scholarly journals Representation of Fuzzy Concept Lattices in the Framework of Classical FCA

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Peter Butka ◽  
Jozef Pócs ◽  
Jana Pócsová
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Concept ◽  
Concept Lattices ◽  
Fuzzy Concept Lattice ◽  
Galois Connections ◽  
Fuzzy Concept ◽  
Needed Information

We describe a representation of the fuzzy concept lattices, defined via antitone Galois connections, within the framework of classical Formal Concept Analysis. As it is shown, all needed information is explicitly contained in a given formal fuzzy context and the proposed representation can be obtained without a creation of the corresponding fuzzy concept lattice.

Some Relationships Between Fuzzy Sets, Mathematical Morphology, Rough Sets, F-Transforms, and Formal Concept Analysis

2016 ◽  
Vol 24 (Suppl. 2) ◽  
pp. 1-32 ◽  
Author(s):  
Jamal Atif ◽  
Isabelle Bloch ◽  
Céline Hudelot
Keyword(s):  
Fuzzy Sets ◽  
Mathematical Morphology ◽  
Rough Sets ◽  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Concept ◽  
Fuzzy Concept Lattice ◽  
Fuzzy Concept ◽  
Potential Interest

In this paper we extend some previously established links between the derivation operators used in formal concept analysis and some mathematical morphology operators to fuzzy concept analysis. We also propose to use mathematical morphology to navigate in a fuzzy concept lattice and perform operations on it. Links with other lattice-based for malisms such as rough sets and F-transforms are also established. This paper proposes a discussion and new results on such links and their potential interest.

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.

Using Formal Concept Analysis and Rough Set Constructing the System of Semantic Web

2011 ◽  
Vol 58-60 ◽  
pp. 1664-1670
Author(s):  
Hong Sheng Xu ◽  
Rui Ling Zhang
Keyword(s):  
Semantic Web ◽  
Rough Set ◽  
Formal Concept Analysis ◽  
Rough Set Theory ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Great Promise ◽  
Formal Concept ◽  
Concept Lattices

Formal concept analysis (FCA) is based on a formalization of the philosophical understanding of a concept as a unit of thought constituted by its extent and intent. The rough set philosophy is founded on the assumption that with every object of the universe of discourse we associate some information. This paper deals with approaches to knowledge reduction in generalized consistent decision formal context. Finally, a new system model of semantic web based on FCA and rough set is proposed, which preserve more structural and featural information of concept lattice. In order to obtain the concept lattices with relatively less attributes and objects, we study the reduction of the concept lattices based on FCA and rough set theory. The experimental results indicate that this method has great promise.

Matrix-based reduction approach for one-sided fuzzy three-way concept lattices

2021 ◽  
pp. 1-18
Author(s):  
Chengling Zhang ◽  
Jinjin Li ◽  
Yidong Lin
Keyword(s):  
Mathematical Model ◽  
Knowledge Discovery ◽  
Formal Concept Analysis ◽  
Real Life ◽  
Concept Analysis ◽  
Formal Concept ◽  
Concept Lattices ◽  
Fuzzy Concept ◽  
Granular Matrix ◽  
Reduction Approach

Three-way concept analysis is a mathematical model of the combination of formal concept analysis and three-way decision, and knowledge discovery plays a significant impact on formal fuzzy contexts since such datasets are frequently encountered in real life. In this paper, a novel type of one-sided fuzzy three-way concept lattices is presented in a given formal fuzzy context with its complement, in which a ternary classification is available. In such case, we comprehensively explore the connections between the proposed models and classical fuzzy concept lattices among elements, sets, and orders. Furthermore, approaches to granular matrix-based reductions are investigated, by which granular consistent sets, and granular reducts via discernibility Boolean matrices are tectonically put forward. At last, the demonstrated results are performed by several experiments which enrich the research of three-way concept analysis.

