能处理证据相关性的不确定推理模型

当前已经提出的许多不确定推理模型都不能很好地处理证据之间的相关性。为了解决这个问题,推广了概率计算公式,并把新的理论引入到MYCIN的CF推理模型中,从而证明了新的理论能较好地处理证据之间的相关性。     

On the revision of probabilistic beliefs using uncertain evidence

We revisit the problem of revising probabilistic beliefs using uncertain evidence, and report results on several major issues relating to this problem: how should one specify uncertain evidence? How should one revise a probability distribution? How should one interpret informal evidential statements? Should, and do, iterated belief revisions commute? And what guarantees can be offered on the amount of belief change induced by a particular revision? Our discussion is focused on two main methods for probabilistic revision: Jeffrey's rule of probability kinematics and Pearl's method of virtual evidence, where we analyze and unify these methods from the perspective of the questions posed above.     

基于信任知识库的概率模糊认知图

模糊认知图较难表示概念间因果关系测度的不确定性、因果联系的时空特性及专家对知识的不确定性．在继承模糊认知图模型优点的前提下，在概念间的因果关系中引入条件概率及信任知识库表示，提出基于信任知识库的概率模糊认知图模型．该模型用条件概率及信任知识库表示因果联系的时空特性、专家对知识及概念间因果关系测度的不确定性，从而将因果关系测度的不确定性、因果联系的时空特性及专家对知识的不确定性有效地融入模糊认知图中，自然扩展了模糊认知图模拟因果关系的能力，较大限度地减少了认知图对现实世界模拟的失真．最后通过实验说明了基于信任知识库的概率模糊认知图模型，具有比FCM更强的模拟能力．     

基于证据理论的前景构建方法

为了解决现有成果只重视前景评价而忽视前景构建的问题, 运用专家投票技术提出方案结果可能集的推断方法. 结合相对比较判断和互补判断赋值的思想构建能够有效提取专家认知信息的概率推断矩阵, 并给出其向基本概率分配函数转换的定理. 在此基础上, 将每个专家视为独立证据源, 基于Dempster 组合规则和DSmP 概率转换方法提出前景构建的具体步骤, 并通过应用案例模拟分析演示了所提出方法的操作过程.

     

Inference procedures under uncertainty for the problem-reduction method

From the viewpoint of efficient utilization of human knowledge in complex decision-making problems, the inference procedure under uncertainty is becoming more important for the problem-reduction method and expert systems. Unlike intuitive procedures employed so far in some expert systems, rational inference procedures are described in this paper on the basis of established Bayesian theory and Dempster and Shafer's theory of evidence. These results are extended to include fuzzy knowledge. As an alternative to the two probabilistic approaches which require idealized assumptions, fuzzy reasoning is introduced.     

基于模糊集和DS证据理论的信息安全风险评估方法*

在信息安全风险评估过程中,存在着很多不确定和模糊的因素,针对专家评价意见的不确定性和主观性问题,提出了一种将模糊集理论与DS证据理论进行结合的的风险评估方法。首先,根据信息安全风险评估的流程和要素,建立风险评估指标体系,确定风险影响因素;其次,通过高斯隶属度函数,求出专家对各影响因素的评价意见隶属于各个不同评价等级的程度;再次,将其作为DS理论所需的基本概率分配,引入基于矩阵分析和权值分配的融合算法综合多位专家的评价意见;最后,结合贝叶斯网络模型的推理算法,得出被测信息系统所面临的风险大小,并对其进行分析。结果显示,将模糊集理论和DS证据理论应用到传统贝叶斯网络风险评估的方法,在一定程度上能够提高评估结果的客观性。     

