Attribute Reduction of Formal Context Based on Concept Lattice

2009 ◽  
Author(s):  
Yue-jin Lv ◽  
Hong-mei Liu ◽  
Jin-hai Li
Keyword(s):  
Concept Lattice ◽  
Attribute Reduction ◽  
Formal Context

scholarly journals Attribute Reduction Based on Property Pictorial Diagram

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.

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

Entropy ◽  
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.

ATTRIBUTE REDUCTION OF CONCEPT LATTICE BASED ON IRREDUCIBLE ELEMENTS

2013 ◽  
Vol 11 (06) ◽  
pp. 1350046 ◽  
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.

scholarly journals A Web Page Clustering Method Based on Formal Concept Analysis

Information ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 228 ◽  
Author(s):  
Zuping Zhang ◽  
Jing Zhao ◽  
Xiping Yan
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Web Pages ◽  
Web Page ◽  
Data Links ◽  
Web Page Clustering ◽  
The Web

Web page clustering is an important technology for sorting network resources. By extraction and clustering based on the similarity of the Web page, a large amount of information on a Web page can be organized effectively. In this paper, after describing the extraction of Web feature words, calculation methods for the weighting of feature words are studied deeply. Taking Web pages as objects and Web feature words as attributes, a formal context is constructed for using formal concept analysis. An algorithm for constructing a concept lattice based on cross data links was proposed and was successfully applied. This method can be used to cluster the Web pages using the concept lattice hierarchy. Experimental results indicate that the proposed algorithm is better than previous competitors with regard to time consumption and the clustering effect.

scholarly journals Attribute Extended Algorithm of Lattice-Valued Concept Lattice Based on Congener Formal Context

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Li Yang ◽  
Yang Xu
Keyword(s):  
Parallel Processing ◽  
Distributed Storage ◽  
Concept Lattice ◽  
Research Work ◽  
Sufficient Conditions ◽  
Formal Context ◽  
Concept Lattices ◽  
Lattice Implication Algebra ◽  
Implication Algebra ◽  
Necessary And Sufficient

This paper is the continuation of our research work about lattice-valued concept lattice based on lattice implication algebra. For a better application of lattice-valued concept lattice into data distributed storage and parallel processing, it is necessary to research attribute extended algorithm based on congener formal context. The definitions of attribute extended formal context and congener formal context are proposed. On condition that the extent set stays invariable when the new attribute is increased, the necessary and sufficient conditions of forming attribute values are researched. Based on these conditions, the algorithms of generating lattice-valued congener formal context and establishing concept lattice are given, by which we can provide a useful basis for union algorithm and constructing algorithm of lattice-valued concept lattices in distributed and parallel system.

The construction of multi-granularity concept lattices

2020 ◽  
Vol 39 (3) ◽  
pp. 2783-2790
Author(s):  
Qian Hu ◽  
Ke-Yun Qin
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Mutual Transformation ◽  
Concept Lattices ◽  
Construction Methods ◽  
Formal Concepts ◽  
Transformation Methods

The construction of concept lattices is an important research topic in formal concept analysis. Inspired by multi-granularity rough sets, multi-granularity formal concept analysis has become a new hot research issue. This paper mainly studies the construction methods of concept lattices in multi-granularity formal context. The relationships between concept forming operators under different granularity are discussed. The mutual transformation methods of formal concepts under different granularity are presented. In addition, the approaches of obtaining coarse-granularity concept lattice by fine-granularity concept lattice and fine-granularity concept lattice by coarse-granularity concept lattice are examined. The related algorithms for generating concept lattices are proposed. The practicability of the method is illustrated by an example.

scholarly journals A New Rapid Incremental Algorithm for Constructing Concept Lattices

Information ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 78 ◽  
Author(s):  
Jingpu Zhang ◽  
Ronghui Liu ◽  
Ligeng Zou ◽  
Licheng Zeng
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Incremental Algorithm ◽  
Formal Context ◽  
Formal Concept ◽  
Concept Lattices ◽  
Covering Relation ◽  
Canonical Generator ◽  
Lattice Construction ◽  
Time And Space Complexity

Formal concept analysis has proven to be a very effective method for data analysis and rule extraction, but how to build formal concept lattices is a difficult and hot topic. In this paper, an efficient and rapid incremental concept lattice construction algorithm is proposed. The algorithm, named FastAddExtent, is seen as a modification of AddIntent in which we improve two fundamental procedures, including fixing the covering relation and searching the canonical generator. The proposed algorithm can locate the desired concept quickly by adding data fields to every concept. The algorithm is depicted in detail, using a formal context to show how the new algorithm works and discussing time and space complexity issues. We also present an experimental evaluation of its performance and comparison with AddExtent. Experimental results show that the FastAddExtent algorithm can improve efficiency compared with the primitive AddExtent algorithm.

scholarly journals Attribute Reduction in Soft Contexts Based on Soft Sets and Its Application to Formal Contexts

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 689
Author(s):  
Won Keun Min
Keyword(s):  
Attribute Reduction ◽  
Extraction Process ◽  
Formal Context ◽  
Soft Sets ◽  
Step Method ◽  
The Relationship

We introduce the notion of the reduct of soft contexts, which is a special notion of a consistent set for soft contexts. Then, we study its properties and show that this notion is well explained by the two classes, 1 0 and 2 0 , of independent attributes. In particular, we describe in detail how to extract a reduct from a given consistent set. Then, based on this extraction process, we propose a six-step method for constructing a reduct from a given consistent set. Additionally, to apply this method to formal contexts, we examine the relationship between the reducts of a given formal context and the reducts of the associated soft context. We finally illustrate the process of obtaining reducts in a formal context using this relationship and the six-step method using an example.

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