Attribute Reduction Based on Property Pictorial Diagram

The Scientific World JOURNAL ◽

10.1155/2014/109706 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9

Author(s):

Qing Wan ◽

Ling Wei

Keyword(s):

Lattice Structure ◽

Concept Lattice ◽

Attribute Reduction ◽

Object Oriented ◽

Formal Context ◽

Reduction Approach

This paper mainly studies attribute reduction which keeps the lattice structure in formal contexts based on the property pictorial diagram. Firstly, the property pictorial diagram of a formal context is defined. Based on such diagram, an attribute reduction approach of concept lattice is achieved. Then, through the relation between an original formal context and its complementary context, an attribute reduct of complementary context concept lattice is obtained, which is also based on the property pictorial diagram of the original formal context. Finally, attribute reducts in property oriented concept lattice and object oriented concept lattice can be acquired by the relations of attribute reduction between these two lattices and concept lattice of complementary context. In addition, a detailed illustrative example is presented.

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A Novel Attribute Reduction Approach Based on the Object Oriented Concept Lattice

Rough Sets and Knowledge Technology - Lecture Notes in Computer Science ◽

10.1007/978-3-642-24425-4_12 ◽

2011 ◽

pp. 71-80

Author(s):

Mingwen Shao ◽

Li Guo ◽

Lan Li

Keyword(s):

Concept Lattice ◽

Attribute Reduction ◽

Object Oriented ◽

Reduction Approach

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Constructing Domain Ontology Based on Fuzzy Set and Concept Lattice

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.63-64.715 ◽

2011 ◽

Vol 63-64 ◽

pp. 715-718

Author(s):

Ting Zhong Wang ◽

Hong Sheng Xu

Keyword(s):

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Lattice Structure ◽

Concept Lattice ◽

Formal Context ◽

Formal Concept ◽

Cpu Time ◽

Analysis Theory ◽

Formal Concepts

The major content in FCA is to extract formal concepts and connections between them from data in form of formal context so as to form a lattice structure of formal concepts. Fuzzy set theory and fuzzy logic are acknowledged as an appropriate formalism for capturing imprecise and vague knowledge. The paper offers a methodology for building ontology for knowledge sharing and reusing based on fuzzy concept lattices union. This paper makes up these defects by applying formal concept analysis theory and fuzzy sets to construct concept hierarchies of ontology, and the experiments shows the CPU Time in the attribute numbers, indicating that FFCA is superior to FCA in building the ontology of semantic web.

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Knowledge Representation Using Formal Concept Analysis

Global Trends in Intelligent Computing Research and Development - Advances in Computational Intelligence and Robotics ◽

10.4018/978-1-4666-4936-1.ch011 ◽

2014 ◽

pp. 306-336 ◽

Cited By ~ 18

Author(s):

Ch. Aswani Kumar ◽

Prem Kumar Singh

Keyword(s):

Formal Concept Analysis ◽

Lattice Structure ◽

Concept Lattice ◽

Concept Analysis ◽

Formal Context ◽

Formal Concept ◽

Mathematical Framework ◽

Formal Concepts ◽

Conceptual Data ◽

The Relationship

Introduced by Rudolf Wille in the mid-80s, Formal Concept Analysis (FCA) is a mathematical framework that offers conceptual data analysis and knowledge discovery. FCA analyzes the data, which is represented in the form of a formal context, that describe the relationship between a particular set of objects and a particular set of attributes. From the formal context, FCA produces hierarchically ordered clusters called formal concepts and the basis of attribute dependencies, called attribute implications. All the concepts of a formal context form a hierarchical complete lattice structure called concept lattice that reflects the relationship of generalization and specialization among concepts. Several algorithms are proposed in the literature to extract the formal concepts from a given context. The objective of this chapter is to analyze, demonstrate, and compare a few standard algorithms that extract the formal concepts. For each algorithm, the analysis considers the functionality, output, complexity, delay time, exploration type, and data structures involved.

