Attribute reduction based on overlap degree and k-nearest-neighbor rough sets in decision information systems

Knowledge reduction is an important issue when dealing with huge amounts of data. Rough set theory provides two fundamental concepts to deal with this special problem: attribute reduction and core, where attribute reduction is the key problem. There are a lot of methods available for attribute reduction, but very little work has been done for attribute reduction for the cases of deleting and modifying. Therefore, in this paper, we introduce a new updating method based on discernibility matrix for attribute reduction for the case of deleting. When a few old objects are deleted from a decision information system, a core and a new attribute reduction can be obtained quickly because it only deletes a few old rows and columns, or inserts a few rows and updates corresponding columns when updating the discernibility matrix.

Attribute reduction is one of the most important research issues in the rough set theory. The purpose of attribute reduction is to find a minimal attribute subset that satisfies some specific criteria, while the minimal attribute subset is called attribute reduct. In this paper, we define a similarity-based attribute reduct based on a clustering perspective. Each decision class is treated as a cluster, and the defined similarity-based attribute reduct can maintain or increase the discriminating ability of different clusters in the case of removing redundant attributes. In view of this, firstly, we define the intra-class similarity for objects in the same decision class and the inter-class similarity for objects between different decision classes. Secondly, we define a similarity-based attribute reduct by maximizing intra-class similarity and minimizing inter-class similarity in the rough set model. Thirdly, by considering the heuristic search strategy, we also design a corresponding reduction method for the proposed attribute reduct. The experimental results indicate that compared with other representative attribute reducts, our proposed attribute reduct can significantly improve the classification performance.

Decision information system based on rough set is an important processing form in data mining. Attribute reduction is one of the most critical issues in rough set theory. Chen et.al. proposed an attribute reduction algorithm for decision information system based on the covering generalized rough sets. In this paper, we first point out that Chen's algorithm applies to the fifth, the sixth and the seventh type of covering generalized rough sets. Then we establish the equivalent relationship between covering and the reflexive and transitive relation. Moreover, we prove that attribute reduction based on covering in this paper is a special case of the one based on general binary relation proposed by Wang et.al. As a result, a new attribute reduction algorithm with lower time complexity is designed. With these discussion, the research provides theoretical and practical significance.

The variable precision rough set (VPRS) model generalizes the Pawlak rough set model with variable parameters. The Bayesian rough set (BRS) model improves the VPRS model with non-parametric modification by using the prior probability as a reference. This paper presents two research results related to rough set model and rough vague sets. One is a modification to the Bayesian rough set model and the other is a modification to rough vague sets. First, the Bayesian rough set model is analyzed and discussed. Second, a modification to this model is proposed and verified. Finally, a modification to rough vague sets is presented and its related properties are discussed..

An incremental approach to attribute reduction from dynamic incomplete decision systems in rough set theory

Rough set is a data evaluation methodology to take care of uncertainty in data. Attribute reduction with rough set goals to achieve a compact and informative attribute set for a given data sets, and incremental mechanism is reasonable selection for attribute reduction in dynamic data sets. This paper focuses on introducing incremental mechanism to develop effective incremental algorithm during the arrival of new attributes in terms of approach of discerning samples. The traditional definition of discernibility matrix is improved first to address fewer samples to be discerned. Based on this improvement, discernible relation is developed for every attribute and utilized to characterize attribute reduction. For dynamic data sets with the dynamically increasing of attributes, an incremental mechanism is introduced to judge and ignore unnecessary new arriving attributes. For necessary new arriving attributes, the original reduct is updated in terms of updating of discernible relations instead of information granular or information entropy. The efficiency and effectiveness of developed incremental algorithm based on this mechanism is demonstrated through experimental comparisons in this paper in terms of running time.

Rough set theory for the interval-valued fuzzy information systems

Rough sets provide a useful tool for data preprocessing during data mining. However, many algorithms related to some problems in rough sets, such as attribute reduction, are greedy ones. Matroids propose a good platform for greedy algorithms. Therefore, it is important to study the combination between rough sets and matroids. In this paper, we investigate rough sets and matroids through their operators, and provide a matroidal method for attribute reduction in information systems. Firstly, we generalize four operators of rough sets to four operators of matroids through the interior, closure, exterior and boundary axioms, respectively. Thus, there are four matroids induced by these four operators of rough sets. Then, we find that these four matroids are the same one, which implies the relationship about operators between rough sets and matroids. Secondly, a relationship about operations between matroids and rough sets is presented according to the induced matroid. Finally, the girth function of matroids is used to compute attribute reduction in information systems.

