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1.
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． 相似文献
2.
Dempster-Shafer evidence theory has been widely used in many applications due to its advantages with weaker conditions than Bayes probability. How to measure the uncertainty of basic probability assignment (BPA) in Dempster-Shafer evidence theory is an open and essential issue. Tsallis entropy as nonextensive entropy proposed according to multifractals has been used in many fields. In this paper, a new uncertainty measure of BPA is presented based on Tsallis entropy. The key issue is to determine the value of
3.
不确定性是决策信息系统的固有特征,对系统的性能具有重要影响.有效地度量决策信息系统的不确定性具有重要意义.粗集理论是处理不确定信息最成功的工具之一.本文评述多种基于粗集理论的系统不确定性度量方式;分析它们的代数特征和数量关系;并通过仿真实验系统地比较它们的性能.结果表明\"全知熵不确定率\"是最有效的不确定性度量方式,其合理性通过它的成功应用得到进一步验证. 相似文献
4.
Measures of two types of uncertainty that coexist in the Dempster-Shafer theory are overviewed. A measure of one type of uncertainty, which expresses nonspecificity of evidential claims, is well justified on both intuitive and mathematical grounds. Proposed measures of the other types of uncertainty, which atlempt to capture conflicts among evidential claims, are shown to have some deficiencies. To alleviate these deficiencies, a new measure is proposed. This measure, which is called a measure of discord, is not only satisfactory on intuitive grounds, but has also desirable mathematical properties. A measure of total uncertainty, which is defined as the sum of nonspecificity and discord, is also discussed. The paper focuses on conceptual issues. Mathematical properties of the measure of discord are only slated; their proofs are given in a companion paper.15 相似文献
5.
DAVID HARMANEC 《国际通用系统杂志》2013,42(1-2):63-72
Abstract The relationship between uncertainty and the Dempster rule of combination in Dempster-Shafer theory is discussed. In particular, a condition is presented that is sufficient to guarantee that uncertainty does not increase by using the rule. A new definition of conflict of pieces of evidence is proposed and discussed. 相似文献
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E. M. OBLOW 《国际通用系统杂志》2013,42(4):357-378
A measurement framework for O-theory, an algebra of random sets, is presented. The framework is probabilistic and derived from experimental measurements of evidential support. It is used to quantify the probabilistic masses needed in O-theory. This framework allows a connection to be made between this random set algebra and the possibilistic form of fuzzy set theory. Instances in which these two different representations of the same experimental data are equivalent are explored. The relationship between some basic operators in both theories are then discussed, along with their connection to Dempster-Shafer theory. Finally, several illustrative examples of deductive inferencing under uncertainty are solved. The equivalence of the representations of the results in both uncertainty theories is demonstrated. 相似文献
8.
Maxitive Belief Structures (MBSs), emerge as a novel class of belief structure to represent imprecise and uncertain information with a specific structure allowing it to model both probability nonspecificity and imprecise. A novel matrix game with payoffs of MBS is presented. The proposed model can be used to describe interactions among players, and an effective method is developed to find the solution of a game through reaching an equilibrium point. A numerical example is given to verify the validness of the proposed model. 相似文献
9.
对数据信息不确定性的度量是学术界和工业界十分关注的课题,目前常用的不确定性度量方法基本上是基于方差或信息熵的,在方差计算的基础上提出了一种简单的度量方法来度量随机数据的不确定性,这种度量方法基于累积方差但与传统方的基于方差的形式有所不同,和信息熵具有类似的表示意义而且计算度更快,分析结果表明该方法可以在对离散随机数据的... 相似文献
10.