A mathematical formulation of uncertain information

This paper introduces a mathematical model of uncertain information. Each body of uncertain information is an information quadruplet, consisting of a code space, a message space, an interpretation function, and an evidence space. Each information quadruplet contains prior information as well as possible new evidence which may appear later. The definitions of basic probability and belief function are based on the prior information. Given new evidence, Bayes' rule is used to update the prior information. This paper also introduces an idea of independent information and its combination. A combination formula is derived for combining independent information. Both the conventional Bayesian approach and Dempster-Shafer's approach belong to this mathematical model. A Bayesian prior probability measure is the prior information of a special information quadruplet; Bayesian conditioning is the combination of special independent information. A Dempster's belief function is the belief function of a different information quadruplet; the Dempster combination rule is the combination rule of independent quadruplets. This paper is a mathematical study of handling uncertainty and shows that both the conventional Bayesian approach and Dempster-Shafer's approach originate from the same mathematical theory.This work was supported in part by the National Science Foundation under grant number IRI-8505735 and a summer research grant of Ball State University.     

Evidence combination based on credibility and non-specificity

This paper addresses the combination of unreliable evidence sources which provide uncertain information in the form of basic probability assignment (BPA) functions. We proposed a novel evidence combination rule based on credibility and non-specificity of belief functions. Following a review of all existing non-specificity measures in evidence theory, a non-specificity measure for evidence theory is discussed. It is claimed that the non-specificity degree of a BPA is related to its ability of pointing to one and only one element. Based on the difference between the largest belief grades and other belief grades, a non-specificity measure is defined. Properties of the proposed non-specificity measure are put forward and proved mathematically. Illustrative examples are employed to show the properties of non-specificity measure. After providing a procedure for the evaluation of evidence credibility, we propose a novel evidence combination rule. Numerical example and application in target identification are applied to demonstrate the performance of our proposed evidence combination rule.     

Representation and combination of uncertainty with belief functions and possibility measures

The theory of evidence proposed by G. Shafer is gaining more and more acceptance in the field of artificial intelligence, for the purpose of managing uncertainty in knowledge bases. One of the crucial problems is combining uncertain pieces of evidence stemming from several sources, whether rules or physical sensors. This paper examines the framework of belief functions in terms of expressive power for knowledge representation. It is recalled that probability theory and Zadeh's theory of possibility are mathematically encompassed by the theory of evidence, as far as the evaluation of belief is concerned. Empirical and axiomatic foundations of belief functions and possibility measures are investigated. Then the general problem of combining uncertain evidence is addressed, with focus on Dempster rule of combination. It is pointed out that this rule is not very well adapted to the pooling of conflicting information. Alternative rules are proposed to cope with this problem and deal with specific cases such as nonreliable sources, nonexhaustive sources, inconsistent sources, and dependent sources. It is also indicated that combination rules issued from fuzzy set and possibility theory look more flexible than Dempster rule because many variants exist, and their numerical stability seems to be better.     

一种新的不确定推理方法

提出了一种基于认知结构的不确定推理方法:采用四值认知结构表达不确定知识,采用定义在认知结构上的双向认知推理结构来处理推理规则的不确定性.介绍的不确定推理方法可以包容精确的概率推理、容忍信息的不确定性、有效地避免推理规则之间的相互关系问题,并且使认知结构最简推理的计算复杂度与推理节点个数成线性关系.     

Acoustic signal interpretation: Reasoning with non-specific and uncertain information

An expert system approach to identifying the sources of underwater acoustic signals is described. Much of the information about ocean vessels, which is derived from acoustic features, is non-specific (i.e. pointing only to general classes of vessels). As well, there is often uncertainty both in the accuracy of the feature identification and in the applicability of the rules in the knowledge base. In order to deal with non-specific and uncertain evidence in the presence of an unknown number of signal sources, we develop an inference network approach which is based on the Dempster-Shafer theory of evidence.     

