On uniqueness of (fuzzy) relation in some generalized rough set model

In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.

Dynamic weighted voting for multiple classifier fusion:a generalized rough set method

To improve the performance of multiple classifier system, a knowledge discovery based dynamic weighted voting （KD-DWV） is proposed based on knowledge discovery. In the method, all base classifiers may be allowed to operate in different measurement/feature spaces to make the most of diverse classification information. The weights assigned to each output of a base classifier are estimated by the separability of training sample sets in relevant feature space. For this purpose, some decision tables （DTs） are established in terms of the diverse feature sets. And then the uncertainty measures of the separability are induced, in the form of mass functions in Dempster-Shafer theory （DST）, from each DTs based on generalized rough set model. From the mass functions, all the weights are calculated by a modified heuristic fusion function and assigned dynamically to each classifier varying with its output. The comparison experiment is performed on the hyperspectral remote sensing images. And the experimental results show that the performance of the classification can be improved by using the proposed method compared with the plurality voting （PV）.

On Multi-Granulation Rough Sets with Its Applications

Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.

Notes on Rough Set Approximations and Associated Measures

We review and compare two definitions of rough set approximations.One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe.The latter definition,although less studied,is semantically superior for interpreting rule induction and is closely related to granularity switching in granular computing.Numerical measures about the accuracy and quality of approximations are examined.Several semantics difficulties are commented.

Definability and Textural Rough Set Algebras

In this paper,a counterpart of definability is studied in texture spaces.The concept of textural complete field is defined and the relations with textural definable sets are investigated.If a texture is discrete,then textural definability coincides with definability.Using this fact,we obtain some basic results for definability in rough set algebras.Further,we discuss on definability for fuzzy rough sets considering textural fuzzy direlations.

Intuitionistic Fuzzy Rough Sets Based on Two Intuitionistic Fuzzy Implicators

This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.

A New Minimal Rough Set Axiom Group

Rough set axiomatization is one aspect of rough set study, and the purpose is to characterize rough set theory using independable and minimal axiom groups. Thus, rough set theory can be studied by logic and axiom system methods. To characterize rough set theory, an axiom group named H consisting of 4 axioms, is proposed. That validity of the axiom group in characterizing rough set theory is reasonable, is proved. Simultaneously, the minimization of the axiom group, which requires that each axiom is an inequality and each is independent, is proved. The axiom group is helpful for researching rough set theory by logic and axiom system methods. Key words rough set - lower approximation - axioms - minimization CLC number TP 18 Foundation item: Supported by the 973 National Basic Research Program of China (2002CB312106) and Science & Technology Program of Zhejiang Province (2004C31G101003)Biography: DAI Jian-hua (1977-), male, Ph. D, research direction: data mining, artificial intelligence, rough sets, evolutionary computation.

Properties and Relations of Several Operators Based on Covering Rough Sets

The coveting rough sets theory is a generalization of traditional rough set theory, and can also describe information with incompleteness and fuzziness in information systems. In this paper, we first provide the definitions of several upper and lower covering approximation operators on the covering approximation space. Then, we study the properties of these operators. Finally, we propose the mutual relations between approximation operators and similar relations of the operator （ I ） based on the covering rough sets.

Rough Sets in Approximate Solution Space

As a new mathematical theory, Rough sets have been applied to processing imprecise, uncertain and incomplete data. It has been fruitful in finite and non-empty set. Rough sets, however, are only served as the theoretic tool to discretize the real function. As far as the real function research is concerned, the research to define rough sets in the real function is infrequent. In this paper, we exploit a new method to extend the rough set in normed linear space, in which we establish a rough set,put forward an upper and lower approximation definition, and make a preliminary research on the property of the rough set.A new tool is provided to study the approximation solutions of differential equation and functional variation in normed linear space. This research is significant in that it extends the application of rough sets to a new field.

Realization of Rough Set Approximation Toplogical Operations Based on Formal Concept Analysis

There is an intimate correlation between rough set theory and formal concept analysis theory, so rough set approximations can be realized by means of formal concept analysis. For any given multiple valued information system, the realization of rough set approximation operation has two major steps, firstly convert the information system from multiple valued one to single valued formal context, secondly realize rough set approximation operations aided by concept lattice, which is equivalent to a query operation under some necessary conditions.

