Dynamic diagnostic and decision procedures under uncertainty

Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 87–104, May–June, 1994.     

不确定条件下生产调度问题的三阶段决策方法

提出了一种可综合考虑多种不确定因素的生产调度问题三阶段决策方法. 首先分析了不确定条件下的生产调度的决策过程, 根据过程的特点将其分为基本调度、在线调整和补偿三个阶段; 对变量进行分类, 从而与3个阶段相对应; 分别建立了基于情景分析以及子问题最(近)优解的两种三阶段调度数学模型, 并给出了变量的处理方法和阶段性的模型求解方法, 来作为不同阶段的决策依据; 最后以化工批处理过程的短期调度为例, 说明了三阶段调度建模和决策过程的实现方法.     

A hyperparameter consensus method for agreement under uncertainty

This paper addresses the problem of information consensus in a team of networked agents by presenting a generic consensus method that permits agreement to a Bayesian fusion of uncertain local parameter estimates. In particular, the method utilizes the concept of conjugacy of probability distributions to achieve a steady-state estimate consistent with a Bayesian combination of each agent’s local knowledge, without requiring complex channel filters or being limited to normally distributed uncertainties. It is shown that this algorithm, termed hyperparameter consensus, is adaptable to many local uncertainty distributions within the exponential family, and will converge to a Bayesian fusion of local estimates with some standard assumptions on the network topology.     

Inference rules for proving the equivalence of recursive procedures

Inspired by Hoare’s rule for recursive procedures, we present three proof rules for the equivalence between recursive programs. The first rule can be used for proving partial equivalence of programs; the second can be used for proving their mutual termination; the third rule can be used for proving the equivalence of reactive programs. There are various applications to such rules, such as proving equivalence of programs after refactoring and proving backward compatibility.     

Maximum compatibility method for data fitting under interval uncertainty

For the linear regression model, the data-fitting problem under the interval uncertainty of the data is studied. As an estimate of the linear function parameters, it is proposed to take their values that deliver the maximum for the so-called recognizing functional of the parameter set compatible with the data (the maximum compatibility method). The properties of the recognizing functional, its interpretation, and the properties of the estimates obtained using the maximum compatibility method are investigated. The relationships to other data analysis methods are discussed, and a practical electrochemistry problem is solved.     

Inference procedures for the Birnbaum–Saunders distribution and its generalizations

Goodness-of-fit tests are constructed for the two-parameter Birnbaum–Saunders distribution in the case where the parameters are unknown and are therefore estimated from the data. With each test the procedure starts by computing efficient estimators of the parameters. Then the data are transformed to normality and normality tests are applied on the transformed data, thereby avoiding reliance on parametric asymptotic critical values or the need for bootstrap computations. Two classes of tests are considered, the first class being the classical tests based on the empirical distribution function, while the other class utilizes the empirical characteristic function. All methods are extended to cover the case of generalized three-parameter Birnbaum–Saunders distributions.     

The use of ordered weighted averaging method for decision making under uncertainty

A decision making under uncertainty (DMUU) prevails at the outset and often evolves into a decision making under partial uncertainty as information on the states of nature, for example, a probability distribution, is advanced. Many methods have emerged for solving the DMUU problems, which includes the classical decision criteria and the domain criterion. Yager (1988) introduced a new approach, the so‐called ordered weighted averaging (OWA) as a viable method for solving the DMUU problems. The OWA weights to be used in the aggregation are generated under the degree of optimism provided by a decision maker and then combined with the reordered payoffs to produce aggregated payoffs for each strategy. The reordering process, one of the characterizing features of the OWA method, enables us to perform various types of aggregations including maximax, maximin, and Hurwicz‐α index in conjunction with the generated weights. The OWA method obviously extends the Hurwicz approach by taking into account the tradeoffs among the entire payoffs while the Hurwicz approach considers a tradeoff only between the two extremes, the maximum and the minimum payoffs. In this paper, we examine the features of the OWA method in light of Milnor's set of requirements for reasonable decision criteria, thus providing a solid methodological foundation for the DMUU. The OWA method can also be used to solve a group DMUU problem by exploiting individual decision results in the situation when the use of a fuzzy majority is advocated.     

