Knowledge acquisition in incomplete fuzzy information systems via the rough set approach

Abstract: Machine learning can extract desired knowledge from training examples and ease the development bottleneck in building expert systems. Most learning approaches derive rules from complete and incomplete data sets. If attribute values are known as possibility distributions on the domain of the attributes, the system is called an incomplete fuzzy information system. Learning from incomplete fuzzy data sets is usually more difficult than learning from complete data sets and incomplete data sets. In this paper, we deal with the problem of producing a set of certain and possible rules from incomplete fuzzy data sets based on rough sets. The notions of lower and upper generalized fuzzy rough approximations are introduced. By using the fuzzy rough upper approximation operator, we transform each fuzzy subset of the domain of every attribute in an incomplete fuzzy information system into a fuzzy subset of the universe, from which fuzzy similarity neighbourhoods of objects in the system are derived. The fuzzy lower and upper approximations for any subset of the universe are then calculated and the knowledge hidden in the information system is unravelled and expressed in the form of decision rules.     

铅锌密闭鼓风炉故障诊断知识获取的粗糙集方法

从粗糙集等价类概念出发，提出从不完整数据集中获取故障诊断知识的密闭鼓风炉故障诊断方法，将不完整数据集的训练事例划分为下近似和上近似两类，首先假设属性的未知特征值为任意可能值，然后根据从驯练事例中得到的上下近似进行提炼，最后从事例与近似互相作用以推导出确定的和可能的规则，得出规则概率，并估计出合适的属性的未知特征值，结合密闭鼓风炉悬料规则库的知识获取及其在故障诊断中的应用过程说明了该方法的有效性和实用性。     

一种从不完备数据集中发现规则的RS方法

Rough集(Rough SetS、Rs)理论被广泛应刑于数据分类问题，该文用基于RS的方法从不完备数据集中产生确定和可能的规则集，提出了一种新的规则发现算法，可以同时从不完备数据集中产生规则和估计缺失值，并指出了进一步的研究方向。     

粗糙集理论在处理不完全信息的应用

对不完全信息的处理相对于完全信息来说是一个比较难的问题。在过去几年里,已经提出了几种处理不完全信息的方法。本文在前人研究的基础上,进一步提出了一种利用粗糙集理论处理不完全信息的方法,该方法不仅能够对不完全信息系统进行属性约简,并且能够在此基础上对最简属性集中包含的不确定信息进行进一步的处理。     

Machine learning by imitating human learning

Learning general concepts in imperfect environments is difficult since training instances often include noisy data, inconclusive data, incomplete data, unknown attributes, unknown attribute values and other barriers to effective learning. It is well known that people can learn effectively in imperfect environments, and can manage to process very large amounts of data. Imitating human learning behavior therefore provides a useful model for machine learning in real-world applications. This paper proposes a new, more effective way to represent imperfect training instances and rules, and based on the new representation, a Human-Like Learning (HULL) algorithm for incrementally learning concepts well in imperfect training environments. Several examples are given to make the algorithm clearer. Finally, experimental results are presented that show the proposed learning algorithm works well in imperfect learning environments.     

Dominance-based rough set approach to incomplete interval-valued information system

Since preference order is a crucial feature of data concerning decision situations, the classical rough set model has been generalized by replacing the indiscernibility relation with a dominance relation. The purpose of this paper is to further investigate the dominance-based rough set in incomplete interval-valued information system, which contains both incomplete and imprecise evaluations of objects. By considering three types of unknown values in the incomplete interval-valued information system, a data complement method is used to transform the incomplete interval-valued information system into a traditional one. To generate the optimal decision rules from the incomplete interval-valued decision system, six types of relative reducts are proposed. Not only the relationships between these reducts but also the practical approaches to compute these reducts are then investigated. Some numerical examples are employed to substantiate the conceptual arguments.     

不完备信息系统中的否定决策规则和知识约简

为了从不完备信息系统中获得否定决策规则,提出了描述子否定支撑集的概念,基于此定义了下、上近似集合,讨论其性质,并给出了如何通过该模型获取确定性和可信性否定决策规则的方法．为了便于应用,给出基于分辨矩阵的否定决策规则约简的方法,实例分析的结果表明了该方法的有效性．     

不完整Vague决策表中的近似集学习方法

含糊性和不可分辨性构成了决策表中不确定性的两个不同侧面,Ｖａｇｕｅ集作为当前模糊信息处理中的一个新兴研究课题,它具有强大的表达不精确数据的能力,然而针对它的学习方法却未见报导 ,大多数现有针对Ｖａｇｕｅ集的研究仍集中于对其本身性质的讨论,在介绍Ｖａｇｕｅ集的有关概念的基础上,借鉴了粗糙集中中有关近似集的概念,特别对不ａｇｕｅ决策表中的学习机制作了研究,解决了数据描述了不确凿时的学习问题,所给出的两     

