直觉模糊集隶属度与非隶属度函数的确定方法

基于证据理论研究直觉模糊集隶属度和非隶属度函数的确定问题是一种新的思路.首先分析信任函数、似然函数与隶属度函数、非隶属度函数的互通性;然后给出广义基本概率分配(BPA)函数、广义信任函数和广义似然函数的定义;最后在这3个改进定义的基础上建立直觉模糊集隶属度函数、非隶属度函数模型,通过证明和实例验证了模型的正确性和有效性.     

一种基于证据理论和模糊集合的信息融合方法

针对证据理论应用中基本概率分配函数难以确定和多传感器之间相互支持程度计算绝对化的问题,提出了一种基于证据理论和模糊集合(FSB-DS)的信息融合方法。该方法首先利用相关性函数定义不确定信息的模糊支持区间和模糊支持概率,然后由隶属函数得到各个传感器提供信息的可信度,再将支持度和可信度转化为基本概率分配函数,最后进行D-S证据合成。仿真实验表明,该方法获得的结果具有更高的精度和可信度。     

直觉模糊框架内的证据动态可靠性评估及应用

基于证据理论与直觉模糊集之间的关系,提出了一种新的证据可靠性评估方法,该方法可以在先验知识缺乏的情况下,对各证据源的可靠性进行评估。首先,将证据理论中的基本概率赋值函数(Basic Probability Assignment,BPA)转化为直觉模糊集;然后,通过直觉模糊集之间的相似度度量对各BPA之间的相似度进行计算;在此基础上,提出证据支持度的概念,通过分析证据支持度与证据可靠性之间的关系,获得证据的相对可靠性和绝对可靠性;最后,基于证据折扣运算对原始证据进行修正,采用Dempster组合规则对修正后的证据进行组合。此外,基于直觉模糊框架内的证据可靠性评估,提出了一种多传感器融合方法,通过数值实验对该方法的性能进行了对比分析,结果表明,该方法可以实现对不可靠证据的有效评估。     

D-S证据理论在审计证据融合中的应用研究

古典概率难以解释审计判断的不确定性,而D-S证据理论是进行不确定性推理的有效方法,因此应用D-S证据理论进行审计证据融合的研究。针对审计证据的组合问题,提出了基于三角形模糊隶属度函数的基本概率分配函数计算方法,给出了证据组合结果的判决规则,并通过实例验证了该方法的有效性。     

基于样本差异度的基本概率指派生成方法

提出一种基于样本差异度的基本概率指派(BPA) 生成方法. 建立三角模糊数模型, 根据所提出的差异度函数计算模型和待测样本的差异度, 生成初始BPA. 为了消除干扰影响, 对初始BPA进行冲突阈值判别并进行相应的冲突消解, 使得传感器在受到干扰等情况下也可输出合理的BPA. 鸢尾花分类实验表明, 所提出的方法简单实用, 具有较强的干扰消除能力.     

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 new probability transformation method based on a correlation coefficient of belief functions

The Dempster-Shafer evidence theory is widely used in many fields of information fusion because of its advantage in handling uncertain information. One of the key issues in this theory is how to make decision based on a basic probability assignment (BPA). Currently, a feasible scheme is transforming a BPA to a distribution of probabilities. However, little attention was paid to the correlation between BPA and probability distribution. In this paper, a novel method about the probability transformation based on a correlation coefficient of belief functions is proposed. The correlation coefficient is a new measurement, which can effectively measure the correlation between BPAs. The proposed method aims at maximizing the correlation coefficient between the given BPA and the transformed probability distribution. On the basis of this idea, the corresponding probability distribution can be obtained and could reflect the original information of the given BPA to the maximum extent. It is valid to consider that the proposed probability transformation method is reasonable and effective. Numerical examples are given to show the effectiveness of the proposed method.     

一种基本概率指派的模糊生成及其在数据融合中的应用

DS证据组合规则可以在没有先验信息的情况下进行融合,这一优点使得DS证据理论在多传感器融合系统中应用非常广泛.但是各个证据的基本概率指派如何生成仍然是一个有待解决的问题.本文基于模糊匹配,提出了一种基本概率指派生成方法,并应用到多传感器目标识别中.用一个多传感器目标识别的实验表明:所提出的方法可以合理地生成基本概率指派,能够准确的识别目标.     

基于可分性测度的模糊隶属函数确定方法

隶属程度的思想是模糊数学的基本思想,应用模糊数学方法解决实际问题的关键在于建立符合实际的隶属函数,然而,如何正确地确定隶属函数仍是至今尚未完全解决的问题.鉴于此,提出一种基于可分性测度的隶属函数确定方法,利用类间在各个特征上的可分性确定模糊集的划分,进而确定描述该模糊集的隶属函数.通过轨道电路故障诊断实验表明了所提出方法的有效性.     

