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。     

自反二元关系下不完备信息系统的粗糙熵及粒度度量

针对不完备信息系统中各种自反二元关系形成了对系统的覆盖而非划分的情况,提出利用对象的邻域来定义粗糙熵和粒度度量以衡量系统的不确定性,证明了以上不确定性度量同完备信息系统的不确定性度量是一致的.同时在覆盖可约简的情况下,定义了覆盖约简对系统的粗糙熵和粒度度量,研究结果表明在系统分类最细或最粗时,覆盖约简的不确定性和知识的不确定性是等价的.     

决策信息系统不确定性的熵度量

提出基于Rough集信息论观点的决策表不确定性的熵度量指标,相比代数论观点的决策表不确定性度量指标在含义上更清晰,对不确定性的度量更全面.运用不同的熵度量指标,可分别度量一致性决策信息系统和不一致性决策信息系统的规则前件不确定性、规则后件不确定性、规则整体随机性以及决策表整体不确定性,并对同一决策信息系统运用不同的熵度量指标对其不确定性进行分析.     

信息系统中的熵理论和信息粒度

不确定性是人工智能中的研究热点,而熵理论和信息粒度是度量信息系统不确定性的两种主要方法。本文在给出信息系统中熵的物理意义基础上,提出了信息系统中熵增加原理,给出了熵和信息粒度的公理化定义,据此构造了两种新的不确定性度量函数—α熵和α粒度,它们是已有熵和粒度度量的进一步推广。研究表明,α熵以及现有的熵度量都是广义熵的特殊形式,而α粒度以及现有的粒度度量都是广义粒度的特殊形式,从而统一、规范和发展了完备与不完备信息系统中的不确定性度量方法。     

一种基于不可区分度的组合熵与组合粒度

组合熵与组合粒度是一种新的度量信息系统不确定性的有效方法。基于对象之间的不可区分度将组合熵与组合粒度的概念推广到非完备信息系统中,并给出二者的性质。经证明,非完备信息系统中的组合熵与组合粒度之间具有严格的互补关系,并可退化为完备信息系统中的组合熵与组合粒度。实例表明该方法能够对非完备信息系统中的不确定性进行有效的度量,拓展了组合熵与组合粒度的应用范围。     

双精度容差关系决策粗糙集及其属性约简

决策粗糙集理论是经典粗糙集理论结合贝叶斯理论拓展而来。为在不完备区间值信息系统下研究决策粗糙集理论,本文首先提出属性相似度的概念,并基于属性相似度定义了双精度容差关系。然后,基于双精度容差关系,结合贝叶斯最小风险决策原则建立不完备区间值信息系统下决策粗糙集模型。针对该模型,对不确定性度量进行修正并基于修正的不确定性度量对该模型的属性约简进行研究。最后提出属性约简算法并应用于目标识别实例。     

不完备信息系统中一种新的不确定性度量方法

不确定性度量是智能计算等领域中一个重要的研究问题。在不完备信息系统中,为了融合众多不确定性度量方法的优点,引入近似粗糙度度量方法,由于该度量方法存在一定的缺陷,接着在近似粗糙度中融合知识粒度度量,提出一种新的不确定性度量方法,同时在所提出度量方法的基础上加入了一个平滑因子,以提高该度量方法在不确定性度量时的适用性。实验结果表明所提出的方法具有更好的不确定性度量效果。     

基于信息结构的区间值决策信息系统鲁棒不确定性度量

现阶段基于单值的信息系统的不确定性度量研究较多,而少有关于区间值决策信息系统的不确定性和噪声标签对系统不确定性影响的研究.因此,文中提出基于信息结构的区间值决策信息系统鲁棒不确定性度量.利用KL散度定义区间值之间的相似度,构造区间值模糊相似关系,并提出区间值决策信息系统的信息结构.为了降低噪声决策对系统不确定性度量的影响,引入K近邻点计算样本关于决策的隶属度,提出2种基于信息结构的鲁棒不确定性度量方法.实验表明文中不确定性度量的有效性和合理性.     