A new belief rule base knowledge representation scheme and inference methodology using the evidential reasoning rule for evidence combination

In this paper, we extend the original belief rule-base inference methodology using the evidential reasoning approach by i) introducing generalised belief rules as knowledge representation scheme, and ii) using the evidential reasoning rule for evidence combination in the rule-base inference methodology instead of the evidential reasoning approach. The result is a new rule-base inference methodology which is able to handle a combination of various types of uncertainty.Generalised belief rules are an extension of traditional rules where each consequent of a generalised belief rule is a belief distribution defined on the power set of propositions, or possible outcomes, that are assumed to be collectively exhaustive and mutually exclusive. This novel extension allows any combination of certain, uncertain, interval, partial or incomplete judgements to be represented as rule-based knowledge. It is shown that traditional IF-THEN rules, probabilistic IF-THEN rules, and interval rules are all special cases of the new generalised belief rules.The rule-base inference methodology has been updated to enable inference within generalised belief rule bases. The evidential reasoning rule for evidence combination is used for the aggregation of belief distributions of rule consequents.     

A computational approach to approximate and plausible reasoning with applications to expert systems

The intended purpose of this paper is twofold: proposing a common basis for the modeling of uncertainty and imprecision, and discussing various kinds of approximate and plausible reasoning schemes in this framework. Together with probability, different kinds of uncertainty measures (credibility and plausibility functions in the sense of Shafer, possibility measures in the sense of Zadeh and the dual measures of necessity, Sugeno's g?-fuzzy measures) are introduced in a unified way. The modeling of imprecision in terms of possibility distribution is then presented, and related questions such as the measure of the uncertainty of fuzzy events, the probability and possibility qualification of statements, the concept of a degree of truth, and the truth qualification of propositions, are discussed at length. Deductive inference from premises weighted by different kinds of measures by uncertainty, or by truth-values in the framework of various multivalued logics, is fully investigated. Then, deductive inferences from imprecise or fuzzy premises are dealt with; patterns of reasoning where both uncertainty and imprecision are present are also addressed. The last section is devoted to the combination of uncertain or imprecise pieces of information given by different sources. On the whole, this paper is a tentative survey of quantitative approaches in the modeling of uncertainty and imprecision including recent theoretical proposals as well as more empirical techniques such as the ones developed in expert systems such as MYCIN or PROSPECTOR, the management of uncertainty and imprecision in reasoning patterns being a key issue in artificial intelligence.     

Evidential reasoning using extended fuzzy Dempster–Shafer theory for handling various facets of information deficiency

This work investigates the problem of combining deficient evidence for the purpose of quality assessment. The main focus of the work is modeling vagueness, ambiguity, and local nonspecificity in information within a unified approach. We introduce an extended fuzzy Dempster–Shafer scheme based on the simultaneous use of fuzzy interval‐grade and interval‐valued belief degree (IGIB). The latter facilitates modeling of uncertainties in terms of local ignorance associated with expert knowledge, whereas the former allows for handling the lack of information on belief degree assignments. Also, generalized fuzzy sets can be readily transformed into the proposed fuzzy IGIB structure. The reasoning for quality assessment is performed by solving nonlinear optimization problems on fuzzy Dempster–Shafer paradigm for the fuzzy IGIB structure. The application of the proposed inference method is investigated by designing a reasoning scheme for water quality monitoring and validated through the experimental data available for different sampling points in a water distribution network. © 2011 Wiley Periodicals, Inc.     

证据推理理论及其应用

证据理论既能够灵活处理不确定信息,包括随机性、模糊性、不准确性和不一致性,又能够有效融合定量信息和定性知识.目前,证据理论已广泛应用于评估与决策等多个领域中,包括多属性决策分析、信息融合、模式识别和专家系统等.本文从D-S证据理论出发,针对Dempster组合规则存在的"反直觉"问题和组合爆炸,主要围绕置信分布理论系统...     

Thinking persons and cognitive science

Cognitive psychology and cognitive science are concerned with a domain of cognition that is much broader than the realm of judgement, belief, and inference. The idea of states with semantic content is extended far beyond the space of reasons and justification. Within this broad class of states we should, however, differentiate between the states distinctive of thinking persons — centrally, beliefs, desires, and intentions — and other states. The idea of consciousness does not furnish a principle of demarcation. But the distinction between states whose content is conceptualized by the person whose states they are and states for which this is not so is more promising. This principle of demarcation contains the seeds of a problem for distributed connectionism. The article ends with some more general reflections about cognitive science.     

