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 Three-Way Concept Analysis for Incomplete Formal Contexts

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Huilai Zhi ◽  
Hao Chao
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Binary Relations ◽  
Formal Concepts ◽  
Target Set ◽  
The Relationship ◽  
Negative Attributes

Recently, incomplete formal contexts have received more and more attention from the communities of formal concept analysis. Different from a complete context where the binary relations between all the objects and attribute are known, an incomplete formal context has at least a pair of object and attribute with a completely unknown binary relation. Partially known formal concepts use interval sets to indicate the incompleteness. Three-way formal concept analysis is capable of characterizing a target set by combining positive and negative attributes. However, how to describe target set, by pointing out what attributes it has with certainty and what attributes it has with possibility and what attributes it does not has with certainty and what attributes it does not has with possibility, is still an open problem. This paper combines the ideas of three-way formal concept analysis and partially known formal concepts and presents a framework of approximate three-way concept analysis. At first, approximate object-induced and attribute-induced three-way concept lattices are introduced, respectively. And then, the relationship between approximate three-way concept lattice and classical three-way concept lattice are investigated. Finally, examples are presented to demonstrate and verify the obtained results.

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.

Knowledge Representation Using Formal Concept Analysis

2014 ◽  
pp. 306-336 ◽  
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.

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.

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 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 Deep First Formal Concept Search

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Tao Zhang ◽  
Hui Li ◽  
Wenxue Hong ◽  
Xiamei Yuan ◽  
Xinyu Wei
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
End Points ◽  
Depth First Search ◽  
Visualization Analysis ◽  
Main Challenge ◽  
Formal Concepts ◽  
Exponential Complexity

The calculation of formal concepts is a very important part in the theory of formal concept analysis (FCA); however, within the framework of FCA, computing all formal concepts is the main challenge because of its exponential complexity and difficulty in visualizing the calculating process. With the basic idea of Depth First Search, this paper presents a visualization algorithm by the attribute topology of formal context. Limited by the constraints and calculation rules, all concepts are achieved by the visualization global formal concepts searching, based on the topology degenerated with the fixed start and end points, without repetition and omission. This method makes the calculation of formal concepts precise and easy to operate and reflects the integrity of the algorithm, which enables it to be suitable for visualization analysis.

The Method of Discover the Attributes' Sequences of Objects in the Formal Context

2013 ◽  
Vol 427-429 ◽  
pp. 2536-2539
Author(s):  
Xue Song Dai ◽  
Yuan Ma ◽  
Wen Xue Hong
Keyword(s):  
Equivalence Relation ◽  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Analysis Method ◽  
Analysis Theory

Formal context is one of the research contents of formal concept analysis theory. In concept lattice, the attributes of the object are equivalent and there is no hierarchy. Facing to this problem, the equivalence relation which is on the attributes' set is defined and the corresponding σ operation is proposed. On this basis, the structure method of attribute hierarchical diagram is presented and attributes' sequences of associated objects are obtained. This conclusion enriches and extends the analysis method of the formal context.

CHARACTERIZING TREES IN CONCEPT LATTICES

2008 ◽  
Vol 16 (supp01) ◽  
pp. 1-15 ◽  
Author(s):  
RADIM BĚLOHLÁVEK ◽  
BERNARD DE BAETS ◽  
JAN OUTRATA ◽  
VILEM VYCHODIL
Keyword(s):  
Formal Concept Analysis ◽  
Input Data ◽  
Concept Lattice ◽  
Sufficient Conditions ◽  
Formal Concept ◽  
Clustering Methods ◽  
Concept Lattices ◽  
Classification Schemes ◽  
Formal Concepts ◽  
Necessary And Sufficient

Concept lattices are systems of conceptual clusters, called formal concepts, which are partially ordered by the subconcept/superconcept relationship. Concept lattices are basic structures used in formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree. On the other hand, tree-like classification schemes are appealing and are produced by several clustering methods. In this paper, we present necessary and sufficient conditions on input data for the output concept lattice to form a tree after one removes its least element. We present these conditions for input data with yes/no attributes as well as for input data with fuzzy attributes. In addition, we show how Lindig's algorithm for computing concept lattices gets simplified when applied to input data for which the associated concept lattice is a tree after removing the least element. The paper also contains illustrative examples.

scholarly journals Detection Of Maximal Balanced Clique In Signed Networks Based On Improved Three-Way Concept Lattice and Modified Formal Concept Analysis

2021 ◽  
Author(s):  
Yixuan Yang ◽  
Doo-Soon Park ◽  
Fei Hao ◽  
Sony Peng ◽  
Min-Pyo Hong ◽  
...  
Keyword(s):  
Social Network ◽  
Formal Concept Analysis ◽  
Industrial Revolution ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Signed Networks ◽  
Social Network Structure ◽  
Real World Datasets

Abstract In the era of artificial intelligence including the fourth industrial revolution, social networks analyzing is a significant topic in big data analysis. Clique detection is a state-of-the-art technique in social network structure mining, which is widely used in a particular social network like signed network. There are positive and negative relationships in signed networks which detect not only cliques or maximal cliques but also maximal balanced cliques.In this paper, two algorithms have been addressed to the problems. First, we modify three-way concept lattice algorithm using a modified formal context and supplement formal context to obtain an object-induced three-way concept lattice (OE-concept) to detect the maximal balanced cliques. Second, in order to improve the cost of memory and efficiency, we modify formal concept analysis algorithm by using modified formal context combine with supplement formal context to find the maximal balance cliques. Additionally, we utilized four real-world datasets to test our proposed approaches as well as the running time in the experimental section.

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