区间值决策系统的局部属性约简

区间值决策系统中已有的属性约简工作主要针对决策属性中所有的决策类。针对区间值决策系统中决策属性的某些特定类,引入了区间值决策系统局部约简的概念,提出了部分决策类约简的判定定理;利用差别矩阵方法研究局部约简的结构,并给出了基于差别矩阵的局部约简算法。通过局部约简的概念对区间值决策系统的全局约简结构进行进一步刻画,讨论了不协调区间值决策系统的局部约简和全局约简之间的关系。最后通过相关实验验证了所提算法的可行性和有效性。     

基于差别矩阵的区间值决策系统β分布约简

当前区间类型数据的规模越来越大,若采用传统的属性约简方法进行处理,就需要对数据进行预处理,而这会损失原始信息。针对上述问题,提出了区间值决策系统β分布的约简算法。首先,给出区间值决策系统β分布的概念和约简目标,并证明了提出的相关定理;然后,对于该约简目标构建了β分布约简的差别矩阵和差别函数,提出了区间值决策系统β分布约简算法;最后,使用14组UCI数据集进行实验验证。在数据集Statlog上,当相似度阈值为0.6,对象数目为100、200、400、600、846时,β分布约简算法的平均约简长度为1.6、2.2、1.4、2.4、2.6,基于差别矩阵的分布约简算法（DRADM）的平均约简长度为2.0、3.0、3.0、4.0、4.0,基于差别矩阵的最大分布约简算法（MDRADM）的平均约简长度为2.0、3.0、3.0、4.0、3.0。实验结果验证了所提β分布约简算法的有效性。     

基于特定类的不完备决策系统的分布约简

现有的不完备决策系统的分布约简研究主要针对决策系统中的所有决策类,而某些实际应用中,人们往往仅关注于某个特定类的属性约简问题。基于这种考虑,首先提出了基于特定类的不完备决策系统的分布约简的理论框架,给出了在相容关系下的基于差别矩阵的约简算法,最后将该算法与基于所有决策类的不完备决策系统分布约简算法进行对比。实验结果表明,当决策类为特定类时,约简结果的平均长度相对较短,约简效率也有显著的提高。     

基于多特定决策类的不完备决策系统正域约简

现有的属性约简方法大部分关注决策系统中的所有决策类，而在实际决策过程中决策者往往仅关注决策系统中的一种或几种决策类。针对上述问题，提出基于多特定决策类的不完备决策系统正域约简的理论框架。首先，给出不完备决策系统单特定决策类正域约简的概念；第二，将单特定决策类正域约简推广到多特定决策类，构造了相应的差别矩阵及区分函数；第三，分析并证明了相关定理，提出基于差别矩阵的不完备决策系统多特定决策类正域约简算法（PRMDM）；最后，选取4组UCI数据集进行实验。在数据集Teaching-assistant-evaluation、House、Connectionist-bench和Cardiotocography上，基于差别矩阵的不完备决策系正域约简算法（PRDM）的平均约简长度分别为4.00、13.00、9.00和20.00，PRMDM算法（多特定决策类中决策类数目为2）的平均约简长度分别为3.00、8.00、8.00和18.00。实验结果验证了PRMDM算法的有效性。     

不完备决策系统下的多特定类广义决策约简

属性约简是粗糙集理论研究中最重要的领域之一。经典的不完备决策系统广义决策约简关注决策系统中的所有决策类,而在实际应用中,决策者往往只关注一个或者几个特定决策类。针对以上问题,提出基于多特定类的不完备决策系统广义决策约简理论框架。首先,定义了单特定类的不完备决策系统广义决策约简的相关概念,提出并证明相关定理,构造相应差别矩阵和区分函数。其次,将单特定类的广义决策约简推广到多特定类,提出基于差别矩阵的多特定类的不完备决策系统广义决策约简算法。最后,采用6组UCI数据集进行实验。实验结果表明,相对全部决策类数量,当选定特定类数量较少时,平均约简长度有不同程度的缩短,占用空间有所减小,约简效率有不同程度的提升。     

