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Ju-sheng Mi - One of the best experts on this subject based on the ideXlab platform.
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On the use of cut set for attribute reduction in L-fuzzy concept lattice
2016 International Conference on Machine Learning and Cybernetics (ICMLC), 2016Co-Authors: Leijun Li, Ju-sheng Mi, Mei-zheng LiAbstract:Concept lattice is an effective tool for knowledge discovery and has been applied to many fields successfully. The objects and attributes have clear relations in the classical Formal Context, but there are a lot of fuzzy information in real-life applications. Therefore, it is important to study the fuzzy Formal Context. As we know, the fuzzy set and the classical set can be transformed into each other based on the cut set. Thus, it is believed that the cut set can be used in the research of fuzzy concept lattice. In this paper, a preliminary exploration to use the cut set is carried out. In particular, the cut set is employed to construct the discernibility matrix of L-fuzzy Formal Context and then all the reducts can be obtained via the use of discernibility function. After that, all the attributes are classified into three types by their significances in constructing the L-fuzzy concept lattice. The characteristics of these types of attributes are also analyzed. The obtained results in this paper are beneficial for the research of fuzzy Formal Context based on the cut set in further.
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Attribute reduction based on maximal rules in decision Formal Context
International Journal of Computational Intelligence Systems, 2014Co-Authors: Leijun Li, Ju-sheng MiAbstract:AbstractOne of the key issues in the theory of concept lattices is to extract the useful rules from the decision Formal Context. The maximal rules implicate the others, thus people are interested in them. This paper proposes two new kinds of attribute reduction in the decision Formal Context based on maximal rules. The reducts preserve all the condition extensions and the decision extensions related to the original maximal rules. The internal relationship between the original maximal rules and the maximal rules in the reduced decision Formal Context is derived. The reducts can make the maximal rules more concise and accurate. The mathematical property of the proposed attribute reduction is investigated and we construct the discernibility matrix and function to compute all the reducts. Finally, all the attributes are classified into three types based on the maximal rules. The characteristics of these types of attributes are also analyzed.
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The strong direct product of Formal Contexts
Information Sciences, 2013Co-Authors: Mei-zheng Li, Ju-sheng MiAbstract:The theory of Formal Concept Analysis is used as a knowledge representation mechanism and as a conceptual clustering method. Formal Context is a basic notion in this theory. This paper proposes a kind of Formal Context, called n-Strong-Direct-Product-Formal-Context (n-SDPFC, for short), by the strong direct product of n Formal Contexts. It is found that the new Context is closely related to the n original Formal Contexts in many aspects, for example, the concept lattices, and the implications between attributes, and so on. With the help of Kronecker product of boolean matrices, the main features of an n-SDPFC is given, and the method how to represent a Formal Context with such features by the strong direct product of some small Formal Contexts is brought forward. With this method, the workload for knowledge acquisition in Formal Context will be eased enormously.
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GrC - Research on combined Formal Context
2011 IEEE International Conference on Granular Computing, 2011Co-Authors: Mei-zheng Li, Hong-qiang Yang, Ju-sheng MiAbstract:Currently, there are many ways to generate new Formal Contexts from the original ones. Among these ways, combining Formal Contexts is the simplest one. This paper mainly discusses the attribute characteristics in the composition of two Formal Contexts, which is called the combined Formal Context. It is proved that there exists a strong connection between the attribute characteristics in a combined Context and those in the original Contexts. Besides, some knowledge acquisition rules from the combined Formal Context are obtained by the rules from the original Contexts. Furthermore, the relationships between the irreducible attributes of the combined Context and those of the original Contexts are studied.
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attribute reduction in decision Formal Context based on homomorphism
International Journal of Machine Learning and Cybernetics, 2011Co-Authors: Ju-sheng MiAbstract:Attribute reduction in concept lattices is one of the key problems in the study of concept lattice theory. This paper defines a homomorphism consistent set and provides an approach to attribute reduction of a consistent decision Formal Context based on concept lattices. We also examine the relationship between homomorphism consistent set and attribute consistent set. The method for judging a homomorphism consistent set is simpler than the existing ones.