Neutrosophic three-way concept lattice and its application in conflict analysis

2021 ◽  
pp. 1-18
Author(s):  
Han Yang ◽  
Keyun Qin
Keyword(s):  
Data Analysis ◽  
Knowledge Discovery ◽  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Conflict Analysis ◽  
Neutrosophic Set ◽  
Formal Context ◽  
Formal Concept ◽  
Concept Lattices

The theory of three-way concept analysis has been developed into an effective tool for data analysis and knowledge discovery. In this paper, we propose neutrosophic three-way concept lattice by combining neutrosophic set with three-way concept analysis and present an approach for conflict analysis by using neutrosophic three-way concept lattice. Firstly, we propose the notion of neutrosophic formal context, in which the relationships between objects and attributes are expressed by neutrosophic numbers. Three pairs of concept derivation operators are proposed. The basic properties of object-induced and attribute-induced neutrosophic three-way concept lattices are examined. Secondly, we divide the neutrosophic formal context into three classical formal contexts and propose the notions of the candidate neutrosophic three-way concepts and the redundant neutrosophic three-way concepts. Two approaches of constructing object-induced (attribute-induced) neutrosophic three-way concept lattices are presented by using candidate, redundant and original neutrosophic three-way concepts respectively. Finally, we apply the neutrosophic formal concept analysis to the conflict analysis and put forward the corresponding optimal strategy and the calculation method of the alliance.

The Method Research on Data Mining of Concept Lattice

2015 ◽  
Vol 713-715 ◽  
pp. 1970-1973
Author(s):  
Chun Liu ◽  
Dong Xing Wang ◽  
Kun Tan
Keyword(s):  
Machine Learning ◽  
Data Mining ◽  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Basic Theory ◽  
Formal Concept ◽  
Concept Lattices ◽  
Hasse Diagrams ◽  
Basic Concepts

Concept lattice in essence describe the links between objects and attributes,demonstratesthe generalization and specialization of concepts. The corresponding Hasse diagrams realize the visualization of the data. At present, formal concept analysis has been extensively studied and applied to many areas, such asinformation retrieval, machine learning andsoftware engineering. Based on the above reasons, it is necessary to research the methods of latticeconcept of data mining. This paper is divided into three parts; the first part introduces the basic concepts of data mining. The second part introduces the basic theory of concept lattices. The last part focuses on the application of concept in data mining.

The Research of Semantic Web Service Matching Algorithm Based on the Formal Concept Analysis

2013 ◽  
Vol 760-762 ◽  
pp. 1708-1712
Author(s):  
Ying Fang Li ◽  
Ying Jiang Li ◽  
Yan Li ◽  
Yang Bo
Keyword(s):  
Semantic Web ◽  
Web Service ◽  
Formal Concept Analysis ◽  
Service Discovery ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Concept ◽  
Semantic Web Service ◽  
Matching Algorithm ◽  
Service Matching

At present, as the number of web services resources on the network drastically increased, how to quickly and efficiently find the needed services from publishing services has become a problem to resolve. Aiming at the problems of low efficiency in service discovery of traditional web service, the formal concept analysis ( FCA) is introduced into the semantic Web service matching, and a Matching Algorithm based semantic web service is proposed. With considering the concept of limited inheritance,this method introduces the concept of limited inheritance to the semantic similarity calculation based on the concept lattice. It is significant in enhancing the service function matching in practical applications through adjust the calculation.

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.

Browsing Large Concept Lattices through Tree Extraction and Reduction Methods

2013 ◽  
Vol 9 (4) ◽  
pp. 16-34 ◽  
Author(s):  
Cassio Melo ◽  
Bénédicte Le-Grand ◽  
Marie-Aude Aufaure
Keyword(s):  
Fault Tolerance ◽  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Hasse Diagram ◽  
Formal Concept ◽  
Concept Lattices ◽  
Direct Graph ◽  
Concept Clustering ◽  
Reduction Methods ◽  
Tree Extraction

Browsing concept lattices from Formal Concept Analysis (FCA) becomes a problem as the number of concepts can grow significantly with the number of objects and attributes. Interpreting the lattice through direct graph-based visualisation of the Hasse diagram rapidly becomes difficult and more synthetic representations are needed. In this work the authors propose an approach to simplify concept lattices by extracting and visualising trees derived from them. The authors further simplify the browse-able trees with two reduction methods: fault-tolerance and concept clustering.

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