A total uncertainty measure for D numbers based on belief intervals

Uncertainty quantification is very important in many applications. As a generalization of Dempster-Shafer theory, the theory of D numbers is a new theoretical framework for uncertainty reasoning. Measuring the uncertainty of knowledge or information represented by D numbers is an unsolved issue in that theory. In this paper, inspired by distance-based uncertainty measures for Dempster-Shafer theory, a total uncertainty measure for a D number is proposed based on its belief intervals. The proposed total uncertainty measure can simultaneously capture the discord, and nonspecificity, and nonexclusiveness involved in D numbers. And some basic properties of this total uncertainty measure, including range, monotonicity, generalized set consistency, are also presented. At last, an illustrative application about feature evaluation is given to verify the effectiveness of the proposed uncertainty measure.     

定性Dempster-Shafer理论

采用一个全序的符号值集合来代替数值信任度集合[0,1],提出定性Dempster-Shafer理论来处理既有不确定性又有不精确性的推理问题．首先,定义了适合对不确定性进行定性表达和推理的定性mass函数、定性信任函数等概念,并且研究了这些概念之间的基本关系;其次,详细讨论了定性证据合成问题,提出了基于平均策略的证据合成规则．这种定性Dempster-Shafer理论与其他相关理论相比,既通过在定性领域重新定义Dempster-Shafer理论的基本概念,继承了Dempster-Shafer理论在不确定推理方面的主要特点,同时又具有适合对不精确性操作的既有严格定义又符合直观特性的定性算子,因此更适合基于Dempster-Shafer理论框架不精确表示和处理不确定性．     

基于模糊AHP和证据理论的混合决策模型

针对模糊层次分析法（Fuzzy AHP,FAHP）用于产品方案评价时存在的逆向排序问题和不确定信息处理问题,分析其原因后将不确定性推理的证据推理（Evidential Reasoning,ER）理论引入FAHP的层次结构进行底层方案评价值的计算,在此基础上提出了FAHP-ER混合决策模型,该模型由于ER的引入而大大提高了它在不确定信息处理方面的能力,从而克服了FAHP方法对不确定信息处理不足的问题。用一个轴承转子系统设计方案的评价实例对混合决策模型进行了验证,很好地处理了方案评价过程中决策者的各种主观不确定信息,在此基础上获得了最佳的转子设计方案。     

Combination calculi for uncertainty reasoning: representing uncertainty using distributions

There are many different methods for incorporating notions of uncertainty in evidential reasoning. A common component to these methods is the use of additional values, other than conditional probabilities, to assert current degrees of belief and certainties in propositions. Beginning with the viewpoint that these values can be associated with statistics of multiple opinions in an evidential reasoning system, we categorize the choices that are available in updating and tracking these multiple opinions. In this way, we develop a matrix of different uncertainty calculi, some of which are standard, and others are new. The main contribution is to formalize a framework under which different methods for reasoning with uncertainty can be evaluated. As examples, we see that both the “Kalman filtering” approach and the “Dempster–Shafer” approach to reasoning with uncertainty can be interpreted within this framework of representing uncertainty by the statistics of multiple opinions. This revised version was published online in June 2006 with corrections to the Cover Date.     

一种基于区间信度结构的混合型多属性决策方法

考虑决策者对语言评估的不确定性,用区间值表示语言评价等级,并将证据理论(DST)和数据包络分析(DEA)两种方法相结合,提出一种基于区间信度结构的混合型多属性决策方法.首先,通过区间型交叉效率模型构造决策单元定量指标的区间信度结构,利用证据推理非线性优化模型对区间信度结构进行集结,并将集结后的区间信度结构进行效用等价转换,得到一个信度为区间型的分布式等级评估向量;然后,通过证据推理非线性优化模型对定量指标和定性指标的区间信度结构进行融合,得到决策单元总的区间信度结构分布式评估向量,并结合期望效用理论对决策单元进行排序;最后,通过具体算例进行比较分析,结果验证了所提出方法的有效性和合理性.     

