信息系统中的熵理论和信息粒度

不确定性是人工智能中的研究热点,而熵理论和信息粒度是度量信息系统不确定性的两种主要方法。本文在给出信息系统中熵的物理意义基础上,提出了信息系统中熵增加原理,给出了熵和信息粒度的公理化定义,据此构造了两种新的不确定性度量函数—α熵和α粒度,它们是已有熵和粒度度量的进一步推广。研究表明,α熵以及现有的熵度量都是广义熵的特殊形式,而α粒度以及现有的粒度度量都是广义粒度的特殊形式,从而统一、规范和发展了完备与不完备信息系统中的不确定性度量方法。     

覆盖粗糙模糊集的组合熵与组合粒度研究

针对覆盖粗糙模糊集的组合熵与组合粒度的度量问题.定义了覆盖粗糙集下对象的相容类,构造了覆盖粗糙集模型的相容关系,提出覆盖近似空间的覆盖簇,引入了覆盖粗糙模糊集模型的组合熵和组合粒度概念,讨论了组合熵和组合粒度的结构并证明了相关的性质并提出了覆盖粗糙模糊集的组合熵粗糙度度量.定义了覆盖簇的相容关系下对象的相容度,提出了相容度下的组合熵概念,证明了相关的定理和性质.最后,引入相容度下组合粒度概念,证明了组合粒度粗糙度存在随覆盖变细,度量单调减少的规律,并通过实例进行了验证.从而为进一步揭示粗糙集、粗糙模糊集及覆盖粗糙模糊集之间的不确定性度量规律提供了理论依据.     

模糊指数熵组合方法的信息系统不确定性度量

在智能信息处理的研究中,信息系统的不确定性度量大多基于单一的度量方法,这样很难达到很好的度量效果。为了融合多种不确定性度量方法的优点,通过将粗糙集理论中代数视角的粗糙度度量和信息论视角的模糊指数熵度量结合起来,提出一种信息系统的组合度量方法,接着分析了所提方法的相关性质,并从理论角度证明了该方法运用于不确定性度量的可行性。UCI数据集的实验结果表明,组合度量方法相比单一度量具有更优越的度量效果。     

自反二元关系下不完备信息系统的粗糙熵及粒度度量

针对不完备信息系统中各种自反二元关系形成了对系统的覆盖而非划分的情况,提出利用对象的邻域来定义粗糙熵和粒度度量以衡量系统的不确定性,证明了以上不确定性度量同完备信息系统的不确定性度量是一致的.同时在覆盖可约简的情况下,定义了覆盖约简对系统的粗糙熵和粒度度量,研究结果表明在系统分类最细或最粗时,覆盖约简的不确定性和知识的不确定性是等价的.     

一种基于邻域容差信息熵的组合度量方法

在实际应用中,大多数信息系统中的数据都是混合的,为了度量混合信息系统的不确定性,本文提出了一种组合度量方法.首先在不完备邻域粗糙集中定义了混合近似精度和混合近似粗糙度的概念;接着考虑到这两种单一度量方法对信息系统不确定性评估的不足,然后,进一步引入邻域容差信息熵的概念;最后将混合近似粗糙度和邻域容差信息熵这两种单一度量进行结合提出一种组合度量方法,并且研究了相关性质.UCI实验结果表明,本文所提出的方法在混合信息系统中具有更好的不确定性度量效果,从而验证了该度量方法具有一定的优越性,并且从理论上也证明了该方法的可行性.     

基于粗糙集的不完备谣言信息系统的知识获取与决策

网络谣言可能扰乱人们的思想、心理和行为,引发社会震荡、危害公共安全,而微博等社交平台的广泛应用使得谣言造成的影响与危害变得更大,因此,谣言检测对于网络空间的有序健康发展具有重要的意义。当前谣言的自动检测技术更多关注检测模型的构建和输入数据的表现形式,而在改善数据质量以提高谣言识别效果方面的研究很少。基于此,本文将粗糙集理论应用于不完备谣言信息系统进行知识获取与决策,实质上是通过粗糙集理论解决不完备谣言信息系统的不确定性度量,冗余性以及不完备性等问题,以获得高质量的数据,改善谣言检测效果。首先系统总结了粗糙集理论中不确定性度量的方法,包括香农熵、粗糙熵、Liang熵以及信息粒度等四种不确定度量方法,并整理和推导了这四种不确定度量方法从完备信息系统到不完备信息系统的一致性拓展。基于上述总结的四种不确定度量方法,提出了基于最大相关最小冗余(MCMR,Maximum CorrelationMinimum Redundancy)的知识约简算法。该方法基于熵度量方式,能够综合考量决策信息与冗余噪音,在UCI及Weibo等8个数据集上实验验证,结果表明本文算法优于几种基线算法,能够有效解决信息系统的冗余性。另外,提出了一种基于极大相容块的不完备决策树算法,在不同缺失程度数据上实验验证,结果表明本文算法能够有效解决信息系统的不完备性。     

基于信息粒化的区间值信息系统不确定性度量方法

目前区间值信息系统的不确定性度量方法大多基于粗糙集的粗糙度度量。实例分析表明该度量方法不满足严格单调性,为了解决这一缺陷,将粒计算方法引入区间值信息系统中,提出一种区间值信息系统的信息粒化模型。引入区间值信息系统的知识粒度和粗糙熵两种度量方法,理论分析出它们具有的严格单调性,在区间值信息系统的不确定性度量方面具有更好的优越性。实验验证了知识粒度和粗糙熵均比传统的粗糙度具有更好的不确定性度量效果。     

