Attribute Reduction in Object Oriented Concept Lattices Based on Congruence Relations

Attribute reduction is one basic issue in the analysis of information tables. In this paper, the approaches to attribute reduction in formal context based on the object oriented concept lattice are investigated. We first introduce the notions of context matrix and the operations of corresponding column vectors. Then present some judgment theorems for attribute reduction in formal contexts. Based on the judgment theorems, we propose an attribute reduction approach and show concrete reduction algorithm.

The study of concept lattices, property oriented concept lattices and object oriented concept lattices provides complementary conceptual structures, which can be used to search, analyze and extract information from data sets. This paper is devoted to the study of rule acquisition and attribute reduction of formal decision context. Based on object oriented concepts and property oriented concepts, the notions of object oriented decision rules and property oriented decision rules are proposed. By using some equivalence relations on the set of extents of the related conditional concept lattices and decision concept lattices, the rule acquisition methods are presented. The attribute reduction approaches for formal decision context to preserve the object oriented decision rules and property oriented decision rules are put forward by using discernibility attributes.

Object-oriented and property-oriented concept lattices are constructed based on rough set theory. In this paper, a uniform mathematical model-concept granular computing system is first established by mappings on two complete lattices. In this framework, object-oriented and property-oriented concept granular computing systems are introduced for property-oriented and object-oriented concept lattices, respectively. Properties of these two kinds of concept granular computing systems are discussed. And relationships between a concept lattice and a corresponding concept granular computing system are also investigated.

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.

An improved attribute reduction scheme with covering based rough sets

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

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.

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.

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.

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.

Tri-level attribute reduction in rough set theory

Rough set theory and formal concept analysis are two complementary mathematical tools for data analysis. In this paper, based on object oriented concept lattice, we first propose one kind of consistency of conditional concepts and decision concepts. Subsequently, notions of consistent set and reduct set of attributes are introduced, and some judgment theorems for consistent set are presented. Finally, discernibility matrix is employed to determine consistent sets and calculate reduct sets in consistent formal decision contexts.

Attribute reduction plays an important role in rough set theory. It is an important application in data mining. In this paper, we focus on discussing the relation between set covering and attribute reduction in rough set theory. Based on the equivalence between minimal set covering and minimal attribute reduction sets, attribute reduction graph (ARG) is constructed. A novel algorithm to find the minimal attribute reduction sets, which is based on combination of binary discernibility matrix and graph theory is proposed in this paper. This algorithm demonstrates its efficiency and feasibility by an example.

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.

Distance metric learning-based multi-granularity neighborhood rough sets for attribute reduction