Selecting concise training sets from clean data

The authors derive a method for selecting exemplars for training a multilayer feedforward network architecture to estimate an unknown (deterministic) mapping from clean data, i.e., data measured either without error or with negligible error. The objective is to minimize the data requirement of learning. The authors choose a criterion for selecting training examples that works well in conjunction with the criterion used for learning, here, least squares. They proceed sequentially, selecting an example that, when added to the previous set of training examples and learned, maximizes the decrement of network squared error over the input space. When dealing with clean data and deterministic relationships, concise training sets that minimize the integrated squared bias (ISB) are desired. The ISB is used to derive a selection criterion for evaluating individual training examples, the DISB, that is maximized to select new exemplars. They conclude with graphical illustrations of the method, and demonstrate its use during network training. Experimental results indicate that training upon exemplars selected in this fashion can save computation in general purpose use as well.     

不完备知识系统非对称相似关系的最小简式

在实际决策时,人们所面临的往往是大量的数据,因此知识约简很重要,已经证明：在知识系统中求解最小简式是NP完全问题。对于完备知识系统,已有很多方法来求解最小简式,而对于不完备知识系统,这方面的研究较少,处理也更困难。对于不完备的知识系统,可以采用一些补齐算法先进行完备化处理,然后再对所得到的完备知识系统采用一些常用的约简算法如分辨矩阵法等进行处理。但是,补齐处理只是以主观估计值,将未知值补齐,不一定完全符合客观事实。因此,需要保持知识系统的原始信息不发生变化的前提下进行约简。设计了二进制矩阵,和不完备知识系统的非对称相似关系结合,证明了一个定理,并提出了一种基于非对称相似关系的遗传算法,求解不完备知识系统中的最小简式。算法的适应度函数较为简单,可以有效求出最小简式子。实验结果显示了算法的有效性。     

Mining fuzzy β-certain and β-possible rules from quantitative data based on the variable precision rough-set model

The rough-set theory proposed by Pawlak, has been widely used in dealing with data classification problems. The original rough-set model is, however, quite sensitive to noisy data. Ziarko thus proposed the variable precision rough-set model to deal with noisy data and uncertain information. This model allowed for some degree of uncertainty and misclassification in the mining process. Conventionally, the mining algorithms based on the rough-set theory identify the relationships among data using crisp attribute values; however, data with quantitative values are commonly seen in real-world applications. This paper thus deals with the problem of producing a set of fuzzy certain and fuzzy possible rules from quantitative data with a predefined tolerance degree of uncertainty and misclassification. A new method, which combines the variable precision rough-set model and the fuzzy set theory, is thus proposed to solve this problem. It first transforms each quantitative value into a fuzzy set of linguistic terms using membership functions and then calculates the fuzzy β-lower and the fuzzy β-upper approximations. The certain and possible rules are then generated based on these fuzzy approximations. These rules can then be used to classify unknown objects. The paper thus extends the existing rough-set mining approaches to process quantitative data with tolerance of noise and uncertainty.     

Incrementally updating a hybrid rule base based on empirical data

Abstract: Neurules are a kind of hybrid rules that combine a symbolic (production rules) and a connectionist (adaline unit) representation. One way that the neurules can be produced is from training examples/patterns, extracted from empirical data. However, in certain application fields not all of the training examples are available a priori. A number of them become available over time. In those cases, updating the neurule base is necessary. In this paper, methods for updating a hybrid rule base, consisting of neurules, to reflect the availability of new training examples are presented. They can be considered as a type of incremental learning method that retains the entire induced hypothesis and all past training examples. The methods are efficient, since they require the least possible retraining effort and the number of neurules produced is kept as small as possible. Experimental results that prove the above argument are presented.     

