Concept lattice is a kind of efficient mathematical tools for data analysis and knowledge discovery. In this paper, dependence space models are constructed to obtain a concept lattice. For a formal context, a congruence relation is first defined based on a sufficiency operator on the power set of the attribute set. A dependence space is generated. By using the dependence space, we introduce a closure operator. Related properties of the operator are discussed. It is also proved that any closed element of the closure operator is the maximum element in the attribute granule generated by the element. Further, the closed element is just the intension of some formal concept. Similarly, we define a congruence relation on the basis of a sufficiency operator, and introduce a dependence space on the power set of the object set. A closure operator is proposed for the subset of objects. The corresponding closed element of the closure operator is the maximum element in each object granule. All maximum elements generate the set of all extensions of the concept lattice. An example is used to show the validity of the approach to obtain all intensions. Finally, we introduce a dominance congruence relation, which is used to produce a closure operator. The dependence of attributes is defined based on the closure operator. The related decision rules are discussed.

Formal concept analysis, which is based on formal contexts and concept lattices, is a data analysis method. Formal concepts reflect the relationship between objects and attributes and realize a formal description of concepts in philosophy. To simplify the information description, this paper proposes concept reduction in the formal concept analysis framework and studies the related theories on concept reduction preserving binary relations. In addition, characteristics analysis of three types of concepts that play different roles in reduction processing is performed from the perspective of operators and a Boolean matrix. Finally, a method to calculate concept reduction is provided.

概念认知学习是指通过具体的认知模型从给定线索中学习概念,以模拟人脑进行概念学习的行为.其基本研究内容包括认知机理、概念认知系统的构建与优化、概念认知过程的系统建模等.文中对概念认知的公理化、概念认知系统、概念认知过程、认知主体的多维性、认知主体的识别局限性、认知主体的记忆遗忘性、认知主体的联想性、认知主体的相对性、多主体认知以及概念认知学习的跨学科交叉研究中存在的一些问题进行归纳、总结与思考,以促进该研究领域进一步发展.

属性特征是研究信息系统中属性重要性的方法之一.本文基于集值信息系统中的拟序关系,给出了对象合成、属性合成集值信息系统,讨论了集值信息系统与合成集值信息系统的协调集、属性特征之间的关系,进而定义了对象(属性)子集值信息系统,研究了子集值信息系统与原集值信息系统等的必要属性及不必要属性之间的关系.

Attribute reduction is one of the main issues in the study of concept lattice. This paper mainly deals with attribute reductions of an object-oriented concept lattice constructed on the basis of rough set. Attribute rank of object-oriented concept lattice is first defined, and relationships between attribute rank and object-oriented concepts are then discussed. Based on attribute rank, generating algorithm of object-oriented concepts is investigated. The object-oriented consistent set and object-oriented reduction of an object-oriented concept lattice are defined. Adjustment theorems of the object-oriented consistent set, and the necessary and sufficient conditions for a attribute subset to be an object-oriented consistent set of an object-oriented concept lattice are discussed. Then the object-oriented discernibility matrix of an object-oriented concept lattice is defined and its properties are also studied. Based on the object-oriented discernibility matrix, an approach to object-oriented reductions of an object-oriented concept lattice is proposed, and the attribute characteristics are also analyzed.

复杂工程对象多为非线性系统，为实现对其有效的管理与控制，需要基于非线性系统的输入输出数据建立描述系统动态特性的数学模型，并对其中状态及参数进行高精度的估计与辨识，这是控制科学与技术领域具有挑战性的难题。

In the paper proposed two new types of the multiple granulation rough set models, where a target concept is approximated from two different kinds of views by using the equivalence classes induced by multiple granulations. A number of important properties of the two types of MGRS are investigated. From the properties, it can be found that Pawlak’s and Qian’s rough set models are special instances of those of our MGRS. Moreover, several important measures are presented in two types of MGRS, such as rough measure and quality of approximation. Furthermore, the relationship and difference are discussed carefully among Pawlak’s rough set, Qian’s MGRS, and two new types of MGRS. In order to illustrate our multiple granulations rough set model, some examples are considered, which are helpful for applying this theory in practical issues. One can get that the paper is meaningful both in the theory and in application for the issue of knowledge reduction in complex information systems.

It is well-known that how to determine the weights of criteria is an important problem of multicriteria decision making. To make further description of the aforementioned, in this paper we introduce an extended TOPSIS method for multicriteria decision making with interval-valued intuitionistic fuzzy information, where the weighted vector of each alternative is determined by ranking corresponding evaluation information. Meanwhile, we construct a new method to measure the distance between alternatives and positive ideal solution as well as negative ideal solution, which is score distance. Finally, the detailed decision making procedure is proposed and an illustrative example is applied to demonstrate its validity. It is worth while to point out that the weights determination for criteria will be helpful to future research on decision making analysis.

Formal concept analysis is an algebraic model based on a Galois connection. It is used for symbolic knowledge exploration from an elementary form of a formal context. This paper mainly presents a general framework for concept lattice in which axiomatic approaches are used. The relationship between concept lattice and dual concept lattice is first studied. Based on set-theoretic operators, generalized concept systems are established. And properties of them are examined. By using axiomatic approaches, a pair of dual concept lattices is characterized by different sets of axioms. The connections between 0-1 binary relations and generalized concept systems are examined. And generalized dual concept systems can be constructed by a pair of dual set-theoretic operators. Axiomatic characterizations of the generalized concept systems guarantee the existence of a binary relation producing a formal context.

