基于粗糙集的证据获取与合成方法研究

证据理论是处理不确定性问题的有效工具,但是其证据往往来源于专家,带有很大的主观性,且合成证据的重要性无优劣之分。提出了一种基于粗糙集的证据获取与合成方法。利用证据信任度计算近似条件概率分配,根据属性重要度和证据支持度计算权重,用合成公式对近似条件概率分配进行合成得到决策。实例结果表明了该方法的有效性。     

基于改进贝叶斯粗糙集和证据理论的决策信息融合方法

针对决策信息信息表中新对象的分类问题,提出一种基于改进的贝叶斯粗糙集和证据理论的决策信息融合方法.对传统的贝叶斯粗糙集进行改进,扩展到多决策类,定义了支持度的概念以此反映确切分类的对象所占的百分比.利用贝叶斯粗糙集的支持度和置信增益函数作为证据的支持程度,得到各准则下的证据基本概率分配函数,并利用证据合成法则对多个证据进行合成,以此进行决策.将上述方法应用于设备故障的诊断问题中,通过方法的对比验证了该方法实践应用的有效性.     

基于Pignistic相似度与改进DS证据理论的综合评估方法

针对标准的Dempster-Shafer（DS）证据理论在证据冲突情况下决策准确率低与评估稳定性差的问题,提出一种基于Pignistic相似度与改进DS证据理论的综合评估方法。由Pignistic概率转换求得各类证据的相似度,计算对应的支持度与自适应权重,引入不确定命题推导出改进的证据合成规则。结合某航道实际通航状况进行算例分析,验证该方法的有效性与可靠性。分析结果表明,所提出的方法能正确处理不确定性条件下证据之间的冲突并能给出稳定决策结果。     

基于改进的D-S证据理论的智慧灌溉决策分析

本文提出了一种基于改进的D-S证据理论的智慧灌溉决策方法.对土壤湿度、气孔导度以及作物水分胁迫指数(CWSI)三个决策因子,通过三角形隶属度函数为作物的灌溉状态分配基本概率,利用D-S证据理论对灌溉时机进行综合决策.当灌溉决策因子的基本概率出现冲突时,利用改进的D-S证据理论,通过证据间距离的方法来替换因子中冲突部分.仿真结果表明,该方法能够降低灌溉决策的不确定性.     

基于直觉模糊证据合成的多传感器目标识别

对证据理论和直觉模糊集理论之间的本质联系进行分析,提出一种基于直觉模糊集改进的证据合成实用算法用于多传感器目标识别.根据直觉模糊集中隶属度和非隶属度的概念,对证据理论的可信度函数模型进行改进,提出了直觉模糊可信度分配函数模型并构造了相应的证据合成规则,以提高证据合成计算效率,使合成结果便于最终决策.通过与其他算法的对比实验验证了所提出算法的有效性.     

基于直觉模糊决策的无人机动力系统FMECA分析方法研究

针对传统无人机FMECA方法存在模糊性、难以进行定量分析并得出精确分析结果的问题,提出了基于直觉模糊决策的综合评判FMECA分析方法。该方法首先在计算直觉模糊值相似度的基础上,考虑专家的信任度,给出了专家基本概率分配函数的计算方法。然后基于证据组合理论进行对单个属性以及综合属性的决策群体基本概率分配函数合成。通过计算故障模式的效用值,来进行故障模式严酷度排序。以无人机系统中的动力系统为例进行了基于直觉模糊决策的FMECA分析,对其各个主要的故障模式进行了模糊综合评判,验证了该方法的正确性和有效性。     

一种改进的证据合成规则

就D-S证据合成规则对于冲突证据合成存在的不足，不少学者基于证据冲突概率再分配思想，提出了相应的修正证据合成规则。针对这些修正合成规则的不足，提出了一种改进的合成规则，该规则在综合考虑证据源可信度和证据支持度的基础上，分析证据集的有效性，合理地实现信息融合。数值实验结果表明，新的合成规则不仅克服了现有规则的不足，而且其结果向合理性方向收敛度好，提高了系统的鲁棒性。     