Wen-xiu Zhang - One of the best experts on this subject based on the ideXlab platform.
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approaches to knowledge reduction in generalized consistent decision Formal Context
Mathematical and Computer Modelling, 2008Co-Authors: Hong Wang, Wen-xiu ZhangAbstract:This paper deals with approaches to knowledge reduction in generalized consistent decision Formal Context. The concept of generalized consistent decision Formal Context is introduced and its equivalent definitions are examined. We suggest a theory of knowledge reduction for generalized consistent decision Formal Context and give the judgement theorems and discernibility matrix. Based on discernibility matrix, we provide the approaches to knowledge reduction in generalized consistent decision Formal Context of concept lattice.
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Generalized attribute reduction in consistent decision Formal Context
2008 International Conference on Machine Learning and Cybernetics, 2008Co-Authors: Hong Wang, Wen-xiu ZhangAbstract:Formal concept analysis, as an effective tool for knowledge discovery, has been successfully applied to various fields. This paper deals with approaches to generalized attribute reduction in consistent decision Formal Context. The concept of generalized attribute reduction in consistent decision Formal Context is first introduced. The judgement theorems and discernibility matrices are established, from which we provide the approaches to generalized attribute reduction in consistent decision Formal Context based on concept lattice.
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Attribute reduction theory of concept lattice based on decision Formal Contexts
Science in China Series F: Information Sciences, 2008Co-Authors: Jianjun Qi, Wen-xiu ZhangAbstract:The theory of concept lattices is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully. One focus of knowledge discovery is knowledge reduction. Based on the reduction theory of classical Formal Context, this paper proposes the definition of decision Formal Context and its reduction theory, which extends the reduction theory of concept lattices. In this paper, strong consistence and weak consistence of decision Formal Context are defined respectively. For strongly consistent decision Formal Context, the judgment theorems of consistent sets are examined, and approaches to reduction are given. For weakly consistent decision Formal Context, implication mapping is defined, and its reduction is studied. Finally, the relation between reducts of weakly consistent decision Formal Context and reducts of implication mapping is discussed.
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Approach to Knowledge Reduction in Formal Context Based on Concept Lattice
2006 International Conference on Machine Learning and Cybernetics, 2006Co-Authors: Hong Wang, Wen-xiu ZhangAbstract:Formal concept analysis of binary relations has proved to be useful in resolve of many problems of theoretical or interest. This paper deals with approach to knowledge reduction in Formal Context based on object oriented concept lattice and attribute oriented concept lattice. The concept of consistent set in Formal Context is first introduced and its equivalent definitions are given. The judgment theorem and discernibility matrix associated with Formal Context reducts are established, from which we can provide the approach to knowledge reduction in Formal Context
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An Approach to Construct Concept Lattices Based on Double Universe Formal Context
2006 International Conference on Machine Learning and Cybernetics, 2006Co-Authors: Wen-xiu ZhangAbstract:In this paper, a double universe Formal Context is constructed based on an information system, and a double universe concept lattice is introduced. Properties of them are discussed. Then a dependence space based on the double universe concept lattice is shown. According to the congruence on the dependence space, a closed set can be obtained, and a new approach to construct the double universe concept lattice is proposed
Jianjun Qi - One of the best experts on this subject based on the ideXlab platform.
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ICDM Workshops - Concept Analysis Based on Granular Formal Contexts
2018 IEEE International Conference on Data Mining Workshops (ICDMW), 2018Co-Authors: Zhen Wang, Jianjun QiAbstract:Formal concept analysis (FCA) is an efficient tool for knowledge discovery and decision making from Formal Contexts. However, in the era of big data, FCA may face some challenges, one of which is that discovering knowledge from a big Formal Context may be hard. To make knowledge discovery from Formal Contexts easier and simpler, this study presents concept analysis based on granular Formal Contexts. First, granular Formal Context is proposed by combining FCA with the hierarchical idea of granular computing (GrC). Then, based on which, the corresponding notions such as granular derivation operators, granular Formal concept, and granular concept lattice are defined. Finally, the connections between classical and granular derivation operators/Formal concepts/concept lattices are presented.