一种基于差别矩阵的启发式属性约简算法

为了获得决策系统中更好的相对属性约简,本文提出了一种基于差别矩阵的启发式属性约简算法。该算法以求差别矩阵为基础,不仅考虑了所选择条件属性与决策属性的互信 息,还考虑了其取值的分布情况,从信息论角度定义了一种新的属性重要性度量方法,将其作为启发式信息,最终求得属性约简集。实例表明,算法能够有效地对决策系统进进行约简,获得比较理想的约简结果,同时约简后的决策规则数目较少。     

关系决策系统的分布约简

基于分辨矩阵和最近已提出的快速算法,对关系系统的约简算法和关系决策系统的分布约简算法进行了研究。证明当决策属性具有自反性时,关系决策系统的分布约简实际上就是关系系统的约简,与决策属性无关。此外,区间值模糊序关系决策系统可视为关系决策系统的一个特例,用提出的关系决策系统的分布约简算法即可获得区间值模糊序关系决策系统的全部约简结果,从而简化了原来的约简算法。     

不协调区间值决策系统的最大分布约简

分布式约简可以保证约简前后决策系统各规则的置信度保持不变,是属性约简的重要方法之一。最大分布式约简保持了约简前后决策系统中可信程度最大的规则不变,提取置信度较大的规则在智能决策中具有广泛的应用价值。本文在相容关系下的不协调区间值决策系统中引入最大置信度的概念,构造最大分布保持不变的可辨识矩阵,并给出基于可辨识矩阵的最大分布约简算法。分析了不协调区间值决策系统的最大分布约简算法与其它约简算法之间的关系。最后,利用UCI标准数据集进行了实验验证,实验结果表明了算法的有效性。     

不协调区间值决策系统的分布约简

知识约简可以保持决策系统中的分类特征不变,是粗糙集理论的重要研究内容之一。分布约简保持约简前后决策系统中各规则的置信度不发生改变。为了给区间值决策系统的论域分类提供合理的度量标准,引入了区间值相似率。通过将Pawlak决策系统中的等价关系扩展到区间值决策系统中的相容关系,提出了区间值决策系统的分布约简目标。针对该目标给出了相应差别矩阵的计算方法,并与现有区间值决策系统的广义决策约简计算方法进行了分析比较。最后,通过人工数据集的实验验证了相关结论的有效性。     

决策系统属性约简优化算法研究

属性约简是粗糙集理论研究的关键问题,针对求取决策系统所有约简的NP问题,基于差别矩阵提出一种决策系统属性约简优化算法.通过改进差别矩阵得到差别集,在获得核与约简候选信息基础上,以属性频度作为启发式信息,快速有效地求取决策系统的所有约简.分析表明了该算法的可行性与有效性.     

Relative reducts in consistent and inconsistent decision tables of the Pawlak rough set model

A relative reduct can be considered as a minimum set of attributes that preserves a certain classification property. This paper investigates three different classification properties, and suggests three distinct definitions accordingly. In the Pawlak rough set model, while the three definitions yield the same set of relative reducts in consistent decision tables, they may result in different sets in inconsistent tables.Relative reduct construction can be carried out based on a discernibility matrix. The study explicitly stresses a fact, that the definition of a discernibility matrix should be tied to a certain property. Regarding the three classification properties, we can define three distinct definitions accordingly.Based on the common structure of the specific definitions of relative reducts and discernibility matrices, general definitions of relative reducts and discernibility matrices are suggested.     

不一致决策表的k阶分配序约简

在不一致决策表中定义了k阶分配序约简，给出了k阶分配序一致集的判定定理。通过定义k阶分配序区分矩阵，给出了求k阶分配序约简的区分矩阵法。为了克服区分矩阵法时间复杂度过高的缺陷，通过定义属性的相对重要性，提出了一种求k阶分配序约简的启发式算法，分析得到该算法的时间复杂度是多项式的结论。实例验证了算法的有效性。     

Decision-relative discernibility matrices in the sense of entropies

Abstract

In rough set theory, attribute reduction is a basic issue, which aims to hold the discernibility of the attribute set. To obtain all of the reducts of an information system or a decision table, researchers have introduced many discernibility matrices based reduction methods. However, the reducts in the sense of positive region can only be obtained by using the existing discernibility matrices. In this paper, we introduce two discernibility matrices in the sense of entropies (Shannon’s entropy and complement entropy). By means of the two discernibility matrices, we can achieve all of the reducts in the sense of Shannon’s entropy and all of the reducts in the sense of complement entropy, respectively. Furthermore, we discover the relationships among the reducts in the sense of preserving positive region, Shannon’s entropy and complement entorpy. The experimental studies show that by the proposed decision-relative discernibility matrices based reduction methods, all the reducts of a decision table in sense of entropies can be obtained.     