一种新的知识表达模型——信度网

A belief network is a new mechanism for knowledge representation based on probability the-ory. Its distinct performance in representing and reasoning about uncertainty makes it a hot researchtopic in artificial intelligence. It is now being Used in many areas. In this paper,we give a comprehensiveintroduction to a belief network,including its historic background ,principles ,the progress of its researchand development ,and some challenging problems.     

时态Dempster—Shafer理论

1 引言不确定性推理是人工智能中一个重要研究方向。在不同的应用领域,基于不同的不确定性度量理论,提出了许多不确定性推理理论和方法,例如确定因子法、概率推理、模糊推理和Dempster-Sharer理论等。Dempster-Shafer理论是Shafer在Dempster提出的概率区间度量理论的基础上进一步发展的不确定性推理理论。与概率推理等相比,Demp     

WSNs deployment framework based on the theory of belief functions

Deployment is a fundamental issue in Wireless Sensor Networks (WSNs). Indeed, the number and locations of sensors determine the topology of the WSN, which will further influence its performance. Usually, the sensor locations are precomputed based on a “perfect” sensor coverage model. However, in reality, there is an inherent uncertainty and imprecision associated with sensor readings. This issue impinges upon the success of any WSN deployment, and it is therefore important to consider it at the design stage. In contrast to existing work, this paper investigates the belief functions theory to design a unified approach for robust uncertainty-aware WSNs deployment. Specifically, we address the issue of handling uncertainty and information fusion for an efficient WSNs deployment by exploiting the belief functions reasoning framework. We present a flexible framework for target/event detection within the transferable belief model. Using this framework, we propose uncertainty-aware deployment algorithms that are able to determine the minimum number of sensors as well as their locations in such a way that full area coverage is provided. Related issues, such as connectivity, preferential coverage, challenging environments and sensor reliability, are also discussed. Simulation results, based on both synthetic data set and data traces collected in a real deployment for vehicle detection, are provided to demonstrate the ability of our approach to achieve an efficient WSNs deployment by exploiting a collaborative target/event detection scheme. Using the devised approach, we successfully deploy an experimental testbed for motion detection. The obtained results are reported, supported by comparison with other works.     

The limitation of Bayesianism

In the current discussion about the capacity of Bayesianism in reasoning under uncertainty, there is a conceptual and notational confusion between the explicit condition and the implicit condition of a probability evaluation. Consequently, the limitation of Bayesianism is often seriously underestimated. To represent the uncertainty of a belief system where revision is needed, it is not enough to assign a probability value to each belief.     

Extending abstract argumentation systems theory

In this paper, we extend the theory of abstract argumentation systems proposed by Vreeswijk (1997). This framework stands at a high abstraction level and provides a general model for argumentation activity. However, the theory reveals an inherent limitation in that the premises of the argumentation process are assumed to be indefeasible, and this introduces the need of an implicit constraint on the strength of the arguments, in order to preserve correctness. In many application contexts the information available to start reasoning is not guaranteed to be completely reliable, therefore it is natural to assume that premises can be discarded during the argumentation process. We extend the theory by admitting that premises can be defeated and relaxing the implicit assumption about their strength.Besides fixing the technical problems related to this hidden assumption (e.g., ensuring that warranted arguments are compatible), our proposal provides an integrated model for belief revision and defeasible reasoning, confirming the suitability of argumentation as a general model for the activity of intelligent reasoning in presence of various kinds of uncertainty.     

An information systems security risk assessment model under uncertain environment

Given there is a great deal of uncertainty in the process of information systems security (ISS) risk assessment, the handling of uncertainty is of great significance for the effectiveness of risk assessment. In this paper, we propose an ISS risk assessment model based on the improved evidence theory. Firstly, we establish the ISS index system and quantify index weights, based on which the evidential diagram is constructed. To deal with the uncertain evidence found in the ISS risk assessment, this model provides a new way to define the basic belief assignment in fuzzy measure. Moreover, the model also provides a method of testing the evidential consistency, which can reduce the uncertainty derived from the conflicts of evidence. Finally, the model is further demonstrated and validated via a case study, in which sensitivity analysis is employed to validate the reliability of the proposed model.     