A modified Benders decomposition method for efficient robust optimization under interval uncertainty

The goal of robust optimization problems is to find an optimal solution that is minimally sensitive to uncertain factors. Uncertain factors can include inputs to the problem such as parameters, decision variables, or both. Given any combination of possible uncertain factors, a solution is said to be robust if it is feasible and the variation in its objective function value is acceptable within a given user-specified range. Previous approaches for general nonlinear robust optimization problems under interval uncertainty involve nested optimization and are not computationally tractable. The overall objective in this paper is to develop an efficient robust optimization method that is scalable and does not contain nested optimization. The proposed method is applied to a variety of numerical and engineering examples to test its applicability. Current results show that the approach is able to numerically obtain a locally optimal robust solution to problems with quasi-convex constraints (≤ type) and an approximate locally optimal robust solution to general nonlinear optimization problems.     

Sequential probabilistic analytical target cascading method for hierarchical multilevel optimization under uncertainty

Probabilistic Analytical Target Cascading (PATC) is a methodology for hierarchical multilevel optimization under uncertainty. In PATC, the statisticalmoments of the stochastic interrelated responses are matched between neighbouring levels to ensure the consistency of the solution. When the interrelated response is far from normal distribution, high order moments may need to be matched in the PATC formulation, which results in great computational difficulty. To overcome this disadvantage, a sequential PATC (SPATC) approach is proposed in this paper. SPATC firstly decouples the original probabilistic design problem into deterministic optimization problem and probabilistic analysis, and then hierarchically decomposes them into subproblems. The statistical information matching between neighbouring levels in the existing PATC framework is eliminated in SPATC. All in one probabilistic analysis and hierarchical probabilistic analysis are established to calculate the probabilistic characteristic of the interrelated responses and linking variables. Three examples are used to demonstrate the effectiveness and efficiency of the proposed SPATC approach. The results show that the SPATC approach is more efficient and accurate than PATC, especially for the multilevel design problem with non-normal interrelated responses.     

An evolved VIKOR method for multiple-criteria compromise ranking modeling under T-spherical fuzzy uncertainty

The development of T-spherical fuzzy (T-SF) sets in qualitative multiple-criteria choice analysis has been well investigated, but little is explored about how the VIKOR (i.e., VIšekriterijumsko KOmpromisno Rangiranje in Serbian) mechanism is generalized into intricate T-SF environments. This paper has the objective of propounding a creative T-SF VIKOR methodology for compromise ranking modeling in multiple criteria analysis. The exploitation of the T-SF configuration brings about superior information space representation in response to intricate realistic environments. However, because of the increased complexity of decision situations involving T-spherical fuzziness, treatment with the T-SF information arises a pragmatic difficulty in developing methodological approaches to T-SF VIKOR. In light of this concern, this paper unfolds an analytical framework for the T-SF VIKOR method predicated on new notions of an evolved T-SF score function and the Minkowski-type T-SF distance measure along with its special cases of the Manhattan-, Euclidean-, and Chebyshev-type distances. The aspired and despised T-SF characteristics can be identified supported by the evolved T-SF score function of T-SF performance ratings. This paper gives a new delineation of the group utility, individual regret, and joint generalized measures with the aid of the Minkowski-type T-SF distance measure relative to the aspired/despised T-SF characteristics. A synthetic mechanism is built to validate the standards of acceptable advantage and stability and yield the ultimate compromise choices for multiple criteria decision aiding. The practicality of the T-SF VIKOR methodology in down-to-earth decision situations has been well demonstrated through the selection issues of warehouse locations and advertisement strategies. Moreover, the developed approach has shown better application outcomes than the past methods did. The comparative study with parametric analysis has revealed the steadiness and effectiveness of the compromise choice results in T-SF circumstances.     

Performance bounds for estimation under uncertainty

For the class of linear Gauss-Markov systems with binary parameters uncertainty, the minimum variance estimate of the state and associated covariance of error expressions were derived in a closed form in [1, 2]. In this paper expressions for the conditional and unconditional covariances of error matrices are presented for the M-ary case. Useful upper and lower bounds for the unconditional covariance of error are also presented which are valid, on the average, for any measurement sequence. A geophysical seismic data filtering example applying these results is also given.     

Inference for Weibull distribution under generalized order statistics

Based on generalized order statistics from Weibull distribution the approach of Bayesian and non-Bayesian estimation are discussed. We present a simple and efficient simulational algorithm for generating a generalized order statistics sample from any continuous distribution. Specializations to Bayesian and non-Bayesian estimators, some lifetime parameters and confidence intervals of progressive II censoring and record values are obtained and compared with the existing results. Two examples are given to illustrate the proposed estimators and the simulation algorithm.     