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Concept Analysis Based on Granular Formal Contexts
2018 IEEE International Conference on Data Mining Workshops (ICDMW), 2018Co-Authors: Zhen Wang, Jianjun QiAbstract:Formal concept analysis (FCA) is an efficient tool for knowledge discovery and decision making from Formal Contexts. However, in the era of big data, FCA may face some challenges, one of which is that discovering knowledge from a big Formal Context may be hard. To make knowledge discovery from Formal Contexts easier and simpler, this study presents concept analysis based on granular Formal Contexts. First, granular Formal Context is proposed by combining FCA with the hierarchical idea of granular computing (GrC). Then, based on which, the corresponding notions such as granular derivation operators, granular Formal concept, and granular concept lattice are defined. Finally, the connections between classical and granular derivation operators/Formal concepts/concept lattices are presented.
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Constructing three-way concept lattices based on apposition and subposition of Formal Contexts
Knowledge Based Systems, 2017Co-Authors: Ting Qian, Jianjun QiAbstract:Three-way concept analysis provides a new model to make three-way decisions. Its basic structure can be shown by the three-way concept lattices. Thus, how to construct three-way concept lattices is an important issue in the three-way concept analysis. This paper proposes approaches to create the three-way concept lattices of a given Formal Context. First, we can transform the given Formal Context and its complementary Context into new Formal Contexts which are isomorphic to the given Formal Context and its complementary Context respectively. And then, Type I-combinatorial Context and Type II-combinatorial Context are defined, which are apposition and subposition of these new Formal Contexts, respectively. Second, we prove that the concept lattice of Type I-combinatorial Context is isomorphic to object-induced three-way concept lattice and the concept lattice of Type II-combinatorial Context is isomorphic to attribute-induced three-way concept lattice of the given Formal Context. And then, the approaches of creating the three-way concept lattices are proposed based on the concept lattices of Type I-combinatorial Context and Type I-combinatorial Context. Finally, we give the corresponding algorithms of constructing three-way concept lattices based on the above approaches and conduct several experiments to illustrate the efficient of proposed algorithms.
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Decomposition methods of Formal Contexts to construct concept lattices
International Journal of Machine Learning and Cybernetics, 2016Co-Authors: Ting Qian, Jianjun QiAbstract:As an important tool for data analysis and knowledge processing, Formal concept analysis has been applied to many fields. In this paper, we introduce a decomposition method of a Formal Context to construct its corresponding concept lattice, which answers an open problem to some extent that how this decomposition method of a Context translates into a decomposition method of its corresponding concept lattice. Firstly, based on subContext, closed relation and pairwise noninclusion covering on the attribute set, we obtain the decomposition theory of a Formal Context, and then we provide the method and algorithm of constructing the corresponding concept lattice by using this decomposition theory. Moreover, we consider the similar decomposition theory and method of a Formal Context from the object set. Finally, we make another decomposition of a Formal Context by combining the above two results.
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Attribute reduction theory of concept lattice based on decision Formal Contexts
Science in China Series F: Information Sciences, 2008Co-Authors: Jianjun Qi, Wen-xiu ZhangAbstract:The theory of concept lattices is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully. One focus of knowledge discovery is knowledge reduction. Based on the reduction theory of classical Formal Context, this paper proposes the definition of decision Formal Context and its reduction theory, which extends the reduction theory of concept lattices. In this paper, strong consistence and weak consistence of decision Formal Context are defined respectively. For strongly consistent decision Formal Context, the judgment theorems of consistent sets are examined, and approaches to reduction are given. For weakly consistent decision Formal Context, implication mapping is defined, and its reduction is studied. Finally, the relation between reducts of weakly consistent decision Formal Context and reducts of implication mapping is discussed.
