LEARNING IN RELATIONAL DATABASES: A ROUGH SET APPROACH

Knowledge discovery in databases, or dala mining, is an important direction in the development of data and knowledge-based systems. Because of the huge amount of data stored in large numbers of existing databases, and because the amount of data generated in electronic forms is growing rapidly, it is necessary to develop efficient methods to extract knowledge from databases. An attribute-oriented rough set approach has been developed for knowledge discovery in databases. The method integrates machine-learning paradigm, especially learning-from-examples techniques, with rough set techniques. An attribute-oriented concept tree ascension technique is first applied in generalization, which substantially reduces the computational complexity of database learning processes. Then the cause-effect relationship among the attributes in the database is analyzed using rough set techniques, and the unimportant or irrelevant attributes are eliminated. Thus concise and strong rules with little or no redundant information can be learned efficiently. Our study shows that attribute-oriented induction combined with rough set theory provide an efficient and effective mechanism for knowledge discovery in database systems.     

基于Rough Set的最小决策算法的研究

在决策表中，每一行对应了一条决策规则，介并非所有的条件属性对该决策都起作用，所以要进行决策规则的简化，简化后的规则集中仍可能会含有可以去掉而又不影响决策制定过程的冗余规则，找到最小规则集，能去掉所有的冗余信息信息，达到最简化目的，因而最小决策算法的研究很有意义，文中提出一种算法，可在不求得核值表的情况下，直接找到各规则的最小前提条件属性集，获得最小决策算法。     

VAGUENESS AND UNCERTAINTY: A ROUGH SET PERSPECTIVE

Vagueness and uncertainty have attracted the attention of philosophers and logicians for many years. Recently, AI researchers contributed essentially to this area of research. Fuzzy set theory and the theory of evidence are seemingly the most appealing topics. On this note we present a new approach, based on the rough set theory, for looking to these problems. The theory of rough sets seems a suitable mathematical tool for dealing with problems of vagueness and uncertainty. This paper is a modified version of the author's lecture titled "An inquiry into vagueness and uncertainty," which was delivered at the AI Conference in Wigry (Poland), 1994.     

A ROUGH SET/FUZZY LOGIC BASED DECISION MAKING SYSTEM FOR MEDICAL APPLICATIONS

Abstract

A method of performing prognostic modeling of disease states is proposed. The technique uses rough sets to extract rules from a database. The data is then reformatted into a fuzzy logic template, and a learning algorithm is used to adjust the fuzzy set membership functions. The method is applied to the POSCH problem, which looks at risk factors associated with the progression of coronary artery disease. The POSCH data has several shortcomings, including a limited number of cases, correlated inputs, as well as noise on both the inputs and outcome. The problem was to predict progression of atherosclerosis in the LAD three years after baseline based on physiologic data available at baseline. The proposed rough/fuzzy set method correctly predicted progression of atherosclerotic disease in 69% of the patients, which is statistically better than neural network, rough set and logistic models performed.     

PRIMEROSE: PROBABILISTIC RULE INDUCTION METHOD BASED ON ROUGH SETS AND RESAMPLING METHODS

Automated knowledge acquisition is an important research issue in machine learning. Several methods of inductive learning, such as ID3 family and AQ family, have been applied to discover meaningful knowledge from large databases and their usefulness is assured in several aspects. However, since their methods are of a deterministic nature and the reliability of acquired knowledge is not evaluated statistically, these methods are ineffective when applied to domains essentially probabilistic in nature, such as medical domains. Extending concepts of rough set theory to a probabilistic domain, we introduce a new approach to knowledge acquisition, which induces probabilistic rules based on rough set theory (PRIMEROSE) and develop a program that extracts rules for an expert system from a clinical database, using this method. The results show that the derived rules almost correspond to those of the medical experts.     

A METHOD FOR COMPUTING ALL MAXIMALLY GENERAL RULES IN ATTRIBUTE-VALUE SYSTEMS

A method for finding all deterministic and maximally general rules for a target classification is explained in detail and illustrated with examples. Maximally general rules are rules with minimal numbers of conditions. The method has been developed within the context of the rough sets model and is based on the concepts of a decision matrix and a decision function. The problem of finding all the rules is reduced to the problem of computing prime implicants of a group of associated Boolean expressions. The method is particularly applicable to identifying all potentially interesting deterministic rules in a knowledge discovery system but can also be used to produce possible rules or nondeterministic rules with decision probabilities, by adapting the method to the definitions of the variable precision rough sets model.     

分布式知识系统中基于粗糙集合的查询策略研究

传统数据库中的数据查询通常忽视了对于知识的应用．随着网络技术的发展,数 据被分布在不同的物理节点上,用户已不太可能对所有数据均有全面的了解．本文讨论了分 布式知识系统中基于粗糙集合的查询策略,强调了系统中知识的重要性．它可大大地降低网 络节点间的通信代价,从而提高查询效率．粗糙集合理论的应用使得查询不必局限于传统的 精确匹配式查询,而可以是一种粗糙、模糊匹配式的查询．     

EXTENSION OF THE RELATIONAL DATABASE AND ITS ALGEBRA WITH ROUGH SET TECHNIQUES

This paper describes a database model based on the original rough sets theory. Its rough relations permit the representation of a rough set of tuples not definable in terms of the elementary classes, except through use of lower and upper approximations. The rough relational database model also incorporates indiscernibility in the representation and in all the operators of the rough relational algebra. This indiscernibility is based strictly on equivalence classes which must be defined for every attribute domain. There are several obvious applications for which the rough relational database model can more accurately model an enterprise than does the standard relational model. These include systems involving ambiguous, imprecise, or uncertain data. Retrieval over mismatched domains caused by the merging of one or more applications can be facilitated by the use of indiscernibility, and naive system users can achieve greater recall with the rough relational database. In addition, applications inherently “rough” could be more easily implemented and maintained in the rough relational database.     