基于直觉模糊可能性分布的三支决策模型的研究

直觉模糊集理论和可能性理论的融合是不确定问题领域的一个研究热点。文中提出了一种基于直觉模糊可能性分布的直觉模糊可能性测度(Intuitionistic Fuzzy Probability Measurement,IFPM),并在此基础上构建了三支决策模型。首先,定义了直觉模糊决策空间及该空间上的直觉模糊可能性分布,并对其性质进行了证明,给出了论域对象的隶属度和非隶属度可能性均值的计算方法。然后,讨论了论域对象的隶属度和非隶属度可能性均值与决策阈值的关系,分析了它们之间的概率分布情况。根据概率分布－可能性分布的转换关系,给出决策规则和三支决策模型,提出了一种基于直觉模糊可能性分布的IFPM决策风险计算方法。最后,考虑论域中对象的增减变化引起的IFPM变化,给出对应公式并对动态决策过程进行分析,同时通过实例验证了该模型的有效性。     

Entailment for intuitionistic fuzzy sets based on generalized belief structures

Entailment for measure-based belief structures can extend the possible probability value range of variables on a space and obtain more information from variables. However, if the variable space comes from intuitionistic fuzzy sets, the classical entailment for measure-based belief structures will not work in this issue. To deal with this situation, we propose the entailment for intuitionistic fuzzy sets based on generalized belief structures in this paper to apply the entailment for measure based belief structures on space, which is made up of non-membership degree, membership degree and hesitancy degree of a given intuitionistic fuzzy sets. Numerical examples are mentioned to prove the effectively and flexibility of this proposed entailment model. The experimental results indicate that the proposed algorithm can extend the possible probability value range of variables of space efficiently and obtain more information from intuitionistic fuzzy sets.     

Intuitionistic fuzzy evidential power aggregation operator and its application in multiple criteria decision-making

The theory of intuitionistic fuzzy sets (IFS) is widely used for dealing with vagueness and the Dempster--Shafer (D-S) evidence theory has a widespread use in multiple criteria decision-making problems under uncertain situation. However, there are many methods to aggregate intuitionistic fuzzy numbers (IFNs), but the aggregation operator to fuse basic probability assignment (BPA) is rare. Power average (P-A) operator, as a powerful operator, is useful and important in information fusion. Motivated by the idea of P-A power, in this paper, a new operator based on the IFS and D-S evidence theory is proposed, which is named as intuitionistic fuzzy evidential power average (IFEPA) aggregation operator. First, an IFN is converted into a BPA, and the uncertainty is measured in D-S evidence theory. Second, the difference between BPAs is measured by Jousselme distance and a satisfying support function is proposed to get the support degree between each other effectively. Then the IFEPA operator is used for aggregating the original IFN and make a more reasonable decision. The proposed method is objective and reasonable because it is completely driven by data once some parameters are required. At the same time, it is novel and interesting. Finally, an application of developed models to the ‘One Belt, One road’ investment decision-making problems is presented to illustrate the effectiveness and feasibility of the proposed operator.     

基于模糊结构元的SFT概念重构及其意义

为解决SFT,特别是DSFT所结果无法表示原始离散故障数据分布特征的缺点,引入模糊结构元理论将SFT中概念及计算方式结构元化来解决该问题。首先模糊结构元特征函数可通过模糊结构元E表示原始数据的离散分布特征,并在计算过程中将E传递至最终结果。通过处理结果中E来得到分析结果的置信度。另一方面,模糊结构元特征函数可将DSFT问题转化为较成熟的CSFT进行处理,而不用为实现相同功能针对DSFT研究新的方法。论文完成了原有SFT中特征函数、基本事件发生概率分布、系统故障概率分布、概率重要度分布、关键重要度分布、系统故障概率分布趋势、因素重要度分布和因素联合重要度分布的模糊结构元化改造,并给出了结构元化后的计算方式。     

一种新的区间直觉模糊集决策方法: 区间证据组合的角度

基于证据理论,提出一种新的区间直觉模糊集决策模型.首先采用区间直觉模糊集表示属性值,将区间直觉模糊数转换为区间BPA;然后利用基于区间数的组合规则进行融合;最后将融合后的区间BPA转换为经典BPA用于决策,可直接方便地实现多属性数据的融合.该模型的优点在于:简单直观,能更有效地反映原始信息的不确定度;通用性好,可以推广到其他区间直觉模糊集的应用领域.算例结果表明了所提出模型的有效性.     