一种通用的不确定性推理和决策模型

基于开世界假设,提出了一个通用的不确定性推理和决策框架.为反映证据的实时关联程度和先验信息,定义了一个证据可信度综合指标,从而提高了融合系统的可靠性.在此基础上,分析冲突的来源,定义了一种新的证据组合规则,将冲突进行合理分配,不仅包含了证据或传感器本身的性能和信息,而且反映了系统本身的知识完备程度,从而可以很好的融合复杂背景下或者不完备知识下的多源异类目标信息,检测新模式和样本噪声,实现最优决策.     

A framework for rule-base evidential reasoning in the interval setting applied to diagnosing type 2 diabetes

A new framework for rule-base evidential reasoning in the interval setting is presented. While developing this framework, two collateral problems such as combining and normalizing interval-valued belief structures from different sources and comparing resulting belief intervals, the bounds of which are intervals, arise. The first problem is solved with the use of the so-called “interval extended zero” method. It is shown that interval valued results of the proposed approach to combining and normalizing interval-valued belief structures are enclosed in those obtained by known methods and possess three desirable intuitively obvious properties of normalization procedure defined in the paper. The second problem is solved using the method for interval comparison based on the Demposter-Shafer theory providing the interval valued results of comparison. The advantages of the proposed framework for rule-base evidential reasoning in the interval setting are demonstrated using the developed expert system for diagnosing type 2 diabetes.     

Integrating gray system theory and logistic regression into case-based reasoning for safety assessment of thermal power plants

Safety assessment of thermal power plants (TPPs) is one of the important means to guarantee the safety of production in thermal power production enterprises. Due to various technical limitations, existing assessment approaches, such as analytic hierarchy process (AHP), Monte Carlo methods, artificial neural network (ANN), etc., are unable to meet the requirements of the complex security assessment of TPPs. Currently, most of the security assessments of TPP are completed by the means of experts’ evaluations. Accordingly, the assessment conclusions are greatly affected by the subjectivity of the experts. Essentially, the evaluation of power plant systems relies to a large extent on the knowledge and length of experience of the experts. Therefore in this domain case-based reasoning (CBR) is introduced for the security assessment of TPPs since this methodology models expertise through experience management. Taking the management system of TPPs as breakthrough point, this paper presents a case-based approach for the Safety assessment decision support of TPPs (SATPP). First, this paper reviews commonly used approaches for TPPs security assessment and the current general evaluation process of TPPs security assessment. Then a framework for the Management System Safety Assessment of Thermal Power Plants (MSSATPP) is constructed and an intelligent decision support system for MSSATPP (IDSS-MSSATPP) is functionally designed. IDSS-MSSATPP involves several key technologies and methods such as knowledge representation and case matching. A novel case matching method named Improved Gray CBR (IGCBR) has been developed in which a statistical approach (logistic regression) and Gray System theory are integrated. Instead of applying Gray System theory directly, it has been improved to integrate it better into CBR. In addition this paper describes an experimental prototype system of IDSS-MSSATPP (CBRsys-TPP) in which IGCBR is integrated. The experimental results based on a MSSATPP data set show that CBRsys-TPP has high accuracy and systematically good performance. Further comparative studies with several other common classification approaches also show its competitive power in terms of accuracy and the synergistic effects of the integrated components.     

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.     

Deriving evidence theoretical functions in multivariate data spaces: a systematic approach.

The mathematical theory of evidence is a generalization of the Bayesian theory of probability. It is one of the primary tools for knowledge representation and uncertainty and probabilistic reasoning and has found many applications. Using this theory to solve a specific problem is critically dependent on the availability of a mass function (or basic belief assignment). In this paper, we consider the important problem of how to systematically derive mass functions from the common multivariate data spaces and also the ensuing problem of how to compute the various forms of belief function efficiently. We also consider how such a systematic approach can be used in practical pattern recognition problems. More specifically, we propose a novel method in which a mass function can be systematically derived from multivariate data and present new methods that exploit the algebraic structure of a multivariate data space to compute various belief functions including the belief, plausibility, and commonality functions in polynomial-time. We further consider the use of commonality as an equality check. We also develop a plausibility-based classifier. Experiments show that the equality checker and the classifier are comparable to state-of-the-art algorithms.     

