterrence Game

We examine the traditional deterrence game between Challenger and Defender. We treat two variations of the game – the complete information game and the one-sided information game where the first mover, Challenger, is the uncertain player. We employ sequential decision theory to analyze the game of incomplete information. The analysis is basic in that we employ a simplifying assumption, specifically that Challenger’s valuation of the status quo is fixed at zero. We examine the behavior of Challenger using both a von-Neumann-Morgenstern decision rule and a Kahneman-Tversky decision rule. The formal results show that given the right combination of outcome valuations and probability values and weightings, Challenger can make choices under the von Neumann-Morgenstern decision rule that are reversed from those made under the Kahneman-Tversky decision rule. We then relate these reversals to the concept of misperception found in the International Relations and Peace Science literatures. Finally, we comment on extensions of the ensuing analysis.

Sufficiency in sequentially planned decision procedures

In this paper we generalize classical results about sufficiency in the sequential decision theory to sequentially planned decision procedures. We obtain the completeness of the class of decision rules based on the sufficient σ-fields family. The concept of sampling plan with respect to a non-isotonic family is introduced, and a complete class of rules is built.

A minimax procedure in the context of sequential testing problems in psychodiagnostics.

The purpose of this paper is to derive optimal rules for sequential testing problems in psychodiagnostics. In sequential psychodiagnostic testing, each time a patient is exposed to a new treatment, the decision then is to declare this new treatment effective, ineffective, or to continue testing and exposing the new treatment to another random patient suffering from the same mental health problem. The framework of minimax sequential decision theory is proposed for solving such testing problems; that is, optimal rules are obtained by minimizing the maximum expected losses associated with all possible decision rules at each stage of testing. The main advantage of this approach is that costs of testing can be explicitly taken into account. The sequential testing procedure is applied to an empirical example for determining the effectiveness of a cognitive-analytic therapy for patients suffering from anorexia nervosa. For a given maximum number of patients to be tested, the appropriate action is indicated at each stage of testing for different numbers of positive reactions to the cognitive-analytic therapy. The paper concludes with a simulation study, in which the minimax sequential strategy is compared for the anorexia nervosa example with other procedures that exist for similar classification decision problems in the literature in terms of average number of patients to be tested, classification accuracy and average loss.

Décision séquentielle et principe de précaution

Sequential decision-making and Precautionary Principle. The Precautionary Principle (Rio Conference, Maastricht Treaty) is becoming increasingly prominent in the environmental protection law or on health safety issues. Given the important literature on the Precautionary Principle in social sciences in general, this paper provides an economic approach to the Precautionary Principle. In crude terms, the Precautionary Principle encourages the prevention of a risk before that full scientific information is available about it. Since this Principle implies that a decision should be taken in advance, even if it may be revised later on, it implies that the decision process is sequential. As a result, this paper proposes an interpretation of the Precautionary Principle based on the sequential decision theory. We report some insights from sequential investment theory (Dixit and Pindyck, 1994) in order to bring closer the notion of option value to that of precaution. We then introduce formally the notion of irreversibility and that of information structure. We also reinterpret the Bayes' rule as a rule that accounts for scientific progress in decision-making. This allows us to distinguish between a preventive and a precautionary strategy. Prevention is a static concept that refers to the management of a risk at a given time and given a stable probability distribution. Precaution is a dynamic concept that recognizes the evolution of scientific knowledge. A precautionary measure is defined as a prudent and temporary decision that permits to manage the current lack of scientific information. In order to examine the efficiency of the Precautionary Principle, we raise the following question : does more scientific uncertainty lead to bias decisions in favor of less current risk exposure ? We show that the Precautionary Principle may be justified on the grounds of irreversibility alone (Henry, 1974). We also generalize this pure "irreversibility effect" to integrate risk aversion and consumption externalities (Gollier et al., 2000). We finally report some empirical results from macroeconomic models that recently assessed the impact of scientific uncertainty on optimal climate policy (Nordhaus, 1994).

