Congxin Wu

Neighborhood rough set based heterogeneous feature subset selection

Feature subset selection is viewed as an important preprocessing step for pattern recognition, machine learning and data mining. Most of researches are focused on dealing with homogeneous feature selection, namely, numerical or categorical features. In this paper, we introduce a neighborhood rough set model to deal with the problem of heterogeneous feature subset selection. As the classical rough set model can just be used to evaluate categorical features, we generalize this model with neighborhood relations and introduce a neighborhood rough set model. The proposed model will degrade to the classical one if we specify the size of neighborhood zero. The neighborhood model is used to reduce numerical and categorical features by assigning different thresholds for different kinds of attributes. In this model the sizes of the neighborhood lower and upper approximations of decisions reflect the discriminating capability of feature subsets. The size of lower approximation is computed as the dependency between decision and condition attributes. We use the neighborhood dependency to evaluate the significance of a subset of heterogeneous features and construct forward feature subset selection algorithms. The proposed algorithms are compared with some classical techniques. Experimental results show that the neighborhood model based method is more flexible to deal with heterogeneous data.

A systematic study on attribute reduction with rough sets based on general binary relations

Attribute reduction is considered as an important preprocessing step for pattern recognition, machine learning, and data mining. This paper provides a systematic study on attribute reduction with rough sets based on general binary relations. We define a relation information system, a consistent relation decision system, and a relation decision system and their attribute reductions. Furthermore, we present a judgment theorem and a discernibility matrix associated with attribute reduction in each type of system; based on the discernibility matrix, we can compute all the reducts. Finally, the experimental results with UCI data sets show that the proposed reduction methods are an effective technique to deal with complex data sets.

Fuzzy rough set based attribute reduction for information systems with fuzzy decisions

Fuzzy rough set is a generalization of crisp rough set to deal with data sets with real value attributes. A primary use of fuzzy rough set theory is to perform attribute reduction for decision systems with numerical conditional attribute values and crisp (symbolic) decision attributes. In this paper we define inconsistent fuzzy decision system and their reductions, and develop discernibility matrix-based algorithms to find reducts. Finally, two heuristic algorithms are developed and comparison study is provided with the existing algorithms of attribute reduction with fuzzy rough sets. The proposed method in this paper can deal with decision systems with numerical conditional attribute values and fuzzy decision attributes rather than crisp ones. Experimental results imply that our algorithm of attribute reduction with general fuzzy rough sets is feasible and valid.

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.

Neighborhood based sample and feature selection for SVM classification learning

Support vector machines (SVMs) are a class of popular classification algorithms for their high generalization ability. However, it is time-consuming to train SVMs with a large set of learning samples. Improving learning efficiency is one of most important research tasks on SVMs. It is known that although there are many candidate training samples in some learning tasks, only the samples near decision boundary which are called support vectors have impact on the optimal classification hyper-planes. Finding these samples and training SVMs with them will greatly decrease training time and space complexity. Based on the observation, we introduce neighborhood based rough set model to search boundary samples. Using the model, we firstly divide sample spaces into three subsets: positive region, boundary and noise. Furthermore, we partition the input features into four subsets: strongly relevant features, weakly relevant and indispensable features, weakly relevant and superfluous features, and irrelevant features. Then we train SVMs only with the boundary samples in the relevant and indispensable feature subspaces, thus feature and sample selection is simultaneously conducted with the proposed model. A set of experimental results show the model can select very few features and samples for training; in the mean time the classification performances are preserved or even improved.

Some properties of relation information systems under homomorphisms

An information system is one of the most important mathematical models in the field of artificial intelligence. The concept of homomorphism is very useful for studying the communication between two information systems. In this work, some properties of relation information systems under homomorphisms are investigated, and it is proved that the reductions of the original system and image system are equivalent to each other under the condition of homomorphism.

Communication Between Information Systems Using Fuzzy Rough Sets

Communication between information systems is a basic problem in granular computing, and the concept of homomorphism is a useful mathematical tool to study this problem. In this paper, some properties of communication between information systems based on fuzzy rough sets are investigated. The concepts of fuzzy relation mappings between universes are first proposed in order to construct a fuzzy relation of one universe according to the given fuzzy relation on the other universe. The main properties of the mappings are studied. The notions of homomorphism of information systems based on fuzzy rough sets are then proposed, and it is proved that properties of relation operations in the original information system and structural features of the system, such as approximations of arbitrary fuzzy sets and attribute reductions, are guaranteed in its image system under the condition of homomorphism.

On the triangle inequalities in fuzzy metric spaces

This paper presents level forms of the triangle inequalities in fuzzy metric spaces (X,d,L,R). To aid discussion, a fuzzy pre-metric condition is introduced. It is first pointed out that under the fuzzy pre-metric condition the first triangle inequality is always equivalent to its level form. The second triangle inequality is equivalent to one level form when R is right continuous, and to another level form also when further conditions are imposed on R. In a fuzzy metric space, the level form of the first triangle inequality and one of the level forms of the second triangle inequality are always valid. The other level form of the second triangle inequality holds for all but at most countable @a@?[0,1). Finally, a fixed point theorem for fuzzy metric spaces is derived as an application of the preceding results.

Fuzzy preference relation rough sets

Preference analysis is a class of important tasks in multi-criteria decision making. The classical rough set theory was generalized to deal with preference analysis by replacing equivalence relations with dominance relation. However, crisp preference relations can not reflect the fuzziness in criteria. In this paper, we introduce the logsig function to extract fuzzy preference relations from samples characterized with numerical attributes. Then we integrate fuzzy preference relations with an improved fuzzy rough set model and develop a fuzzy preference rough set model. We generalize the dependency used in classical rough sets and fuzzy rough sets to compute the relevance between the criteria and decision. The proposed model is used to analyze a fuzzy preference data. It shows the effectiveness of the proposed model.

A New Kind of Fuzzy Riemann-Stieltjes Integral

In this paper, we define a new kind of fuzzy Riemann-Stieltjes integral of fuzzy-number-valued functions directly; discuss properties of the integral, present a necessary and sufficient condition of integrability and obtain an existence theorem