通过语义分析,提出了一种拓展的粗糙集不确定性度量公理化定义;将香农熵函数推广到严凹函数,提出了一类以条件概率为自变量、基于严凹函数的粗糙集不确定性度量公式,它是严凹函数值的加权平均.在此基础上,得到一系列粗糙集不确定性度量方法.从严凹函数视角讨论了基于模糊熵的不确定性度量方法,发现现有多种能够用于度量粗糙集不确定性的模糊熵函数都是所提出方法的特殊情形.比较了粗糙度、改进粗糙度和所提出方法的区别和联系,最后设计了一些算例,比较了各种方法的异同,验证了基于严凹函数的粗糙集不确定性度量与粗糙集不确定性语义是一致的. 相似文献
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GEORGE J. KLIR 《国际通用系统杂志》2013,42(2-3):249-275
The paper introduces a new principle, referred to as the principle of uncertainty and information invariance, for making transformations between different mathematical theories by which situations under uncertainty can be characterized. This principle requires that the amount of uncertainty (and related information) be preserved under these transformations. The principle is developed in sufficient details for transformations between probability theory and possibility theory under interval, log-interval and ordinal scales. Its broader use is discussed only in general terms and illustrated by an example. 相似文献
12.
模糊粗糙集理论目前在数据挖掘和机器学习等领域受到了广泛的关注. 该理论提供了一种能克服离散化问题的有效工具,并能直接应用于数值或混合属性数据. 在模糊粗糙集模型中,定义模糊关系来测量对象之间的相似性,数值属性值不再需要离散化. 模糊粗糙集理论已经被成功应用于许多领域,如属性约简、规则提取、聚类分析和离群点检测. 信息熵被引入到模糊粗糙集理论进行模糊和不确定信息的表示,产生了不同形式的模糊不确定性度量,如模糊信息熵、模糊补熵和模糊互信息等. 然而,大部分所提关于决策的模糊互信息都是非单调的,这可能导致一个不收敛的学习算法. 为此,基于混杂核模糊补熵,定义了关于决策的模糊补互信息,证明了其随特征呈单调性变化. 进而,利用混杂核模糊补互信息探索特征选择方法并且设计了相关的算法. 实验结果展示了在大多数情况下所提算法可以选取更少的特征且能保持或提高分类准确率. 相似文献
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Entropy is commonly used as a way to measure the uncertainty of random variables. In uncertain set theory, a concept of entropy for uncertain sets has been defined by using logarithm. However, such an entropy fails to measure the uncertain degree of some uncertain sets. This paper aims at proposing a concept of elliptic entropy for uncertain sets and investigating its properties such as translation invariance and positive linearity. It also provides some formulas for calculating the elliptic entropy via inverse membership functions. Additionally, elliptic relative entropy for uncertain sets is presented as a measure of the difference between two membership functions, and some applications are considered in portfolio selection and clustering. 相似文献
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This paper provides an overview of fuzzy measures, fuzzy integration theories and Choquet's capacity theory. Belief, plausibility, and possibility measures are characterized as Choquet capacities and as fuzzy measures. The relationship between possibility measures, fuzzy sets, and approximate reasoning is established. Recent results on extensions of fuzzy measures, structural characteristics of fuzzy measures, and convergence of function sequences on fuzzy measure spaces are presented. Fuzzy measure integration concepts due to Sugeno and Choquet and their applications are discussed. An extensive list of references to the literature of fuzzy measures, Sugeno and Choquet integrals, fuzzy probabilities, fuzzy random variables, probabilistic sets, and random sets is provided. Applicalions discussed or referenced include information fusion, information retrieval, approximate reasoning, artificial intelligence, uncertainty theory, and control and decision theory. 相似文献
15.
MICHAEL KELLY 《国际通用系统杂志》2013,42(2):173-175
The greatest portion of papers dealing with the Dempster-Shafer theory consider the case when the basic universe is a finite set, so that all the numerical characteristics introduced and investigated in the D-S theory, including the believeability and plausibility functions as the most important ones, can be easily defined by well-known combinatoric formulas outgoing from a simple probability distribution (basic belief assignment, in the terms of D-S theory) on the power-set 𝒫(S) of all subsets of S. The obvious fact that these numerical characteristics can be equivalently defined also by appropriate set-valued random variables becomes to be of greater importance in the case when S is infinite. We investigate, in this paper, the case when the power-set 𝒫(S) over an infinite set S is equipped by a nonempty σ-field ? 𝒫(𝒫(S)) andwhen the belief and plausibility functions are defined by a set-valued random variable (i.e., -measurable mapping) which takes a given probability space into the measurable space (𝒫(S),) In general, the values of the two functions in question need not be defined for each subset T of S. Therefore, we define four extensions of these functions to whole the (S) based on the well-known concepts of inner and outer measure, and investigate their properties; interesting enough, just one of them respect the philosophy of the D-S approach to uncertainty quantification and processing and keeps the properties possessed by believeability and plausibility functions defined over finite spaces. 相似文献
16.