基于三支决策的证据融合策略

针对现有证据合成改进方法过程复杂，计算量较大，不加判别地处理证据冲突等问题，提出一种基于三支决策的证据融合策略.首先将证据关系分为一致、冲突和中立3种，建立基于三支决策的证据关系模型.设计算法筛选出证据支持的主要焦元.利用焦元集合的相似度和向量距离分别计算一致概率和代价函数.依据贝叶斯最小风险决策理论来判定证据关系.接着，在该模型的基础上提出基于三支决策的证据融合策略.根据各证据的主要焦元确定初始证据集的焦元分布.通过把证据划分到不同证据集内部或边界上来实现证据的三支划分.最后对加权修正的证据集融合结果和边界证据进行合成.算例分析表明，本文方法不仅能处理证据悖论，还使融合结果更稳定可靠.     

基于距离测度的证据合成方法

为解决经典证据理论无法处理高度冲突证据的不足,提出了一种基于距离测度的证据合成方法。将证据视为空间向量,定义距离测度空间,计算空间中两两证据之间的距离,并通过距离测度矩阵确立证据之间的一致性测度,在此基础上求得辨识框架对各证据的支持度,通过归一化支持度得到证据一致性因子,以此作为冲突概率的分配权重,最后给出改进的证据合成公式。数值算例证明了改进公式既能处理冲突证据,又能合成非冲突证据,与其他合成方法的比较验证了改进合成公式的有效性。     

基于粗集理论和证据理论的多源信息融合方法

本文针对多源信息融合问题，首先利用基于Kohonen网络的离散化算法和粗集理论对样本信息进行离散化和约简，形成了待决策问题的经验决策表．在此基础上，利用经验决策表以及粗集理论和证据理论的关系，计算了待决策信息的有关证据的基本概率指派和条件概率指派．最后，按照合成规则对上述条件概率指派进行了合成，并根据决策规则进行决策．实例研究表明，该方法实验结果令人满意．     

Degrees of conditional (in)dependence: A framework for approximate Bayesian networks and examples related to the rough set-based feature selection

Bayesian networks provide the means for representing probabilistic conditional independence. Conditional independence is widely considered also beyond the theory of probability, with linkages to, e.g. the database multi-valued dependencies, and at a higher abstraction level of semi-graphoid models. The rough set framework for data analysis is related to the topics of conditional independence via the notion of a decision reduct, to be considered within a wider domain of the feature selection. Given probabilistic version of decision reducts equivalent to the data-based Markov boundaries, the studies were also conducted for other criteria of the rough-set-based feature selection, e.g. those corresponding to the multi-valued dependencies. In this paper, we investigate the degrees of approximate conditional dependence, which could be a topic corresponding to the well-known notions such as conditional mutual information and polymatroid functions, however, with many practically useful approximate conditional independence models unmanageable within the information theoretic framework. The major paper’s contribution lays in extending the means for understanding the degrees of approximate conditional dependence, with appropriately generalized semi-graphoid properties formulated and with the mathematical soundness of the Bayesian network-like representation of the approximate conditional independence statements thoroughly proved. As an additional contribution, we provide a case study of the approximate conditional independence model, which would not be manageable without the above-mentioned extensions.     

Lukasiewicz n值命题逻辑中公式的条件随机真度

基于条件概率的思想,利用赋值集的随机化方法,在Lukasiewicz n值命题逻辑系统中引入公式的条件随机真度,证明了条件随机真度的MP规则和HS规则。引入公式间的条件随机相似度和条件伪距离,建立了条件随机逻辑度量空间,推导出条件伪距离的若干性质,证明了条件随机逻辑度量空间中逻辑运算的连续性,初步研究了给定条件下的近似推理理论。     

基于CP-nets 的偏好感知交互式遗传算法及其个性化搜索

针对用户显式评价导致用户疲劳,进而限制交互式遗传算法搜索性能的问题,研究基于用户交互行为和条件偏好网络(CP-nets)的隐式评价模式的交互式遗传算法,并将其应用于图书商品个性化搜索。首先,给出用户交互行为的数学描述,建立基于用户少量交互行为的条件偏好网络模型以拟合用户偏好;然后,利用CP-nets模型估计用户对进化个体的评价值,实施进化操作以帮助用户尽快找到满意解。在个性化搜索中的应用验证了所提出算法的有效性。     

Fuzzy Conditional Probability Relations and their Applications in Fuzzy Information Systems