Tong-jun Li - One of the best experts on this subject based on the ideXlab platform.
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Attribute Reduction in Formal Contexts: A Covering Rough Set Approach
Fundamenta Informaticae, 2020Co-Authors: Tong-jun Li, Wei-zhi WuAbstract:This paper proposes an approach to attribute reduction in Formal Contexts via a covering rough set theory. The notions of reducible attributes and irreducible attributes of a Formal Context are first introduced and their properties are examined. Judgment theorems for determining all attribute reducts in the Formal Context are then obtained. According to the attribute reducts, all attributes of the Formal Context are further classified into three types and the characteristic of each type is characterized by the properties of irreducible classes of the Formal Context. Finally, by using the discernibility attribute sets, a method of distinguishing the reducible attributes and the irreducible attributes in Formal Contexts is presented.
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GrC - Granule structures in Formal Contexts from covering rough set aspect
2012 IEEE International Conference on Granular Computing, 2012Co-Authors: Tong-jun LiAbstract:Formal concept analysis and covering rough set theory are two important mathematical tools for knowledge representation and knowledge discovery. Formal Context is common framework of this two theories. The set of all extents of al object concepts of a Formal Context is a basic granulation of the object set, by which many compound granules can be generated. This paper focuses on the granular comuting based on the basic granulation. With respect to Formal concept analysis and covering rough set theory, the granular structures in Formal Context are examined in detail.
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ICMLC - A type of attribute reduction of Formal Contexts
2012 International Conference on Machine Learning and Cybernetics, 2012Co-Authors: Tong-jun LiAbstract:Formal concept analysis is an important mathematical tool for knowledge representation and knowledge discovery. Attribute reduction is a crucial research issue attracting many attention of researchers on Formal concept analysis. This paper proposes one type of attribute reduction of Formal Context, in which all join-irreducible elements of a concept lattice are preserved. The join-irreducible elements of a Formal Context and their properties are first discussed. Then, the concept of join-irreducible-attribute reduction of Formal Context is then introduced. Finally, an equivalence condition of join-irreducible-consistent attribute set is given.
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Granule structures in Formal Contexts from covering rough set aspect
2012 IEEE International Conference on Granular Computing, 2012Co-Authors: Tong-jun LiAbstract:Formal concept analysis and covering rough set theory are two important mathematical tools for knowledge representation and knowledge discovery. Formal Context is common framework of this two theories. The set of all extents of al object concepts of a Formal Context is a basic granulation of the object set, by which many compound granules can be generated. This paper focuses on the granular comuting based on the basic granulation. With respect to Formal concept analysis and covering rough set theory, the granular structures in Formal Context are examined in detail.
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RSKT - Dependence and algebraic structure of Formal Contexts
Rough Sets and Knowledge Technology, 2011Co-Authors: Tong-jun Li, Ying-xue Wu, Xiaoping YangAbstract:Formal concept analysis is an important approach of knowledge representation and data analysis. This paper focus on the dependence among Formal Contexts with common object set. A partial order relation among Formal Contexts is first introduced and its properties are examined. Subsequently, The notion of independence of a Formal Context is proposed by which attribute reduction of Formal Context is investigated. An useful conclusion is obtained, that is, all Formal Contexts with common object set form a lattice.
Mei-zheng Li - One of the best experts on this subject based on the ideXlab platform.