极小极大规则学习及在决策树规则简化中的应用

文中在粗糙集理论中的约简概念的启发下提出极小规则和极大规则的概念及极小极大规则学习。     

Consistency and Completeness in Rough Sets

Consistency and completeness are defined in the context of rough set theory and shown to be related to the lower approximation and upper approximation, respectively. A member of a composed set (union of elementary sets) that is consistent with respect to a concept, surely belongs to the concept. An element that is not a member of a composed set that is complete with respect to a concept, surely does not belong to the concept. A consistent rule and a complete rule are useful in addition to any other rules learnt to describe a concept. When an element satisfies the consistent rule, it surely belongs to the concept, and when it does not satisfy the complete rule, it surely does not belong to the concept. In other cases, the other learnt rules are used. The results in the finite universe are extended to the infinite universe, thus introducing a rough set model for the learning from examples paradigm. The results in this paper have application in knowledge discovery or learning from database environments that are inconsistent, but at the same time demand accurate and definite knowledge. This study of consistency and completeness in rough sets also lays the foundation for related work at the intersection of rough set theory and inductive logic programming.     

Knowledge base refinement: A bibliography

Knowledge base refinement is a learning process aimed at adjusting a knowledge base for the purpose of improving the breadth, accuracy, efficiency, and efficacy of the associated knowledge-based system(s). This annotated bibliography gives an overview of this emerging field.     

一种新的覆盖粗糙集及其模糊性度量

在覆盖近似空间中定义了一类新的模糊集,给出了该类模糊集的模糊性度量,讨论模糊集及其模糊度量的性质,最后通过实例给出直观解释.     

粗糙集理论及其应用

在很多实际系统中均不同程度地存在着不确定性因素，采集到的数据常常包含着噪声，不精确甚至不完整，粗糙集理论是继概率论，模糊集，证据理论之后的又一个处理不确定性的数学工具，作为一种较新的软计算方法，粗糙集近年来越来越受到重视，其有效性已在许多科学与工程领域的成功应用于得到证实，是当前国际上人工智能理论及其应用领域中的研究热点之一，本文介绍了粗糙集理论的基本概念，特点及有关应用。     

DATA-BASED ACQUISITION AND INCREMENTAL MODIFICATION OF CLASSIFICATION RULES

One of the most important problems in the application of knowledge discovery systems is the identification and subsequent updating of rules. Many applications require that the classification rules be derived from data representing exemplar occurrences of data patterns belonging to different classes. The problem of identifying such rules in data has been researched within the field of machine learning, and more recently in the context of rough set theory and knowledge discovery in databases. In this paper we present an incremental methodology for finding all maximally generalized rules and for adaptive modification of them when new data become available. The methodology is developed in the context of rough set theory and is based on the earlier idea of discernibility matrix introduced by Skowron.     

CONFIDENCE LIMITS ON ROUGH SET RULES GENERATED FROM A LIMITED NUMBER OF EXAMPLES

Abstract

The rough sets method is used for extracting both certain and possible rules from data. This paper shows that, in reality, there are no certain rules. Probability theory is used to determine the best distribution to use when evaluating the sirength of rules. A method of determining the confidence limits for rules is presented, and this is used to determine what rule to follow when conflicts occur. Finally, a way to apply these results to situations where the cost of wrong decisions is different from the rewards for correct decisions is discussed.     

一种不确定性条件下的自主式知识学习模型

在没有领域先验知识条件下的不确定知识主动式学习是机器学习领域中的一个难题.通过研究决策表和决策规则的不确定性,建立基于粗集表示、度量和处理不确定性信息和知识的理论,并且结合Skowron的缺省规则获取算法,提出一种不确定性条件下的数据自主式学习模型和方法,以解决这一问题.通过仿真实验,验证了该自主式学习方法的有效性.     

Discovering rules for water demand prediction: An enhanced rough-set approach

Prediction of consumer demands is a pre-requisite for optimal control of water distribution systems because minimum-cost pumping schedules can be computed if water demands are accurately estimated. This paper presents an enhanced rough-sets method for generating prediction rules from a set of observed data. The proposed method extends upon the standard rough set model by making use of the statistical information inherent in the data to handle incomplete and ambiguous training samples. It also discusses some experimental results from using this method for discovering knowledge on water demand prediction.     

RSL:基于Rough Set的表示语言

本文绘出了一种基于RoughSet理论的表示语言—RSL，该语言包括面向应用与面向研究两部分.应用部分主要服务于对信息表进行分析与处理的用户，研究部分则主要是为研究RoughSet及利用RoughSet理论构造更复杂算法的研究者所设计.鉴于RoughSet理论中求最小约简的过程是NP完全问题，为了使RSL表示语言可以分析与处理规模更大的信息表，本文还为RSL表示语言设计了一个新的对求取最小约简而言的领域独立的近似算法.     

The Variable Precision Rough Set Inductive Logic Programming Model and Strings

The Variable Precision Rough Set Inductive Logic Programming model (VPRSILP model) extends the Variable Precision Rough Set (VPRS) model to Inductive Logic Programming (ILP). The generic Rough Set Inductive Logic Programming (gRS-ILP) model provides a framework for ILP when the setting is imprecise and any induced logic program will not be able to distinguish between certain positive and negative examples. The gRS-ILP model is extended in this paper to the VPRSILP model by including features of the VPRS model. The VPRSILP model is applied to strings and an illustrative experiment on transmembrane domains in amino acid sequences is presented.