基于邻域粗糙集组合度量的混合数据属性约简算法

属性约简是一种重要的数据挖掘方法。为了对混合型信息系统达到更好的属性约简性能,提出一种邻域组合度量的启发式属性约简算法。邻域依赖度是构造混合信息系统属性约简的常用方法,根据粒计算的视角,在混合信息系统中提出邻域知识粒度用于评估属性的粒化能力。将邻域依赖度与邻域知识粒度进行结合,提出混合信息系统下的邻域组合度量,并将该度量方法作为启发式函数,提出一种属性约简算法。实验分析表明,该算法比混合信息系统的其他相关属性约简算法具有更高的约简性能。     

不完备信息系统中知识粒度的公理化定义与度量方法

给出不完备信息系统中知识粒度的公理化定义,在此基础上提出一系列知识粒度度量方法.其中有不带参数的具体度量,也有带参数的一般性度量,并比较3个知识粒度的大小.另外,还给出不同粒度的4种组合形式.本文所给出的知识粒度度量方法对于在不完备信息系统中建立粒度计算有着重要的理论意义和应用价值.     

知识不确定性度量及其关系研究

知识的不确定性度量研究是人工智能领域的一个热点问题。在回顾几种经典知识不确定性度量方法的基础上,系统研究了这些度量方法之间的联系与区别,结果表明信息粒度等度量与知识粒度是等价的,而Rough熵和协同熵等则可看作是信息熵的派生,并通过实例验证了结论的正确性。     

Knowledge granulation, knowledge entropy and knowledge uncertainty measure in ordered information systems

In this paper, concepts of knowledge granulation, knowledge entropy and knowledge uncertainty measure are given in ordered information systems, and some important properties of them are investigated. From these properties, it can be shown that these measures provides important approaches to measuring the discernibility ability of different knowledge in ordered information systems. And relationship between knowledge granulation, knowledge entropy and knowledge uncertainty measure are considered. As an application of knowledge granulation, we introduce definition of rough entropy of rough sets in ordered information systems. By an example, it is shown that the rough entropy of rough sets is more accurate than classical rough degree to measure the roughness of rough sets in ordered information systems.     

Information granules and entropy theory in information systems

Information granulation and entropy theory are two main approaches to research uncertainty of an information system, which have been widely applied in many practical issues. In this paper, the characterizations and representations of information granules under various binary relations are investigated in information systems, an axiom definition of information granulation is presented, and some existing definitions of information granulation become its special forms. Entropy theory in information systems is further developed and the granulation monotonicity of each of them is proved. Moreover, the complement relationship between information granulation and entropy is established. This investigation unifies the results of measures for uncertainties in complete information systems and incomplete information systems.     

集值序信息系统的信息熵和知识粒度

针对已有文献中二元优势关系定义过于宽松的不足,在集值序信息系统中结合对象间的不同优势程度,提出δ-优势关系的概念;基于δ-优势关系,将信息熵和知识粒度引入集值序信息系统中进行不确定性的度量。结论表明提出的信息熵和知识粒度可以精确地度量集值序信息系统的不确定性。     

Entropy measures and granularity measures for interval and set-valued information systems

In many practical situations, some of the attribute values for an object may be interval and set-valued. The interval and set-valued information systems have been introduced. According to the semantic relation of attribute values, interval and set-valued information systems can be classified into two categories, disjunctive (type 1) and conjunctive (type 2) systems. This paper mainly focuses on semantic interpretation of type 1. Then, a new fuzzy preference relation for interval and set-valued information systems is defined. Moreover, based on the new fuzzy preference relation, the concepts of fuzzy information entropy, fuzzy rough entropy, fuzzy knowledge granulation and fuzzy granularity measure are studied and relationships between entropy measures and granularity measures are investigated. Finally, an illustrative example to substantiate the theoretical arguments is given. These results may supply a further understanding of the essence of uncertainty in interval and set-valued information systems.     

直觉模糊信息系统中的信息熵

在直觉模糊信息系统上,直觉模糊信息熵和直觉模糊信息粒度是两种有效地进行不确定性研究的重要工具。在直觉模糊信息系统上,引入直觉模糊粒结构的交、并、差、补等四种运算。提出了基于直觉模糊粒结构的直觉模糊信息熵;并研究了直觉模糊信息熵与直觉模糊信息粒度之间的关系。     

Intelligent unmanned ground vehicle navigation via information evaluation

Sensor-centric navigation of unmanned ground vehicles (UGVs) operating in rugged and expansive terrains requires the competency to evaluate the utility of sensor information such that it results in intelligent behavior of the vehicles. Highly imperfect, inconsistent information and incomplete a priori knowledge introduce uncertainty in such unmanned navigation systems. Understanding and quantifying uncertainty yields a measure of useful information that plays a critical role in several robotic navigation tasks such as sensor fusion, mapping, localization, path planning and control. In this article, within a probabilistic framework, the utility of estimation and information-theoretic concepts towards quantifying uncertainty using entropy and mutual information metrics in various contexts of UGV navigation via experimental results is demonstrated.     

Partial ordering of information granulations: a further investigation

The notion of information systems provides a convenient tool for knowledge representation of objects in terms of their attribute values, while partial ordering is usually used to research the rough monotonicity of an uncertainty measure in information systems. In this paper, we first reveal the limitations of existing partial orderings to describe information granulations in information systems with several illustrative examples. Then, a generalized partial ordering with a set‐size nature is proposed to overcome their shortcoming and some of its important properties are derived. Finally, we prove that several existing information granulations all satisfy the granulation monotonicity induced by the proposed partial ordering. The presented partial ordering appears to be well suited to characterize the nature of information granulations in an information system. These results will be very helpful for studying granular computing and uncertainty in information systems.