Generalized rough sets over fuzzy lattices

This paper studies generalized rough sets over fuzzy lattices through both the constructive and axiomatic approaches. From the viewpoint of the constructive approach, the basic properties of generalized rough sets over fuzzy lattices are obtained. The matrix representation of the lower and upper approximations is given. According to this matrix view, a simple algorithm is obtained for computing the lower and upper approximations. As for the axiomatic approach, a set of axioms is constructed to characterize the upper approximation of generalized rough sets over fuzzy lattices.     

Consistency,Turing Computability and Gödel’s First Incompleteness Theorem

It is well understood and appreciated that Gödel’s Incompleteness Theorems apply to sufficiently strong, formal deductive systems. In particular, the theorems apply to systems which are adequate for conventional number theory. Less well known is that there exist algorithms which can be applied to such a system to generate a gödel-sentence for that system. Although the generation of a sentence is not equivalent to proving its truth, the present paper argues that the existence of these algorithms, when conjoined with Gödel’s results and accepted theorems of recursion theory, does provide the basis for an apparent paradox. The difficulty arises when such an algorithm is embedded within a computer program of sufficient arithmetic power. The required computer program (an AI system) is described herein, and the paradox is derived. A solution to the paradox is proposed, which, it is argued, illuminates the truth status of axioms in formal models of programs and Turing machines.     

The minimization of axiom sets characterizing generalized approximation operators

In the axiomatic approach of rough set theory, rough approximation operators are characterized by a set of axioms that guarantees the existence of certain types of binary relations reproducing the operators. Thus axiomatic characterization of rough approximation operators is an important aspect in the study of rough set theory. In this paper, the independence of axioms of generalized crisp approximation operators is investigated, and their minimal sets of axioms are presented.     

The roles of inductive modelling and coherence in Bayesian statistics

Summary The role of the inductive modelling process (IMP) seems to be of practical importance in Bayesian statistics; it is recommended that the statistician should emphasise meaningful real-life considerations rather than more formal aspects such as the axioms of coherence. It is argued that whilst axiomatics provide some motivation for the Bayesian philosophy, the real strength of Bayesianism lies in its practical advantages and in its plausible representation of real-life processes. A number of standard procedures, e.g., validation of results, choosing between different models, predictive distributions, the linear model, sufficiency, tail area behaviour of sampling distributions, and hierarchical models are reconsidered in the light of the IMP philosophy, with a variety of conclusions. For example, whilst mathematical theory and Bayesian methodology are thought to prove invaluable techniques at many local points in a statician’s IMP, a global theoretical solution might restrict the statistician’s inductive thought processes. The linear statistical model is open to improvement in a number of medical and socio-economic situations; a simple Bayesian alternative related to logistic discrimination analysis often, leads to better conclusions for the inductive modeller.     

On minimization of axiom sets characterizing covering-based approximation operators

Rough set theory was proposed by Pawlak to deal with the vagueness and granularity in information systems. The classical relation-based Pawlak rough set theory has been extended to covering-based generalized rough set theory. The rough set axiom system is the foundation of the covering-based generalized rough set theory, because the axiomatic characterizations of covering-based approximation operators guarantee the existence of coverings reproducing the operators. In this paper, the equivalent characterizations for the independent axiom sets of four types of covering-based generalized rough sets are investigated, and more refined axiom sets are presented.     

覆盖粗糙集的公理化

粗糙集的公理系统是粗糙集理论与应用的基础.覆盖粗糙集是粗糙集理论的自然的有意义的推广.基于Xu等提出的新的覆盖粗糙集模型,研究了新模型的公理系统,用4条简洁且相互独立的公理刻画了覆盖粗糙集.这些研究有助于覆盖粗糙集理论研究的深入和完善.     

Axiomatic Design Theory for Systems

A general theory for system design is presented based on axiomatic design. The theory is applicable to many different kinds of systems, including machines, large systems, software systems, organizations, and systems consisting of a combination of hardware and software. Systems are represented by means of a system architecture, which takes the form of the {FR}/{DP}/{PV}hierarchies, a ‘junction-module’ diagram, and the ‘flow diagram’. The ‘flow diagram’ for system architecture concisely represents the system design, the relationship among modules, and the control sequence in operating systems. The flow diagram of the system architecture can be used for many different tasks: design, construction, operation, modification, and maintenance of the system. It should also be useful for distributed design and operation of systems, diagnosis of system failures, and for archival documentation.     

贯穿射影几何的一条主线定理——蝴蝶定理的研究

利用射影几何的对合对应、交比不变量、二次曲线射影定义、完全四边形的调和性、二次曲线束理论,给合蝴蝶定理的多种证法,并用这些理论研究蝴蝶定理的推广命题。     

On axiomatic characterizations of three pairs of covering based approximation operators

Rough set theory is a useful tool for dealing with inexact, uncertain or vague knowledge in information systems. The classical rough set theory is based on equivalence relations and has been extended to covering based generalized rough set theory. This paper investigates three types of covering generalized rough sets within an axiomatic approach. Concepts and basic properties of each type of covering based approximation operators are first reviewed. Axiomatic systems of the covering based approximation operators are then established. The independence of axiom set for characterizing each type of covering based approximation operators is also examined. As a result, two open problems about axiomatic characterizations of covering based approximation operators proposed by Zhu and Wang in (IEEE Transactions on Knowledge and Data Engineering 19(8) (2007) 1131-1144, Proceedings of the Third IEEE International Conference on Intelligent Systems, 2006, pp. 444-449) are solved.     

基于本体的城市交通的知识分析和推理

以城市交通为研究和应用背景,基于本体模型的知识表示技术,建立城市交通本体。对城市交通领域知识进行规范描述,详细描述了定义类层次及类的属性和关系,以及实例的基本规则,并从领域知识中提取出类内公理和类间公理,建立公理库,用于领域知识的一致性分析和知识推理。解决了语义层次上信息共享和交互的问题,为上海城市交通信息网格的交通信息服务提供语义支撑。