Inference under imprecise probability assessments

Under partial knowledge, the use of the precise probability might be misleading. However, it is possible to process imprecise assessments, such as comparative previsions or grades of previsions. Rules for checking their coherence with the theoretical model and for making inference are given. Sometimes the derived conclusions might provide us with a complete answer for a given problem. In any case, technical tools can measure the imprecision of the answer and reveal if the analysis is thorough enough.     

A framework for building knowledge-bases under uncertainty

Managing uncertainty during the knowledge engineering process from elicitation to validation and verification requires a flexible, intuitive, and semantically sound knowledge representation. This is especially important since this process is typically highly interactive with the human user to add, update, and maintain knowledge. In this paper, we present a model of knowledge representation called Bayesian Knowledge-Bases (BKBs). It unifies a ‘if-then’ style rules with probability theory. We also consider the computational efficiency of reasoning over BKBs. We can show that through careful construction of the knowledge-base, reasoning is computationally tractable and can in fact be polynomial-time. BKBs are currently fielded in the PESKI intelligent system development environment.     

Semimyopic measurement selection for optimization under uncertainty

The following sequential decision problem is considered: given a set of items of unknown utility, an item with as high a utility as possible must be selected ("the selection problem"). Measurements (possibly noisy) of item features prior to selection are allowed at known costs. The goal is to optimize the overall sequential decision process of measurements and selection. Value of information (VOI) is a well-known scheme for selecting measurements, but the intractability of the problem typically leads to using myopic VOI estimates. In the selection problem, myopic VOI frequently badly underestimates the VOI, leading to inferior measurement policies. In this paper, the strict myopic assumption is relaxed into a scheme termed semimyopic, providing a spectrum of methods that can improve the performance of measurement policies. In particular, the efficiently computable method of "blinkered" VOI is proposed, and theoretical bounds for important special cases are examined. Empirical evaluation of "blinkered" VOI in the selection problem with normally distributed item values shows that it performs much better than pure myopic VOI.     

Reasoning under uncertainty for plant disease diagnosis

The present work describes an operational knowledge-based system able to reason with uncertain knowledge, by using methodologies and formalisms that provide for representation of facts and rules with various degrees of certainty and precision. The user interface is windows based, and its design allows high flexibility both in describing the facts in the knowledge base and in adapting the reasoning mechanism. It can therefore be used to evaluate user-generated hypotheses on plant disorders and diagnostic scenarios, as well as provide an environment for education and training in phytopathology.     

Knowledge-based system for three-way decision-making under uncertainty

Knowledge and Information Systems - Knowledge-based systems developed based on Dempster–Shafer theory and prospect theory enhances decision-making under uncertainty. But at times, the...     

不完备信息系统下的不确定性度量方法

在不完备信息系统中,不确定性度量是Rough Set理论中的一个难题。文中通过分析现有完备信息系统的不确定度量方法以及不完备信息系统的特性,提出了广义相似关系,并以之为基础给出了一个直接度量不完备信息系统不确定性的方法。通过实例分析,验证了该方法的有效性。     

Leximin rules for bankruptcy problems under uncertainty

We model bankruptcy problems under uncertainty under the assumption that there are several possible states of nature, each of which is identified with a different bankruptcy problem. For this multi-dimensional extension of classic bankruptcy problems, we consider situations in which agents exhibit at the same time additive preferences and leximin preferences on their possible results. We propose division rules which combine different rationality principles and guarantee efficiency with respect to leximin preferences.     

Bayesian optimization for learning gaits under uncertainty

Designing gaits and corresponding control policies is a key challenge in robot locomotion. Even with a viable controller parametrization, finding near-optimal parameters can be daunting. Typically, this kind of parameter optimization requires specific expert knowledge and extensive robot experiments. Automatic black-box gait optimization methods greatly reduce the need for human expertise and time-consuming design processes. Many different approaches for automatic gait optimization have been suggested to date. However, no extensive comparison among them has yet been performed. In this article, we thoroughly discuss multiple automatic optimization methods in the context of gait optimization. We extensively evaluate Bayesian optimization, a model-based approach to black-box optimization under uncertainty, on both simulated problems and real robots. This evaluation demonstrates that Bayesian optimization is particularly suited for robotic applications, where it is crucial to find a good set of gait parameters in a small number of experiments.