A non-parametric method to determine basic probability assignment for classification problems

As an important tool for knowledge representation and decision-making under uncertainty, Dempster-Shafer evidence theory (D-S theory) has been used in many fields. The application of D-S theory is critically dependent on the availability of the basic probability assignment (BPA). The determination of BPA is still an open issue. A non-parametric method to obtain BPA is proposed in this paper. This method can handle multi-attribute datasets in classification problems. Each attribute value of the dataset sample is treated as a stochastic quantity. Its non-parametric probability density function (PDF) is calculated using the training data, which can be regarded as the probability model for the corresponding attribute. The BPA function is then constructed based on the relationship between the test sample and the probability models. The missing attribute values in datasets are treated as ignorance in the framework of the evidence theory. This method does not have the assumption of any particular distribution. As a result, it can be flexibly used in many engineering applications. The obtained BPA can avoid high conflict between evidence, which is desired in data fusion. Several benchmark classification problems are used to demonstrate the proposed method and to compare against existing methods. The constructed classifier based on the proposed method compares well to the state-of-the-art algorithms.     

D-S理论在多传感器短临震预报中的应用

在D-S理论的基础上,结合模糊数学理论,依据地震前兆,给出了短临震预报的信息融合算法。首先,对在现场工作的地电、地应力、地下水位、短水准、水氡等传感器的数值进行特征提取,把模糊数学中隶属度函数的概念运用到D-S理论中,得出每种前兆出现时地震发生的信度函数分配,然后,采用多传感器分布式融合算法进行信息融合,利用判决规则来预报地震。通过对1976年唐山7.8级地震预报的仿真,结果表明:D-S理论在地震预报中具有一定的有效性和优越性。     

基于可拓理论的网络安全评估研究

针对目前网络安全评估算法存在的不足,提出了一种基于可拓模糊层次分析的安全评估算法。该算法在模糊层次分析法的基础上,结合可拓理论,将调查问卷表收集到的指标值映射到可拓区间中,通过相对隶属度的计算,构建了新的判决矩阵,利用模糊层次分析法计算各指标的综合权重。通过对相对隶属度的加权排序,得到网络安全评估值。通过实例分析,说明该方法能综合考虑专家打分的权威性和调查问卷的普遍性,提高了网络安全评估的准确性和有效性。     

基于模糊神经网络的电力调度自动化设备健康评估

针对电力调度自动化设备健康评估过程中存在的评估方式简单、评估方式可解释性弱以及评估效果不精确的问题,本文提出了一种基于模糊神经网络的电力自动化设备健康评估模型.用模糊理论进行分析,用模糊集合描述评价指标,用数据指标的隶属度描述设备运行情况,结合神经网络的自适应功能,针对个体设备提供更加准确的、更具个性化的健康评估.     

A new distance between BPAs based on the power-set-distribution pignistic probability function

In Dempster-Shafer evidence theory, the pignistic probability function is used to transform the basic probability assignment (BPA) into pignistic probabilities. Since the transformation is from the power set of the frame of discernment to the set itself, it may cause some information loss. The distance between betting commitments is constructed on the basis of the pignistic probability function and is used to measure the dissimilarity between two BPAs. However, it is a pseudo-metric and it may bring unreasonable results in some cases. To solve such problem, we propose a power-set-distribution (PSD) pignistic probability function based on the new explanation of the non-singleton focal elements in the BPA. The new function is directly operated on the power set, so it takes more information contained in the BPA than the pignistic probability function does. Based on the new function, the distance between PSD betting commitments which can better measure the dissimilarity between two BPAs is also proposed, and the proof that it is a metric is provided. In order to demonstrate the performance of the new distance, numerical examples are given to compare it with three existing dissimilarity measures. Moreover, its applications in combining the conflicting BPAs are also presented through two examples.     

正态模糊集合——Fuzzy集理论的新拓展

直觉模糊集（intuitionistic fuzzy sets）、区间值模糊集（interval-valued fuzzy sets）以及Vague集对普通fuzzy集的扩展是给出了隶属度的上下限,把隶属度从[0,1]区间中的一个单值推广到了[0,1]的子区间。但是该子区间犹如一个黑洞,隶属度在其内部的分布情况我们无从知晓,即这个子区间中的每一个值是等可能地作为元素的隶属度还是区间中的某些值较另外的值有更大的可能性呢？为了清晰的刻画出元素的隶属度在[0,1]区间中的分布情况,本文通过对投票模型的分析及正态分布理论,提出了一种新的模糊集合——正态模糊集合,同时对正态模糊集合的交、并、补等基本运算性质进行了讨论,文章最后对正态模糊集与fuzzy集、直觉模糊集的相互关系也作出了详细阐述。正态模糊集合是模糊集合理论的进一步推广,为我们处理模糊信息提供了一种全新的思想方法。