基于Rough Set理论的典型振动故障诊断

在分析旋转机械振动特点和Rough Set理论的基础上,针对传统的频谱分析方法对质量不平衡、动静碰摩、支座松动等3种典型故障识别效率低的缺点,提出了一个基于Rough Set的振动故障诊断模型.该模型根据故障和能量的映射关系,分别在时域、频域、时-频域中定义4种信息熵作为条件属性,推导了3种典型振动的决策规则,实现了对振动信号中不一致信息的处理.通过汽轮发电机组振动实验对上述方法进行了验证.结果表明,该模型能够很好地识别这3种典型故障.

Transformation and entropy for fuzzy rough sets

A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed. This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.

L-Fuzzy Rough Set Based on Complete Residuated Lattice

Residuated lattice is an important non-classical logic algebra, and L-fuzzy rough set based on residuated lattice can describe the information with incompleteness, fuzziness and uncomparativity in information systems. In this paper, the representation theorems of L-fuzzy rough sets based on residuated lattice are given. The properties and axiomatic definition of the lower and upper approximarion operators in L-fuzzy rough sets are discussed.

New judging model of fuzzy cluster optimal dividing based on rough sets theory

To investigate the judging problem of optimal dividing matrix among several fuzzy dividing matrices in fuzzy dividing space, correspondingly, which is determined by the various choices of cluster samples in the totality sample space, two algorithms are proposed on the basis of the data analysis method in rough sets theory： information system discrete algorithm （algorithm 1） and samples representatives judging algorithm （algorithm 2）. On the principle of the farthest distance, algorithm 1 transforms continuous data into discrete form which could be transacted by rough sets theory. Taking the approximate precision as a criterion, algorithm 2 chooses the sample space with a good representative. Hence, the clustering sample set in inducing and computing optimal dividing matrix can be achieved. Several theorems are proposed to provide strict theoretic foundations for the execution of the algorithm model. An applied example based on the new algorithm model is given, whose result verifies the feasibility of this new algorithm model.

Applications of Generalized Rough Set Theory in Evaluation Index System of Radar Anti-Jamming Performance

Radar anti-jamming performance evaluation is a necessary link in the process of radar development,introduction and equipment. The applications of generalized rough set theory are proposed and discussed in this paper to address the problems of big data, incomplete data and redundant data in the construction of evaluation index system. Firstly, a mass of real-valued data is converted to some interval-valued data to avoid an unacceptable number of equivalence classes and classification rules, and the interval similarity relation is employed to make classifications of this interval-valued data. Meanwhile, incomplete data can be solved by a new definition of the connection degree tolerance relation for both interval-valued data and single-valued data, which makes a better description of rough set than the traditional limited tolerance relation. Then, E-condition entropy-based heuristic algorithm is applied to making attribute reduction to optimize the evaluation index system, and final decision rules can be extracted for system evaluation. Finally, the feasibility and advantage of the proposed methods are testified by a real example of radar anti-jamming performance evaluation.

Fuzzy rough sets in Sostak sense

In this paper,we defined the fuzzy operator Φ_(λ) in a fuzzy ideal approximation space(X,R,I)associated with a fuzzy rough set λ in Sostak sense.Associated with Φ_(λ),there are fuzzy ideal interior and closure operators int_(Φ)^(λ) and cl_(Φ)^(λ),respectively.r-fuzzy separation axioms,r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces.There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces.Lastly,using a fuzzy grill,we will get the same results given during the context.

Interval-Valued Intuitionistic Fuzzy-Rough Sets

This paper combines interval-valued intuitionistic fuzzy sets and rough sets.It studies rougheness in interval-valued intuitionistic fuzzy sets and proposes one kind of interval-valued intuitionistic fuzzy-rough sets models under the equivalence relation in crisp sets.That extends the classical rough set defined by Pawlak.

Rough Sets理论与信任函数理论的比较研究

给出了在 Pawlak粗集代数中信任函数的一种解释 ,并且讨论了信任函数在 Rough Sets上知识的组合规则 ,发现信任函数的综合规则无法用 Rough Sets来表示。

Machine intelligence,rough sets and rough-fuzzy granular computing:uncertainty handling in bio-informatics and Web intelligence

Machine intelligence,is out of the system by the artificial intelligence shown.It is usually achieved by the average computer intelligence.Rough sets and Information Granules in uncertainty management and soft computing and granular computing is widely used in many fields,such as in protein sequence analysis and biobasis determination,TSM and Web service classification Etc.