An improved attribute reduction scheme with covering based rough sets

In the face of the explosive growth in data volume, current technologies have encountered many difficulties in both storage and knowledge discovery processes. Moreover, the quality of data has also deteriorated due to excessive noisy information, which reduces the effectiveness of machine learning models. Therefore, many solutions have been proposed, in which attribute reduction has emerged as an important research direction. Currently, research on attribute reduction has become very active and is primarily focused on the processing of decision tables. In this area, research on attribute reduction based on rough set theory and its extensions is considered a promising direction, which has been yielding many impressive results. To gain a clearer understanding of the attribute reduction research direction, this study will provide an overview of the methods of attribute reduction from their inception to the methods proposed in recent times.

Rough set theory is emerging as a powerful toll for reasoning about data. Attribute reduction is one of important topics in the research on the rough set theory. Heuristic, discernibility matrix and matrix method are three usually methods for designing attribute reduction algorithm in attribute reduction based on rough set. Some researchers use matrix method to design attribute reduction algorithm. The time complexity of the algorithm is O(|C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> |U| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), and the computation of the algorithm is time consuming. To lower the time complexity, it was first proposed a new matrix, and provided an attribute reduction definition based on the new matrix. Then it was proved that the new attribute reduction definition is the same as the old reduction. At last, we used the matrix of attribute to define the significance of attribute, and designed a new attribute reduction algorithm, which time complexity is cut to O(|C||U|)+O(|C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> |U/C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). At the same time, an example was used to illustrate the new algorithm.

Soft rough fuzzy sets and soft fuzzy rough sets

Bayesian Decision theoretic rough set has been invented by the author. In this paper the attribute reduction by the aid of Bayesian decision theoretic rough set has been studied. Lot of other methods are there for attribute reduction such as Variable precision method, probabilistic approach, Bayesian method, Pawlaks rough set method using Boolean function. But with the help of some example it is shown that Bayesian decision theoretic rough set model gives better result than other method. Lastly an example of HIV /AIDS is taken and attribute reduction is done by this new method and various other method. It is shown that this method gives better result than the previously defined methods. By this method the authors get only the reduced attribute age which is the best significant attribute. Though in Pawlak model age sex or age living status are the reduced attribute and variable precision method fails to work here. In this paper attribute reduction is done by the help of discernibility matrix after determining the positive, boundary and negative region. This model is a hybrid model of Bayesian rough set model and decision theory. So this technique gives better result than Bayesian method and decision theoretic rough set method.

As an effective tool for knowledge acquisition, attribute reduction is one of the key issues in rough set theory. In current research, most researchers choose to reduce redundant attributes as many as possible through some attribution reduction algorithms. However, the misclassification cost induced by attribute reduction is ignored. Thus, it is worth studying that how to reduce redundant attributes based on preserving the misclassification cost. Firstly, in this paper, the degree of minimum misclassification is defined. Then, by introducing decision process into variable precision rough set, a new model which is based on minimum misclassification cost with variable precision rough set (VPRS) is proposed. Moreover, based on the minimum misclassification cost, a heuristic attribute reduction algorithm is proposed. Finally, the simulation result shows that a feasible and reliable set of attributes can be obtained with our algorithm. These results further enrich attribute reduction to effectively deal with the uncertain classification problems.

Credit becomes an import issue for community and enterprise development. The development of internet makes available of enterprise credit data, which makes it possible to research enterprise credit evaluation. In this work, we propose an attribute reduction algorithm based on semantic analysis, rough set (RS) theory and conditional entropy. The collection of topic-related words is produced on the basis of semantic analysis and it is considered as the conditional attribute set. Then attribute reduction is actualised based on RS theory and conditional entropy. The method is applied to enterprise and community credit data which is available from the web. Extensive experiments on real-word data show that our method can obtain optimal attribute efficiently.