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On the use of cut set for attribute reduction in L-fuzzy concept lattice
2016 International Conference on Machine Learning and Cybernetics (ICMLC), 2016Co-Authors: Leijun Li, Ju-sheng Mi, Mei-zheng LiAbstract:Concept lattice is an effective tool for knowledge discovery and has been applied to many fields successfully. The objects and attributes have clear relations in the classical Formal Context, but there are a lot of fuzzy information in real-life applications. Therefore, it is important to study the fuzzy Formal Context. As we know, the fuzzy set and the classical set can be transformed into each other based on the cut set. Thus, it is believed that the cut set can be used in the research of fuzzy concept lattice. In this paper, a preliminary exploration to use the cut set is carried out. In particular, the cut set is employed to construct the discernibility matrix of L-fuzzy Formal Context and then all the reducts can be obtained via the use of discernibility function. After that, all the attributes are classified into three types by their significances in constructing the L-fuzzy concept lattice. The characteristics of these types of attributes are also analyzed. The obtained results in this paper are beneficial for the research of fuzzy Formal Context based on the cut set in further.
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The strong direct product of Formal Contexts
Information Sciences, 2013Co-Authors: Mei-zheng Li, Ju-sheng MiAbstract:The theory of Formal Concept Analysis is used as a knowledge representation mechanism and as a conceptual clustering method. Formal Context is a basic notion in this theory. This paper proposes a kind of Formal Context, called n-Strong-Direct-Product-Formal-Context (n-SDPFC, for short), by the strong direct product of n Formal Contexts. It is found that the new Context is closely related to the n original Formal Contexts in many aspects, for example, the concept lattices, and the implications between attributes, and so on. With the help of Kronecker product of boolean matrices, the main features of an n-SDPFC is given, and the method how to represent a Formal Context with such features by the strong direct product of some small Formal Contexts is brought forward. With this method, the workload for knowledge acquisition in Formal Context will be eased enormously.
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GrC - Research on combined Formal Context
2011 IEEE International Conference on Granular Computing, 2011Co-Authors: Mei-zheng Li, Hong-qiang Yang, Ju-sheng MiAbstract:Currently, there are many ways to generate new Formal Contexts from the original ones. Among these ways, combining Formal Contexts is the simplest one. This paper mainly discusses the attribute characteristics in the composition of two Formal Contexts, which is called the combined Formal Context. It is proved that there exists a strong connection between the attribute characteristics in a combined Context and those in the original Contexts. Besides, some knowledge acquisition rules from the combined Formal Context are obtained by the rules from the original Contexts. Furthermore, the relationships between the irreducible attributes of the combined Context and those of the original Contexts are studied.
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Attribute reduction in fuzzy decision Formal Contexts
2011 International Conference on Machine Learning and Cybernetics, 2011Co-Authors: Mei-zheng Li, Ju-sheng MiAbstract:The classical concept lattices express the precise relation between object sets and attribute sets, but fuzzy concept lattices express the uncertain relation between object sets and attribute sets. Therefore, it is important to study hierarchy fuzzy knowledge from a fuzzy Formal Context. In this paper, a kind of fuzzy decision Formal Context is proposed and (α, β) reduct based on this fuzzy decision Formal Context is defined. Furthermore, we propose a method to judge attribute consistent sets and reducts in fuzzy decision Formal Contexts. Finally, a Boolean method is also formulated to attribute reduction in fuzzy decision Formal Context from the view of the discernibility matrix.
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ICMLC - Attribute reduction in fuzzy decision Formal Contexts
2011 International Conference on Machine Learning and Cybernetics, 2011Co-Authors: Mei-zheng Li, Ju-sheng MiAbstract:The classical concept lattices express the precise relation between object sets and attribute sets, but fuzzy concept lattices express the uncertain relation between object sets and attribute sets. Therefore, it is important to study hierarchy fuzzy knowledge from a fuzzy Formal Context. In this paper, a kind of fuzzy decision Formal Context is proposed and (α, β) reduct based on this fuzzy decision Formal Context is defined. Furthermore, we propose a method to judge attribute consistent sets and reducts in fuzzy decision Formal Contexts. Finally, a Boolean method is also formulated to attribute reduction in fuzzy decision Formal Context from the view of the discernibility matrix.