A TENGRAM method based part-of-speech tagging of multi-category words in Hindi language

In this paper, we have dealt on the problem of part-of-speech tagging of multi-category words which appear within the sentences of Hindi language. Firstly, a Hindi tagger is proposed which provides part-of-speech tags developed using grammar of Hindi language. For this purpose, Hindi Devanagari alphabets are used and their Hindi transliteration is done within the proposed tagger. Thereafter, a Rules’ based TENGRAM method is described with an illustrative example, which guides to disambiguate multi-category words within sentences of Hindi corpus. The rules generated in TENGRAM are the result of computation of discernibility matrices, discernibility functions and reducts. These computations have been generated from decision tables which are based on theory of Rough sets. Basically, a discernibility matrix helps in cutting down indiscernible condition attributes; a discernibility function has rows corresponding to each column in the discernibility matrix which develops reducts; and the reducts provide a minimal subset of attributes which preserve indiscernibility relation of decision tables and hence they generate the decision rules.     

Analysis of alternative objective functions for attribute reduction in complete decision tables

Attribute reduction and reducts are important notions in rough set theory that can preserve discriminatory properties to the highest possible extent similar to the entire set of attributes. In this paper, the relationships among 13 types of alternative objective functions for attribute reduction are systematically analyzed in complete decision tables. For inconsistent and consistent decision tables, it is demonstrated that there are only six and two intrinsically different objective functions for attribute reduction, respectively. Some algorithms have been put forward for minimal attribute reduction according to different objective functions. Through a counterexample, it is shown that heuristic methods cannot always guarantee to produce a minimal reduct. Based on the general definition of discernibility function, a complete algorithm for finding a minimal reduct is proposed. Since it only depends on reasoning mechanisms, it can be applied under any objective function for attribute reduction as long as the corresponding discernibility matrix has been well established.     

基于标记可辨识矩阵的增量式属性约简算法

针对现有增量式属性约简算法中存在的约简传承性差以及不完备现象,提出基于标记可辨识矩阵的增量式属性约简算法.本文首先定义了标记函数,对样本之间的可辨识性进行分类,并将之引入一个新的可辨识矩阵,在新增样本时,结合标记信息可以快速识别可辨识矩阵元素集的异动,获得强传承性的约简超集,在此基础上,设计与标记可辨识矩阵匹配的必要矩阵,用以快速判断并删除冗余属性,确保约简的完备性. 理论分析以及实验测试表明,本算法具有约简传承性强,约简集完备等特点,具有较强的实用性.     

优势关系下广义决策约简和上近似约简

论文定义了决策表的优势关系下广义决策约简和上近似约简,给出了优势关系下广义决策约简和上近似约简的判定定理和辨识矩阵。同计算优势关系下上近似约简的辨识矩阵相比,计算优势关系下广义决策约简的辨识矩阵的时间复杂度低,由于论文已证明优势关系下广义决策约简和上近似约简是等价的,因此,可以利用优势关系下广义决策约简的辨识矩阵计算优势关系下广义决策约简和上近似约简。     

Rule acquisition and attribute reduction in real decision formal contexts

Formal Concept Analysis of real set formal contexts is a generalization of classical formal contexts. By dividing the attributes into condition attributes and decision attributes, the notion of real decision formal contexts is introduced. Based on an implication mapping, problems of rule acquisition and attribute reduction of real decision formal contexts are examined. The extraction of “if–then” rules from the real decision formal contexts, and the approach to attribute reduction of the real decision formal contexts are discussed. By the proposed approach, attributes which are non-essential to the maximal s rules or l rules (to be defined later in the text) can be removed. Furthermore, discernibility matrices and discernibility functions for computing the attribute reducts of the real decision formal contexts are constructed to determine all attribute reducts of the real set formal contexts without affecting the results of the acquired maximal s rules or l rules.