一种基于邻域容差信息熵的组合度量方法

在实际应用中,大多数信息系统中的数据都是混合的,为了度量混合信息系统的不确定性,本文提出了一种组合度量方法.首先在不完备邻域粗糙集中定义了混合近似精度和混合近似粗糙度的概念;接着考虑到这两种单一度量方法对信息系统不确定性评估的不足,然后,进一步引入邻域容差信息熵的概念;最后将混合近似粗糙度和邻域容差信息熵这两种单一度量进行结合提出一种组合度量方法,并且研究了相关性质.UCI实验结果表明,本文所提出的方法在混合信息系统中具有更好的不确定性度量效果,从而验证了该度量方法具有一定的优越性,并且从理论上也证明了该方法的可行性.     

绝对信息量不完备信息系统的数据补齐算法

现实中的信息系统往往是不完备的。处理不完备信息系统的一种常用方法是根据一定的规则对缺失的属性值予以赋值,从而将其补齐成完备的信息系统。文中提出了一种基于绝对信息量的赋值规则,根据该规则提出了补齐不完备信息系统的算法。该算法基于信息系统的内在性质,减少了数据补齐时人为引入的不确定性,因而更加合理、有效。     

Information theoretic sensor data selection for active objectrecognition and state estimation

We introduce a formalism for optimal sensor parameter selection for iterative state estimation in static systems. Our optimality criterion is the reduction of uncertainty in the state estimation process, rather than an estimator-specific metric (e.g., minimum mean squared estimate error). The claim is that state estimation becomes more reliable if the uncertainty and ambiguity in the estimation process can be reduced. We use Shannon's information theory to select information-gathering actions that maximize mutual information, thus optimizing the information that the data conveys about the true state of the system. The technique explicitly takes into account the a priori probabilities governing the computation of the mutual information. Thus, a sequential decision process can be formed by treating the a priori probability at a certain time step in the decision process as the a posteriori probability of the previous time step. We demonstrate the benefits of our approach in an object recognition application using an active camera for sequential gaze control and viewpoint selection. We describe experiments with discrete and continuous density representations that suggest the effectiveness of the approach     

Agent oriented intelligent fault diagnosis system using evidence theory

Multi sensors fusion is a very important process for fault diagnosis system. Information obtained from multi sensors need to be fused because no single sensor can get all the information for fault diagnosis. Moreover, information from different sensors may be uncertainty, inaccuracy, or even conflicting. Evidence theory can be used for information fusion, which is regarded as an extension form of Bayesian reasoning, but it has a better fusion result by simple reasoning process using belief function without knowing the prior probability. All the information collected from multi sensors in the system can be described as the evidence for diagnosis so that the fault diagnosis problem can then be modeled as a problem of evidence fusion and decision. In this paper, the classical Dempster-Shafer evidence theory is discussed, and the disadvantages of the combination rule are also analyzed. The notion of support degree of focal element is suggested in order to evaluate the conflicts between multi sensors. The new combination rule is then built to allocate the conflicted information from multi sensors based on the support degree of focal element. Furthermore, the decision rules for fault diagnosis are also proposed, as well as the architecture of the agent oriented intelligent fault diagnosis system. Finally, a case study is given to illustrate the performance of the proposed model.     

基于Rough集的规则分辨矩阵研究

文章提出了一种新的规则分辨矩阵,相比原对象分辨矩阵节省了存储空间,减少了比较计算量。在此规则分辨矩阵的基础上,提出了求决策信息系统信息论观点下核属性及约简的方法,还利用此矩阵分析了约简过程中决策信息系统不确定性的变化,并对同一决策信息系统的不同约简的不确定性差异进行了比较。     

Jeffrey’s rule of conditioning with various forms for uncertainty

We first introduce Jeffrey’s rule of conditioning and explain how it allows us to determine the probability of an event related to one variable from information about a collection of conditional probabilities of that event conditioned on the state another variable. We note that in the original Jeffrey paradigm we have the uncertainty about the state of the conditioning variable expressed as a probability distribution. Here we extend this by allowing alternative formulations for the uncertainty about the conditioning variable. We first consider the case where our uncertainty is expressed in terms of a measure. This allows us to consider the case where our uncertainty is a possibility distribution. We next consider the case where our uncertainty about the conditioning variable is expressed in terms of a Dempster–Shafer belief structure. Finally we consider the case where we are ignorant about the underlying distribution and must use the decision maker’s subjective attitude about the nature of uncertainty to provide the necessary information to use in the Jeffrey rule.     