The Reasonableness of Possibility From the Perspective of Cox

The possibility calculus is shown to be a reasonable belief representation in Cox's sense, even though possibility is formally different from probability. So‐called linear possibility measures satisfy the equations that appear in Cox's theorem. Linear possibilities are known to be related to the full range of possibility measures through a method for representing belief based on sets that is similar to a technique pioneered by Cox in the probabilistic domain. Exploring the relationship between possibility and Cox's belief measures provides an opportunity to discuss some of the ways in which Cox dissented from bayesian orthodoxy, especially his tolerance of partially ordered belief and his rejection of prior probabilities for inference which begins in ignorance.     

Iterative learning belief rule-base inference methodology using evidential reasoning for delayed coking unit

The belief rule-base inference methodology using evidential reasoning (RIMER) approach has been proved to be an effective extension of traditional rule-based expert systems and a powerful tool for representing more complicated causal relationships using different types of information with uncertainties. With a predetermined structure of the initial belief rule-base (BRB), the RIMER approach requires the assignment of some system parameters including rule weights, attribute weights, and belief degrees using experts’ knowledge. Although some updating algorithms were proposed to solve this problem, it is still difficult to find an optimal compact BRB. In this paper, a novel updating algorithm is proposed based on iterative learning strategy for delayed coking unit (DCU), which contains both continuous and discrete characteristics. Daily DCU operations under different conditions are modeled by a BRB, which is then updated using iterative learning methodology, based on a novel statistical utility for every belief rule. Compared with the other learning algorithms, our methodology can lead to a more optimal compact final BRB. With the help of this expert system, a feedforward compensation strategy is introduced to eliminate the disturbance caused by the drum-switching operations. The advantages of this approach are demonstrated on the UniSim? Operations Suite platform through the developed DCU operation expert system modeled and optimized from a real oil refinery.     

一种基于证据理论和模糊距离的融合方法

针对决策支持系统中专家不确定性意见难以融合的问题。本文提出了一种基于证据理论和模糊距离相结合的决策融合方法。首先运用模糊距离方法来获得专家的权重和属性指标的相对权重,并对专家决策中由于主观认识的局限性带来的不确定性问题进行了研究。然后运用DS证据理论识别框架计算出概率分配函数,并对所有方案进行排序选择,得出最终的决策融合意见。最后,通过实验表明,运用此方法对不确定性信息的融合具有很好的可行性和有效性。     

An inquiry into computer understanding

This essay addresses a number of issues centered around the question of what is the best method for representing and reasoning about common sense (sometimes called plausible inference). Drew McDermott has shown that a direct translation of commonsense reasoning into logical form leads to insurmountable difficulties, from which McDermott concluded that we must resort to procedural ad hocery. This paper shows that the difficulties McDermott described are a result of insisting on using logic as the language of commonsense reasoning. If, instead, (Bayesian) probability is used, none of the technical difficulties found in using logic arise. For example, in probability, the problem of referential opacity cannot occur and nonmonotonic logics (which McDermott showed don't work anyway) are not necessary. The difficulties in applying logic to the real world are shown to arise from the limitations of truth semantics built into logic–probability substitutes the more reasonable notion of belief. In Bayesian inference, many pieces of evidence are combined to get an overall measure of belief in a proposition. This is much closer to commonsense patterns of thought than long chains of logical inference to the true conclusions. Also it is shown that English expressions of the “IF A THEN B” form are best interpreted as conditional probabilities rather than universally quantified expressions. Bayesian inference is applied to a simple example of linguistic information to illustrate the potential of this type of inference for AI. This example also shows how to deal with vague information, which has so far been the province of fuzzy logic. It is further shown that Bayesian inference gives a theoretical basis for inductive inference that is borne out in practice. Instead of insisting that probability is the best language for commonsense reasoning, a major point of this essay is to show that real inference is a complex interaction between probability, logic, and other formal representation and reasoning systems.