不完备知识下的形式概念表示与计算

从集合的角度来说,知识就是数据集合在某种关系下的划分。如果这个数据集的某些属性值是未知的或丢失了,那么知识就是不完备（incomplete）的。传统形式概念分析是源于完备数据集的（完备知识）。在不完备知识下的概念分析一般说来比完备知识更困难。本文提出了一个新的不完备知识下形式概念表示与计算的方法,这种方法是基于泛化粗糙集理论的,其目的是扩展形式概念分析研究的领域。文中研究了一个基于自反相似关系的粗糙集模型,讨论了基于这种模型的形式概念分析方法。一个实例表明了这种方法的可行性。     

基于神经网络的知识获取

本文提出了用基于规则专家系统与神经网络的集成，该系统实现了从实例中自动获取知识的功能．在产生和控制不完全情况方面提高了专家系统的推理能力．它使用无导师学习算法的神经网络来获取正规数据，并用一个符号生成器把这些正规的数据变换成规则．生成规则和训练后的神经网络作为知识库嵌于专家系统中．在诊断阶段，为了诊断不明情况，可同时使用知识库和人类专家的知识，而且系统可以利用训练过的神经网络的综合能力进行诊断，并使不相符数据完整化．     

基于样本学习的广义粗糙集知识约简

由于条件属性在各样本的分布特性和所反映的主观特性的不同,每一个样本对应于真实情况的局部映射。建立了粗糙集理论中样本知识与信息之间的对应表示关系,给出了由属性约简求约简决策表的方法。基于后离散化策略处理连续属性,实现离散效率和信息损失之间的动态折衷。提出相对值条件互信息的概念衡量单一样本中各条件属性的相关性,可以充分利用现有数据处理不完备信息系统。即使在先验知识不足的情况下,也能通过主动学习构造新的规则补充进知识库中。拓广了粗糙集理论的应用范围,在UCI机器学习数据集上的实验结果和样例分析证明了该算法的合理性和有效性。     

一种基于模糊粗糙集知识获取方法

本文介绍了粗糙集和模糊粗糙集的上下近似。并且利用模糊粗糙上下近似算子，论述了在不完备模糊信息系统中知识获取的一种方法。应用这种方法能够让隐藏在不完备模糊信息系统中的知识，以决策规则的形式表示出来。最后给出了一种实现算法和实例。     

基于二元决策系统的粗集知识获取方法研究

提出一种新的粗集知识获取方法,首先将事例集表示成二元决策系统,然后奖其分解成一系列单一二元决策子系统。利用粗集理论对每一子系统进行分析,推理出最优规则。在对决策系统进行条件属性和规则简化时,提出了概率最佳简约准则和概率最小规则准则,按照这两种最优准则可以获得概率意义上数目最小规则集。通过实例分析,具体说明了该方法的实现步骤,结果表明该方法具有明显的优越性。     

Inductive rule generation and interpretation

Abstract

The problem of knowledge acquisition has been recognized as the major bottleneck in the development of knowledge-based systems. An encouraging approach to alleviate this problem is inductive learning. Inductive learning systems accept, as input, a set of data that represent instances of the problem domain and produce, as output, the rules of the knowledge base. Each data item is described by a set of attribute values and is assigned to a unique decision class. A common characteristic of the existing inductive learning systems, is that they are empirical in nature and do not take into account the implications of the inductive rule generation process on the performance of the resulting set of rules. That performance is assessed when the rules are used to classify new unlabelled data. This paper demonstrates that the performance of a rule set is a function of the rule generation and rule interpretation processes. These two processes are interrelated and should not be considered separately. The interrelation of rule generation and rule interpretation is analysed and suggestions to improve the performance of existing inductive learning systems, are forwarded.     

基于概念格的规则产生集挖掘算法

传统的规则提取算法产生的规则集合相当庞大，其中包含许多冗余的规则．使用闭项集可以减少规则的数目，而概念格结点问的泛化和例化关系非常适用于规则提取．基于概念格理论和闭项集的概念，提出了一种新的更有利于规则提取的格结构，给出了相应的基于闭标记的渐进式构造算法和规则提取算法．最后提供给用户的是直观的、易理解的规则子集，用户可以有选择地从中推导出其他的规则．实验表明该方法能够高效地挖掘规则产生集．     

Partitioning of feature space for pattern classification

The article proposes a simple approach for finding a fuzzy partitioning of a feature space for pattern classification problems. A feature space is initially decomposed into some overlapping hyperboxes depending on the relative positions of the pattern classes found in the training samples. A few fuzzy if-then rules reflecting the pattern classes by the generated hyperboxes are then obtained in terms of a relational matrix. The relational matrix is utilized in the modified compositional rule of inference in order to recognize an unknown pattern. The proposed system is capable of handling imprecise information both in the learning and the processing phases. The imprecise information is considered to be either incomplete or mixed or interval or linguistic in form. Ways of handling such imprecise information are also discussed. The effectiveness of the system is demonstrated on some synthetic data sets in two-dimensional feature space. The practical applicability of the system is verified on four real data such as the Iris data set, an appendicitis data set, a speech data set and a hepatic disease data set.