Montserrat Casanovas José M. Merigó 《Expert systems with applications》2012,39(8):7138-7149
We study the decision-making problem with Dempster-Shafer theory of evidence. We analyze how to deal with this model when the available information is uncertain and it can be represented with fuzzy numbers. We use different types of aggregation operators that aggregate fuzzy numbers such as the fuzzy weighted average (FWA), the fuzzy ordered weighted averaging (FOWA) operator and the fuzzy hybrid averaging (FHA) operator. As a result, we get the belief structure fuzzy weighted average (BS-FWA), the belief structure fuzzy ordered weighted averaging (BS-FOWA) operator and the belief structure fuzzy hybrid averaging (BS-FHA) operator. We further generalize this new approach by using generalized and quasi-arithmetic means. We also develop an illustrative example regarding the selection of investments where we can see the different results obtained by using different types of fuzzy aggregation operators. 相似文献
17.
基于证据理论的不确定性推理方法及其应用 总被引：1，自引：0，他引：1
针对民航无线电管理中遇到的干扰问题以及客观世界中描述客观现象的知识和信息具有不确定性的特点,结合民航无线电干扰查处的实际情况,提出基于一种产生式规则的知识表示方法,以区间确定因子描述不确定性。提出基于Dempster-Shafer证据理论和区间确定因子的不确定性推理方法。进一步根据领域专家经验建立民航无线电干扰查处规则,以基于Dempster-Shafer证据理论和区间确定因子的不确定性推理方法为推理机,给出民航无线电干扰查处专家系统的结构及工作流程,采用C#语言结合MySQL数据库开发民航无线电干扰查处专家系统,并通过案例分析说明该系统的有效性和实用性。 相似文献
18.
Xinyang Deng 《国际智能系统杂志》2018,33(9):1869-1879
Measuring the uncertainty of pieces of evidence is an open issue in belief function theory. A rational uncertainty measure for belief functions should meet some desirable properties, where monotonicity is a very important property. Recently, measuring the total uncertainty of a belief function based on its associated belief intervals becomes a new research idea and has attracted increasing interest. Several belief interval based uncertainty measures have been proposed for belief functions. In this paper, we summarize the properties of these uncertainty measures and especially investigate whether the monotonicity is satisfied by the measures. This study provide a comprehensive comparison to these belief interval based uncertainty measures and is very useful for choosing the appropriate uncertainty measure in the practical applications. 相似文献
19.
D–S证据理论中一个关键问题是度量传感器给出的基本概率赋值(BPA)的不确定性大小,它的准确度量对于评估信任结构传递的信息量至关重要.本文首先提出了改进的归一化投影方法(iNP),然后基于i NP提出了一种新的投影不确定性(PU)广义度量方法,理论证明和实验仿真说明了PU满足非负性、有界性、不变性、单调性、不反直观性、较高的敏感性和较低的计算负担等性质,这些性质保证了PU可以有效对BPA的不确定性广义度量.与现有的不确定性度量方法相比,所提出的方法对证据的变化更为敏感.最后,基于PU方法给出了一种新的证据组合方法,通过数值实例和实际应用,说明了本文所提方法的有效性和合理性. 相似文献
20.
For the sake of great ability of handling uncertain information, Dempster-Shafer evidence theory is extensively used in information fusion. Nevertheless, when there exists highly inconsistent evidences, using classical Dempster's combination rule may lead to counter-intuitive results. To address this issue, a new conflicting evidences combination method based on distance function and Tsallis entropy is proposed. Numerical examples are used to illustrate the feasibility and efficiency of the proposed method. Further, an fault diagnosis problem is used as an example to show the effectiveness and superiority of the proposed method. The proposed method outperforms other methods that the proposed method recognize the target by the probability 99.49%, which is higher than other methods. 相似文献