An extension of statistical decision theory with information theoretic cost functions to decision fusion: Part I

A review of information theory and statistical decision theory has led to the recognition that decisions in statistical decision theory can be interpreted as being determined by the similarity between the distribution of probabilities obtained from measurements and characteristic distributions of probabilities representing the members of the set of decisions. The obscure interpretation was found during a review of statistical decision theory for the special case where the cost function of statistical decision theory is an information theoretic cost function.Additional research has found that the resulting information theoretic decision rule has a number of interesting characteristics that may have previously been recognized in terms of mathematical interest, but until now have not been recognized for their implications for information fusion. Bayesian probability theory has been criticized for problematic changes in decisions when hypotheses and decisions are reorganized to different levels of abstraction, weak justification for the selection of prior probabilities, and the need for all probability density functions to be defined. The characteristics of the information theoretic decision rule show that the decisions are less sensitive to changes in the reorganization of hypothesis and decision sets to different levels of abstraction in comparison to Bayesian probability theory. Extension of the information theoretic rule to a fusion rule (to be provided in a companion paper) will be shown to provide increased justification for the selection of prior probabilities through the adoption of Laplace’s principle of indifference. The criticism of the need for all probability density functions can be partially mitigated by arguing that the hypothesis abstraction levels can be selected so that all the probability density functions may be obtained. Further refutation of the third criticism will require that the assumption that the probability density functions are not definitively known but may be ambiguous as well and will not be pursued as a line of inquiry within the two companion papers.     

A Bayesian decision model for cost optimal record matching

In an error-free system with perfectly clean data, the construction of a global view of the data consists of linking - in relational terms, joining - two or more tables on their key fields. Unfortunately, most of the time, these data are neither carefully controlled for quality nor necessarily defined commonly across different data sources. As a result, the creation of such a global data view resorts to approximate joins. In this paper, an optimal solution is proposed for the matching or the linking of database record pairs in the presence of inconsistencies, errors or missing values in the data. Existing models for record matching rely on decision rules that minimize the probability of error, that is the probability that a sample (a measurement vector) is assigned to the wrong class. In practice though, minimizing the probability of error is not the best criterion to design a decision rule because the misclassifications of different samples may have different consequences. In this paper we present a decision model that minimizes the cost of making a decision. In particular: (a) we present a decision rule: (b) we prove that this rule is optimal with respect to the cost of a decision: and (c) we compute the probabilities of the two types of errors (Type I and Type II) that incur when this rule is applied. We also present a closed form decision model for a certain class of record comparison pairs along with an example, and results from comparing the proposed cost-based model to the error-based model, for large record comparison spaces.     

Robust adaptive control: stability and asymptotic performance

Robust stability and asymptotic performance results are provided for adaptive control in the presence of both compact real parametric uncertainty and frequency-weighted bounded unstructured uncertainty. It is shown that a class of parameter adaptive control systems is robustly stable. The asymptotic robust performance bound can be made arbitrarily close to that of the nonadaptive design which would result from perfect parameter estimation. The key assumptions are: (1) the unknown parameters lie in a known compact convex set, (2) a certain bound on the initial state of the system is known, (3) the control design rule is Lipschitzian, and (4) the control design rule would produce a robust controller if given perfect parameter information. In addition, the location of the parametric and nonparametric uncertainty within the known system dynamic must satisfy certain structural assumptions     

A Strategy of Dynamic Reasoning in Knowledge-Based System with Fuzzy Production Rules

Fuzzy production rules have been successfully applied to represent uncertainty in a knowledge-based system. The knowledge organized as a knowledge base is static. On the other hand, a real system such as the stock market is dynamic in nature. Therefore we need a strategy to reflect the dynamic nature of a system when we make reasoning with a knowledge-based system.This paper proposes a strategy of dynamic reasoning that can be used to takes account the dynamic behavior of decision-making with the knowledge-based system consisted of fuzzy rules. A degree of match (DM) between actual input information and antecedent of a rule is represented by a value in interval [0, 1]. Weights of relative importance of attributes in a rule are obtained by the AHP (Analytic Hierarchy Process) method. Then these weights are applied as exponents for the DM, and the DMs in a rule are combined, with the Min operator, into a single DM for the rule. In this way, the importance of attributes of a rule, which can be changed from time to time, can be reflected to reasoning in knowledge-based system with fuzzy rules.With the proposed reasoning procedure, a decision maker can take his judgment on the given decision environment into a static knowledge base with fuzzy rules when he makes decision with the knowledge base. This procedure can be automated as a pre-processing system for fuzzy expert systems. Thereby the quality of decisions could be enhanced.