In this paper, as a naturally generalization of classical information systems, lattice-valued information systems based on dominance relation is proposed. An approach for ranking all objects in this system is constructed consequently, and decision makers can find objects with better property to make an useful and effective decision. In addition, the rough set approach to lattice-valued information systems based on dominance relation is established. And evidence theories in this system are formulated for the analysis of lattice-valued information systems based on dominance relation. What is more, in order to acquire concise knowledge representation and extract much simpler decision rules, the methods of attribute reductions based on discernibility matrix and evidence theory are investigated carefully. These results will be helpful for decision-making analysis in lattice-valued information systems based on dominance relation.

With granular computing point of view, the classical dominance-based rough set model is based on a single granulation. For an ordered information system, this paper proposes two new types of multiple granulation rough set (MGRS) models, where a target concept is approximated from different kinds of views by using dominant classes induced by multiple granulations. And a number of important properties of the two types of MGRS are investigated in an ordered information system. From the properties, it can be found that Greco's rough set model is a special instance compared to our MGRS model. Moreover, the relationships and differences are discussed carefully among Greco's rough set and two new types of MGRS. Furthermore, several important measures are presented in two types of MGRS models, such as rough measure, quality of approximation in an ordered information system. In order to illustrate our MGRS models in an ordered information system, a real life example is considered, which is helpful for applying this theory in practical issues. One can see get that the research is meaningful in applications for the issue of knowledge reduction in complex ordered information systems.

The theory of concept lattice proposed by Wille has been generalized in three different ways based on binary formal contexts, and substantive properties with respect to these formal concepts have been derived. In this paper, we study a reverse problem, that is, how to characterize the notions of formal concepts in terms of their properties. Axiomatic characterizations for the theory of formal concept analysis are presented. By this approach, four types of conceptual knowledge system are defined, and axiom sets that must be satisfied by the conceptual knowledge system are stated. It is proved that axioms of the conceptual knowledge system guarantee the existence of certain types of binary relations producing the same formal concepts. The independence of axiom sets characterizing the conceptual knowledge system is examined.

The extension of rough set model is an important research direction in rough set theory. The aim of this paper is to present new extensions of the rough set model over two different universes which are rough fuzzy set model in a generalized approximation space, rough set model in a fuzzy approximation space and rough fuzzy set model in a fuzzy approximation space based over two different universes. Moreover, the properties of the approximation operators in these models are investigated. Furthermore, by employing cut set of fuzzy set and fuzzy relation, classical representations of fuzzy rough approximation operators are studied. Finally, the measures of fuzzy rough set models are presented, and the relationships among the fuzzy rough models and rough set model over two universes are investigated.

In formal concept analysis, various fuzzy generalizations of formal concepts have been made. The fuzzy concept operators defined under the condition that the truth values (degrees) coming from a complete residuated lattice satisfy many interesting properties. Conversely, fuzzy concept operators can be characterized in terms of their properties. In this paper, the axiomatic approaches in the theory of fuzzy formal concept analysis based on a complete residuated lattice are presented. In the axiomatic approach, the fuzzy conceptual knowledge system is defined, and axiom sets satisfied by the fuzzy conceptual knowledge system are stated. It is proved that axioms of the fuzzy conceptual knowledge system guarantee the existence of certain types of binary fuzzy relations producing the same fuzzy formal concepts. The independence of axiom sets characterizing the fuzzy conceptual knowledge system is examined.

工程硕士专业学位研究生教育必须与相应的工程领域职业资格相衔接,而这种衔接困难重重、步履维艰。高层次工程技术人才的工程师职业资格认证是解决工程硕士研究生教育与职业资格相衔接的根本保证。结合我国目前的实际情况,应当构建政府支持与引导下的由培养单位的专家与企业行业的专家共同组成的职业资格认证管理体系。

Probability space is established by introducing a portion function in information system based on general binary-relation,this avoids the limitations that systems based on general binary-relation can't be seen as a partition but only a cover. Moreover,granularity representation of knowledge is proposed in information system based on general binary-relation,and some important properties are obtained.It can be proved that the algebra representation of knowledge is equal to the granularity representation of knowledge in information system.Finally,the validity is examined by two examples,and the proposed frame- work paves the road for the further study of knowledge representation in information system.

工程硕士专业学位是我国研究生教育实施学位条例后的一项重大改革。本文回顾了工程硕士教育的探索之路与改革历程,指出建立高层次工程技术人才的职业资格认证制度是工程硕士专业学位研究生教育质量的重要保障。

In this paper, some important issues of granularity are discussed mainly in information systems (ISs) based on binary relation. Firstly, the vector representation method of knowledge granules is proposed in an infor-mation system based on binary relation to eliminate limitations of set representation method. Secondly, operators among knowledge granularity are introduced and some important properties of them are studied carefully. Thirdly, distance between two knowledge granules is established and granular space is constructed based on it. Fourthly, axiomatic definition of knowledge granularity is investigated, and one can find that some existed knowledge granularities are special cases under the definition. In addition, as an application of knowledge granular space, an example is employed to validate some results in our work.

This paper proposes a representation theorem for an arbitrary interval-valued fuzzy J-equivalence relations. Firstly, we present a note on representations of fuzzy T-equivalence relations in which the representation theorem should be applied to a fuzzy similarity measure better. Secondly, an representation theorem is proposed that the interval-valued fuzzy J-equivalence relations can be generated by a family of similar interval-valued fuzzy subsets. Then some interval-valued fuzzy J-equivalence relations are presented.