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Attribute Reduction of Formal Context Based on Concept Lattice

2009 Sixth International Conference on Fuzzy Systems and Knowledge Discovery ◽

10.1109/fskd.2009.153 ◽

2009 ◽

Cited By ~ 1

Author(s):

Yue-jin Lv ◽

Hong-mei Liu ◽

Jin-hai Li

Keyword(s):

Concept Lattice ◽

Attribute Reduction ◽

Formal Context

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An Incremental Attribute Reduction Approach with Concept Lattice for ALDD

2010 International Conference on Intelligent Computation Technology and Automation ◽

10.1109/icicta.2010.844 ◽

2010 ◽

Author(s):

Hong-chun Yuan ◽

Yan-hua Wang ◽

De-xing Wang

Keyword(s):

Concept Lattice ◽

Attribute Reduction ◽

Reduction Approach

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The Method of Data Analysis in Intuitionistic Fuzzy Generalized Consistent Decision Formal Context

Entropy ◽

10.3390/e21030262 ◽

2019 ◽

Vol 21 (3) ◽

pp. 262

Author(s):

Binbin Sang ◽

Binghan Long ◽

Jinzhong Pang ◽

Weihua Xu

Keyword(s):

Data Analysis ◽

Lattice Theory ◽

Fuzzy Theory ◽

Concept Lattice ◽

Attribute Reduction ◽

Formal Context ◽

Intuitionistic Fuzzy ◽

Decision Formal Context ◽

Intuitionistic Fuzzy Theory

Concept lattice has been successfully applied to various fields as an effective tool for data analysis and knowledge discovery, with attribute reduction being the key problem. This paper combines the intuitionistic fuzzy theory with the concept lattice theory and proposes one kind of concept lattice in intuitionistic fuzzy generalized consistent decision formal context. Furthermore, an approach to attribute a reduction in the discernibility matrix is proposed and investigated, making the discovery of implicit knowledge easier and the representation simpler in the data system and perfecting the theory of concept lattice. Moreover, this paper studies, in detail, the algorithms and case study of data analysis in the intuitionistic fuzzy generalized consistent decision formal context. The potential value of the method to deal with information discussed in this paper, especially the value of forecasting and decision-making, is expected in future.

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ATTRIBUTE REDUCTION OF CONCEPT LATTICE BASED ON IRREDUCIBLE ELEMENTS

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s021969131350046x ◽

2013 ◽

Vol 11 (06) ◽

pp. 1350046 ◽

Cited By ~ 3

Author(s):

TONG-JUN LI ◽

MING-ZHI LI ◽

YU GAO

Keyword(s):

Formal Concept Analysis ◽

Concept Lattice ◽

Attribute Reduction ◽

Concept Analysis ◽

Formal Context ◽

Formal Concept ◽

Irreducible Elements

Attribute reduction of formal context is a crucial reseach issue in formal concept analysis. In this paper, based on the meet-irreducible elements and join-irreducible elements of concept lattice, two kinds of attribute reductions of formal context are proposed, which are called MI-attribute reduction and JI-attribute reduction. Subsequently, we discuss the relationships among them and two existing attribute reductions of formal context, lattice-based attribute reduction and granular reduction. Consequently, we find that the MI-attribute reduction and lattice-based attribute reduction are identical. For JI-attribute reduction, the judgement theorems of JI-consistent attribute sets are obtained. Finally, by using the discernibility attribute sets, a method of computing all JI-attribute reducts of a formal context is presented.

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The Feature Description of Formal Context Based on the Relationships among Concept Lattices

Entropy ◽

10.3390/e23111397 ◽

2021 ◽

Vol 23 (11) ◽

pp. 1397

Author(s):

Ting Qian ◽

Yongwei Yang ◽

Xiaoli He

Keyword(s):

Concept Lattice ◽

Object Oriented ◽

Concept Analysis ◽

Formal Context ◽

Formal Concept ◽

Type I ◽

Type Ii ◽

Concept Lattices ◽

Feature Description ◽

The Relationship

Three-way concept analysis (3WCA) is extended research of formal concept analysis (FCA) by combining three-way decision. The three-way object oriented concept lattice (OEOL) is one of the important data structures which integrates rough set, concept lattice and three-way decision in 3WCA. In the paper, we investigate the characteristics of formal context based on the isomorphic relationship among the kinds of concept lattices with OEOL. Firstly, II-dual intersectable attributes and II-dual intersectable context are proposed and the relationship between the type I-dual intersectable context(dual intersectable context) and the type II-dual intersectable context are studied. In addition, the relationship among the kinds of concept lattices with OEOL are studied when the formal context is both I-dual intersectable context and II-dual intersectable context. Finally, the inverse problems of the above conclusions are discussed and the following two conclusions are obtained: (1) the formal context is the type II-dual intersectable context, when the object oriented concept lattice and OEOL are isomorphic. (2) In addition, the formal context is the type I-dual intersectable context, when the concept lattice and OEOL are anti-isomorphic.

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