A general approach to attribute reduction in rough set theory

The concept of a consistent approximation representation space is introduced. Many types of information systems can be treated and unified as consistent ap- proximation representation spaces. At the same time, under the framework of this space, the judgment theorem for determining consistent attribute set is established, from which we can obtain the approach to attribute reductions in information systems. Also, the characterizations of three important types of attribute sets (the core attribute set, the relative necessary attribute set and the unnecessary attribute set) are examined.     

Reduct and attribute order

Based on the principle of discernibility matrix, a kind of reduction algorithm with attribute order has been developed and its solution has been proved to be complete for reduct and unique for a given attribute order. Being called the reduct problem, this algorithm can be regarded as a mapping R = Reduct(S) from the attribute order space O to the reduct space R for an information system (U, C ∪ D）, where U is the universe and C and D are two sets of condition and decision attributes respectively. This paper focuses on the reverse problem of reduct problem S = Order(R), i.e., for a given reduct R of an information system, we determine the solution of S = Order(R) in the space θ. First, we need to prove that there is at least one attribute order S such that S = Order(R). Then, some decision rules are proposed, which can be used directly to decide whether the pair of attribute orders has the same reduct. The main method is based on the fact that an attribute order can be transformed into another one by moving the attribute for limited times. Thus, the decision of the pair of attribute orders can be altered to the decision of the sequence of neighboring pairs of attribute orders. Therefore,the basic theorem of neighboring pair of attribute orders is first proved, then, the decision theorem of attribute order is proved accordingly by the second attribute.     

A new knowledge reduction algorithm for information system

The discernible Boolean matrix of information system is defined. The model of attribute reduction in the form of linear logical equations is established. The necessary and sufficient condition for determining whether the attribute is absolutely necessary, relatively necessary and absolutely superfluous is given. Finally, an elementary knowledge reduction algorithm is proposed.     

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.     

Second Attribute Algorithm Based on Tree Expression

One view of finding a personalized solution of reduct in an information system is grounded on the viewpoint that attribute order can serve as a kind of semantic representation of user requirements. Thus the problem of finding personalized solutions can be transformed into computing the reduct on an attribute order. The second attribute theorem describes the relationship between the set of attribute orders and the set of reducts, and can be used to transform the problem of searching solutions to meet user requirements into the problem of modifying reduct based on a given attribute order. An algorithm is implied based on the second attribute theorem, with computation on the discernibility matrix. Its time complexity is O（n^2 × m） （n is the number of the objects and m the number of the attributes of an information system）. This paper presents another effective second attribute algorithm for facilitating the use of the second attribute theorem, with computation on the tree expression of an information system. The time complexity of the new algorithm is linear in n. This algorithm is proved to be equivalent to the algorithm on the discernibility matrix.     

模式转换未知的一类混杂系统的状态估计

Since the state of hybrid systems is determined by interacting continuous and discrete dynamics, the state estimation of hybrid systems becomes a challenging problem. It is more complicated when the discrete mode transition information is not available, and the modes of hybrid systems are nonlinear stochastic dynamic systems. To address this problem, this paper proposes a novel hybrid strong tracking filter (HSTF) for state estimation of a class of hybrid nonlinear stochastic systems with unknown mode transition, the method for designing HSTF is presented. The HSTF can estimate the continuous state and discrete mode accurately with unknown mode transition information, and the estimation of hybrid states is robust against the initial state. Simulation results illustrate the effectiveness of the proposed approach.     

Analyzing and mining ordered information tables

Work in inductive learning has mostly been concentrated on classifying.However,there are many applications in which it is desirable to order rather than to classify instances.Formodelling ordering problems,we generalize the notion of information tables to ordered information tables by adding order relations in attribute values.Then we propose a data analysis model by analyzing the dependency of attributes to describe the properties of ordered information tables.The problem of mining ordering rules is formulated as finding association between orderings of attribute values and the overall ordering of objects.An ordering rules may state that “if the value of an object x on an attribute a is ordered ahead of the value of another object y on the same attribute,then x is ordered ahead of y“.For mining ordering rules,we first transform an ordered information table into a binary information table,and then apply any standard machine learning and data mining algorithms.As an illustration,we analyze in detail Maclean‘s universities ranking for the year 2000.     

Platform technology of Web services-oriented DCS data exchanging

To solve the problem of information interdiction among various kinds of DCS and systems of MIS and ERP, through using a kind of universal Web services object＇s encapsulation technique, a Web services-oriented DCS data exchanging platform is constructed, and the functional architecture and Key Enabling Technologies of the platform are introduced in detail. Accordingly, the enterprise information integration across different platforms and languages is realized, and an open, unified application integration environment is provided for the heterogeneous control systems and management systems.     

Formal Ontology: Foundation of Domain Knowledge Sharing and Reusing

Domain analysis is the activity of identifying and representing the relevant information in a domain,so that the information can be shared and reused in similar systems.But until now,no efficient approaches are available for capturing and representing the results of domain analysis and then for sharing and reusing the domain knowledge.This paper proposes an ontology-oriented approach for formalizing the domain models.The architecture for the multiple-layer structure of the domain knowledge base is also discussed.And finally,some genetic algorithm-based methods have been given for supporting the knowledge sharing and reusing.     