Applications of Bayesian Decision Theory to Sequential Mastery Testing

The purpose of this paper is to formulate optimal sequential rules for mastery tests. The framework for the approach is derived from Bayesian sequential decision theory. Both a threshold and linear loss structure are considered. The binomial probability distribution is adopted as the psychometric model involved. Conditions sufficient for sequentially setting optimal cutting scores are presented. Optimal sequential rules will be derived for the case of a subjective beta distribution representing prior true level of functioning. An empirical example of sequential mastery esting for concept-learning in medicine concludes the paper.

A sequential sampling procedure for genetic algorithms

In this paper, we apply sequential decision theory for scheduling tests in genetic algorithms and investigate an efficient sampling procedure for improving its performance. We use a loss function specifically defined for our analysis and obtain sequential decision equations for the optimal procedure. We derive simplified equations so that the procedure can be applied in practice. Finally, we compare the performance of our heuristic sampling procedure with that of the original genetic algorithms.

Statistical Theory and Modeling: In Honour of Sir David Cox, FRS.

Part 1 Statistical theory - theoretical concepts significance tests theory of optimal tests estimation asymptotic theory. Part 2 Applied statistics - preliminary considerations statistical models statistical inference model adequancy exploratory and robust methods multi-variate methods use of computers. Part 3 Generalized linear models - a class of non-linear regression models likelihood functions estimation analysis of deviance checking the model. Part 4 Residuals and diagnostics - general remarks normal theory linear model a general definition general regression models. Part 5 Life table analysis - survival distributions inference for a single sample dependence on explanatory variables inference for models involving explanatory variables graphical methods - goodness of fit several types of failure: competing risks multi-variate failure distributions. Part 6 Sequential methods - Wald's theory of the SPRT sequential tests with nuisance parameters sequential estimation sequential clinical trials decision theory and optimality in clinical trials inference and decisions sequential design and related topics. Part 7 Time series methods - stationary models frequency domain parametric models non-parametric estimation regression with correlated errors. Part 8 Modelling stochastic phenomena - independence and the Markov property semi-Markov and Markov renewal processes point processes spatial processes applications. Part 9 Optimal design of experiments - convex design theory numerical methods some specific designs for standard problems non-standard problems. Part 10 Likelihood theory - the primary theory some refinements pseudo-likelihoods. Part 11 Quasi-likelihood and estimating functions - least squares quasi-likelihood estimation quasi-likelihood function estimating functions confidence sets an open problem. Part 12 Approximations and asymptotics - basic theory and notation edgeworth expansion saddlepoint expansion Laplace approximations stochastic asymptotic expansion.

A “misrepresentation” of method as theory: Reply

The fundamental “misrepresentation” ( F. Wilkening, 1988 Developmental Review, 8, 361–367 ) resides in Wilkening's failure to distinguish method from theory. This error results in contradictory statements, nonparsimonious models, inaccurate attributions, and misinterpretations of both theories as well as our review of them ( D. D. Kerkman, & J. C. Wright, 1988, Developmental Review, 8, 323–360 ). A hybrid model that combines sequential decision theory (SDT) and information integration theory (IIT) may be of little value beyond the level of description. SDT compares favorably with IIT in describing and predicting developmental transitions as well as guiding instruction. A strategy selection model may explain some apparent taskwise discrepancies in rule use that Wilkening (1988) notes.

The Impact of Cross-Rate Interference on LORAN-C Receivers

Wong [1] recommends that 16 additional LORAN-C ground stations are needed to provide redundant coverage throughout the conterminous U.S. so that LORAN-C can provide the primary navigation service to civil aviation. The purpose of this paper is to estimate the effect of the interference from the additional stations on the acquisition (phase code identification and third cycle selection) and track modes of a LORAN-C receiver whose detection process is based on the sequential decision theory. This receiver model represents a modern design using microprocessor technology. The results are compared against the requirement that acquisition be completed 90 percent of the time within 7.5 minutes. The impact of cross-rate interference (CRI) on the track mode is estimated using a time-domain analysis.