In our real-world applications, data may be imprecise in which levels or degrees of preciseness of data are intuitively different. In this case, fuzzy set expressions are considered as an alternative to represent the imprecise data. In general, the degree of similarity relationship between two fuzzy (imprecise) data in real-world applications may not necessarily be symmetric or transitive. In order to provide such a degree of similarity between two fuzzy data, we introduced the fuzzy conditional probability relation. The concept of a fuzzy conditional probability relation may be considered as a concrete example of weak similarity relation which in turn is a special type of fuzzy binary relation generalizing similarity relation. Two important applications concerning the application of Knowledge Discovery and Data Mining (KDD) in the presence of a fuzzy data table (usually called fuzzy information system), namely removing redundant objects and recognizing partial or total dependency of (domain) attributes, are considered induced by the fuzzy conditional probability relation. Here, the fuzzy information system contains precise as well as imprecise data (fuzzy values) about objects of interest characterized by some attributes. Related to the dependency of attributes, we introduce the fuzzy functional dependency that satisfies Armstrongs Axioms. In addition, we also discuss some interesting applications such as approximate data reduction and projection, approximate data querying and approximate joining in order to extend the query system.     

赋值:物理对象上的操作(英文)

研究了命令式程序的形式语义。赋值被看成当作物理对象的变量上的操作。变量x一方面是个可以容纳数据值的物理对象,另一方面当它出现在数学表达式中时又代表它所容纳的值。作为物理对象,变量x允许它的值用读/写操作来观察或改变,读操作则是写操作的逆操作。事实上赋值就是对物理对象施加写操作。提出了与单变量赋值、多重赋值、顺序赋值及条件赋值等相对应的操作,提出了这些操作应服从的公理,并给出了用这些公理证明程序性质的实例。     

Measures of general fuzzy rough sets on a probabilistic space

Fuzzy rough set is a generalization of crisp rough set, which deals with both fuzziness and vagueness in data. The measures of fuzzy rough sets aim to dig its numeral characters in order to analyze data effectively. In this paper we first develop a method to compute the cardinality of fuzzy set on a probabilistic space, and then propose a real number valued function for each approximation operator of the general fuzzy rough sets on a probabilistic space to measure its approximate accuracy. The functions of lower and upper approximation operators are natural generalizations of the belief function and plausibility function in Dempster-Shafer theory of evidence, respectively. By using these functions, accuracy measure, roughness degree, dependency function, entropy and conditional entropy of general fuzzy rough set are proposed, and the relative reduction of fuzzy decision system is also developed by using the dependency function and characterized by the conditional entropy. At last, these measure functions for approximation operators are characterized by axiomatic approaches.     

Distribution of assignments among participants under conditions of constraints

The distribution problem of assignments among participants in the presence of constraints is considered. For each assignment participants are defined, whom this assignment can be transferred to, and participants who cannot take the given assignment. Some collections of assignments are marked as clusters, i.e., all assignments of each such cluster can be given up only to one participant; and clusters can be intersected. Estimates of the extremum are set out, an approximate algorithm of the solution is proposed. The problems of this type can be met with, for example, in multiprocessor computing complexes in the distribution of assignments among processors, in the distribution of jobs among executors, and in a number of other cases.     

On the state estimation for non-linear dynamic systems †

The object of this paper is to present an approximate technique for state estimation of non-linear dynamical systems under noisy observations. The conditional cumulant is introduced, by which the conditional probability density can be characterized. A set of dynamical equations satisfied by conditional cumulants is derived, and an approximate method is proposed for computing the cumulants. The relation of the cumulant method to the stochastic linearization technique is also discussed. Finally the state estimation problem for linear stochaatic system with state-dependent disturbance is solved to illustrate the use of the Gaussian approximation.     

基于GP的多目标决策函数稳定性分析

在多目标决策问题中，必须设定许多值．由于受到主观因素的影响，不同目标的重要性和可行性方案的效用值有时非常逼近．因此，分析设定值的微小变动对决策结果的敏感度影响尤为重要，根据期望的要求选择一个决策函数，尽可能地求出一个稳定的解，这是求解决策问题的根本任务．提出了一种基于遗传程序设计（GP）的新方法，该方法能产生比普通方法更好的决策函数，理论上的期望值得到实例的验证。