A Fault-Tolerant and Heuristic Routing Algorithm for Faulty Hypercubes

A fault-tolerant and heuristic routing algorithm for faulty hypercube systems is described.To improve the efficiency,the algorithm adopts a heuristic backtracking strategy and each node has an array to record its all neighbors‘ faulty link information to avoid unnecessary searching for the known faulty links.Furthermore,the faulty link information is dynamically accumulated and the technique of heuristically searching for optimal link is used.The algorithm routes messages through the minimum feasible path between the sender and receiver if at least one such path exists,and takes the optimal path with higher probability when faulty links exist in the faulty hypercube.     

序信息系统的启发式属性约简算法

属性约简是粗糙集理论的核心问题之一,序信息系统中的属性约简也逐渐受到关注。基于优势类的概念,引入了序信息系统的一种信息粒度,用于度量属性集在序意义下的不确定性,进而给出了序信息系统中属性重要度的定义。在此基础上,设计了一种序信息系统的启发式属性约简算法,并通过实例分析进行了有效性检验。     

Approaches to knowledge reduction of covering decision systems based on information theory

In this paper, we propose some new approaches for attribute reduction in covering decision systems from the viewpoint of information theory. Firstly, we introduce information entropy and conditional entropy of the covering and define attribute reduction by means of conditional entropy in consistent covering decision systems. Secondly, in inconsistent covering decision systems, the limitary conditional entropy of the covering is proposed and attribute reductions are defined. And finally, by the significance of the covering, some algorithms are designed to compute all the reducts of consistent and inconsistent covering decision systems. We prove that their computational complexity are polynomial. Numerical tests show that the proposed attribute reductions accomplish better classification performance than those of traditional rough sets. In addition, in traditional rough set theory, MIBARK-algorithm [G.Y. Wang, H. Hu, D. Yang, Decision table reduction based on conditional information entropy, Chinese J. Comput., 25 (2002) 1-8] cannot ensure the reduct is the minimal attribute subset which keeps the decision rule invariant in inconsistent decision systems. Here, we solve this problem in inconsistent covering decision systems.     

基于优势关系下模糊目标信息系统的属性约简

在现实生活中,许多信息系统不仅是模糊的还是基于优势关系的。在基于优势关系下模糊目标信息系统中引入了广义决策的概念,提出了分别保持下广义决策、上广义决策、广义决策不变的三种不同约简,进一步给出了各属性约简的判定定理和辨识矩阵,提供了在优势关系下模糊目标信息系统属性约简的具体方法。通过实例验证了该方法的有效性,进一步丰富了粗糙集理论。     

基于证据理论的覆盖决策信息系统的属性约简

覆盖决策信息系统的属性约简是粗糙集理论中的重要研究内容之一.文中讨论决策为覆盖的覆盖决策信息系统的属性约简,针对覆盖决策信息系统的一类约简,利用证据理论中的信任函数和似然函数给出约简的等价刻画.根据决策类的似然函数值定义覆盖的重要度和相对重要度,给出求解约简的算法,并以实例说明算法的有效性.     

Communicating between information systems

Communication between information systems is a basic problem in granular computing. The concept of homomorphism is a useful mathematical tool to study the communication between two information systems. In this paper, some properties of information systems under homomorphisms are investigated. The concepts of consistent functions are first introduced and their properties are investigated. The concepts of relation mappings between two universes are then proposed in order to construct a binary relation on one universe according to the given binary relation on the other universe. The main properties of the mappings are studied. Finally, the notions of homomorphisms of information systems based on arbitrary binary relations are proposed, and it is proved that attribute reductions in the original system and image system are equivalent to each other under the condition of homomorphism.     

Attribute reduction in ordered information systems based on evidence theory

Attribute reduction is one of the most important problems in rough set theory. However, in real-world lots of information systems are based on dominance relation in stead of the classical equivalence relation because of various factors. The ordering properties of attributes play a crucial role in those systems. To acquire brief decision rules from the systems, attribute reductions are needed. This paper deals with attribute reduction in ordered information systems based on evidence theory. The concepts of plausibility and belief consistent sets as well as plausibility and belief reducts in ordered information systems are introduced. It is proved that a plausibility consistent set must be a consistent set and an attribute set is a belief reduct if and only if it is a classical reduction in ordered information system.     

大变量多输出逻辑函数实质项识别算法

在对Espresso算法进行分析改进的基础上，提出了一种基于全域识别的多输入多输出逻辑函数实质本源项、完全冗余项和相对冗余项生成算法，该算法通过对基于积项表示的多输入多输出逻辑函数的余因子计算来进行全域判断，根据全域判断结果来识别实质本源项、完全冗余项和相对冗余项，从而构成实质本源项集合、完全冗余项集合和相对冗余项集合。对基于二级SOP型的多输入多输出逻辑函数设计了多输入多输出逻辑函数优化识别软件系统，允许的最大输入变量数为128、最大输出变量数为256、最大输入输出变量总和为300、最大输入积项数为20 000。软件系统在Pentium 1.8GHz、512MB内存的计算机上通过了Benchmark例题的测试。