Model of the human observer and decision maker—Theory and validation

A model of the human decision maker observing a dynamic system is presented. The decision process is described in terms of classical sequential decision theory by considering the hypothesis that an abnormal condition has occurred by means of a generalized likelihood ratio test. For this, a sufficient statistic is provided by the innovation sequence which is the result of the perception and information processing submodel of the human observer. On the basis of only two model parameters the model predicts the decision speed/accuracy trade-off and various attentional characteristics. A preliminary test of the model for single variable failure detection tasks resulted in a very good fit of the experimental data. In a formal validation programme a variety of multivariable failure detection tasks was investigated. A very good overall agreement between the model and experimental results showed the predictive capability of the model. In addition, the specific effect of almost all task variables (number, bandwidth and mutual correlation of display variables and various failure characteristics) was accurately predicted by the model.

Model of the Human Observer and Decision Maker — Theory and Validation

A model of the human decision maker observing a dynamic system is presented. The decision process is described in terms of classical sequential decision theory by considering the hypothesis that an abnormal condition has occurred by means of a generalized likelihood ratio test. For this, a sufficient statistic is provided by the innovation sequence which is the result of the perception and information processing submodel of the human observer. On the oasis of only two model parameters the model predicts the decision speed/accuracy trade-off and various attentional characteristics.A preliminary test of the model for single variable failure detection tasks resulted in a very good fit of the experimental data.In a formal validation program a variety of multivariable failure detection tasks was investigated. A very good overall agreement between the model and experimental results showed the predictive capability of the model. In addition, the specific effect of almost all task variables (number, bandwidth and mutual correlation of display variables and various failure characteristics) was accurately predicted by the model.

The influence of the nonrecent past in prediction for stochastic processes

Consider the stochastic processes X 1, X 2,… and Λ 1, Λ 2,… where the X process can be thought of as observations on the Λ process. We investigate the asymptotic behavior of the conditional distributions of X t+ v given X 1,…, X t and Λ t+ v given X 1,…, X t with regard to their dependency on the “early” part of the X process. These distributions arise in various time series and sequential decision theory problems. The results support the intuitively reasonable and often used (as a basic tenet of model building) assumption that only the more recent past is needed for near optimal prediction.

Verallgemeinerte bayes-verfahren bei sequentiellen testproblemen

In this paper, problems of sequential decision theory are taken into consideration by extending the definition of the BAYES rule and treating BAYES rules. This generalisation is quite useful for practice. In many cases only BAYES rules can be calculated. The conditions under which such sequential decision procedures exist are demonstrated, as well as how to construct them on a scheme of backward induction resulting in the conclusion that the existence of BAYES rules needs essentially weaker assumptions than the existence of BAYES rules.Futhermore, methods are searched to simplify the construction of optimal stopping rules. Some illustrative examples are given.

Bayes theorem, information number and behavior of posteior distributions

According to the sequential decision theory, one is directed to; (i) stop when the posterior distribution, having been successively watched, frist enters the domain in which by stopping he loses less, and then (ii) take that action which gives him the least loss averaged w.r.t. the current posterior distribution (Blackwell-Girshick [1], p. 254). For some reasons we don't know, however, the successive behavior of posterior distribution never draws the full attention of statisticians and probabilists, though some of them have developed the asymptotic theory. As far as the sequential decision theory is concerned, however, the asymptotic behavior tells us nothing, since the stopping rule is only related to finite time. Toe compute the posterior distribution time by time is a laborious task. But to site all possible posterior distributions sometimes facilitates our manipulation of the sequential decision problem. This paper proposes some methods.

An Analysis of Cut-Off Rules for Optimization Algorithms

The problem of optimal stopping has long bee of intrest to various scientific disciplines. Most notably, the approacbes taken have been based on sequential decision theory and modeling techniqes. Aiming at optimization algorithms, we propose in this paper to combine the present approaches and study the cut-off rule problem, using asymptotic convergence behavior of sequences. A unifying framework for the design and analysis of stopping rules for algorithms generating a monotonically convergent sequence is presented while methodology for optimal design is discussed. The concavity structure should be observed to play an important role in our analysis.