A Multisensor Decision Fusion System for Terrain Safety Assessment

This paper describes an onboard automated hybrid reasoning system for terrain safety assessment using multiple heterogeneous sensors onboard a spacecraft. An innovative feature of this system is integration of multiple sensing modalities and different reasoning engines into a unified approach. Three different frameworks for representation of data uncertainty are considered: fuzzy set theory, Bayesian probability theory, and Dempster–Shafer belief theory. The hybrid reasoning system is composed of three subsystems, namely, multisensor fusion, multidecision fusion, and tier-based fusion selection, where each tier represents a range of spacecraft altitudes. Simulation results are presented to illustrate the multisensor decision fusion methodology described in this paper. The developed capabilities will enable future spacecraft to land safely in more challenging planetary regions with scientifically interesting terrain features.      

On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty

In multiple attribute decision analysis (MADA), one often needs to deal with both numerical data and qualitative information with uncertainty. It is essential to properly represent and use uncertain information to conduct rational decision analysis. Based on a multilevel evaluation framework, an evidential reasoning (ER) approach has been developed for supporting such decision analysis, the kernel of which is an ER algorithm developed on the basis of the framework and the evidence combination rule of the Dempster-Shafer (D-S) theory. The approach has been applied to engineering design selection, organizational self-assessment, safety and risk assessment, and supplier assessment. In this paper, the fundamental features of the ER approach are investigated. New schemes for weight normalization and basic probability assignments are proposed. The original ER approach is further developed to enhance the process of aggregating attributes with uncertainty. Utility intervals are proposed to describe the impact of ignorance on decision analysis. Several properties of the new ER approach are explored, which lay the theoretical foundation of the ER approach. A numerical example of a motorcycle evaluation problem is examined using the ER approach. Computation steps and analysis results are provided in order to demonstrate its implementation process.     

A probabilistic reasoning model: Formulation and control strategy

It has been recognized that past experiences of a decision maker often plays a pivotal role in solving new problem instances. Therefore, the ability to model human reasoning processes has become an important subject of research in recent years. In many applications, the reasoning process must deal with uncertainty inherent in the problem domain. This research addresses the issue of supporting the model formulation and data acquisition processes for situations that (i) operate under uncertain conditions, and (ii) utilize evidential information that is gathered in stages. A theoretical framework is presented for the probabilistic formulation of the reasoning process that incorporates past experiences. The model is validated by testing its performance on simulated data, and is shown to work well when a sufficiently large number of cases are available for estimating probabilities. The probabilistic reasoning system can revise beliefs in an intuitively appealing and theoretically sound manner when information is acquired in an incremental fashion. Two dynamic information gathering strategies are discussed for such a reasoning system, one using information theoretic techniques, and the other using decision theoretic techniques.     

Managing uncertainty in location services using rough set and evidence theory

Uncertainty in service management stems from the incompleteness and vagueness of the conditioning attributes that characterize a service. In particular, location based services often have complex interaction mechanisms in terms of their neighborhood relationships. Classical location service models require rigorous parameters and conditioning attributes and offers limited flexibility to incorporate imprecise or ambiguous evidences. In this paper we have developed a formal model of uncertainty in service management. We have developed a rough set and Dempster–Shafer’s evidence theory based formalism to objectively represent uncertainty inherent in the process of service discovery, characterization, and classification. Rough set theory is ideally suited for dealing with limited resolution, vague and incomplete information, while Dempster–Shafer’s evidence theory provides a consistent approach to model an expert’s belief and ignorance in the classification decision process. Integrating these two formal approaches in spatial domain provides a way to model an expert’s belief and ignorance in service classification. In an application scenario of the model we have used a cognitive map of retail site assessment, which reflects the partially subjective assessment process. The uncertainty hidden in the cognitive map can be consistently formalized using the proposed model. Thus we provide a naturalistic means of incorporating both qualitative aspects of intuitive knowledge as well as hard empirical information for service management within a formal uncertainty framework.