scholarly journals Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 565
Author(s):  
Roberto G. Aragón ◽  
Jesús Medina ◽  
Eloísa Ramírez-Poussa
Keyword(s):  
Algebraic Structure ◽  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Attribute Reduction ◽  
Concept Analysis ◽  
Equivalence Classes ◽  
Formal Concept ◽  
Reduction Techniques ◽  
Quotient Set ◽  
Original Concept

The detection of redundant or irrelevant variables (attributes) in datasets becomes essential in different frameworks, such as in Formal Concept Analysis (FCA). However, removing such variables can have some impact on the concept lattice, which is closely related to the algebraic structure of the obtained quotient set and their classes. This paper studies the algebraic structure of the induced equivalence classes and characterizes those classes that are convex sublattices of the original concept lattice. Particular attention is given to the reductions removing FCA’s unnecessary attributes. The obtained results will be useful to other complementary reduction techniques, such as the recently introduced procedure based on local congruences.

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.

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.

scholarly journals Construction Search Engine Based on Formal Concept Analysis and Association Rule Mining

2012 ◽  
Vol 6-7 ◽  
pp. 625-630 ◽  
Author(s):  
Hong Sheng Xu
Keyword(s):  
Search Engine ◽  
Association Rule ◽  
Formal Concept Analysis ◽  
Association Rule Mining ◽  
High Efficiency ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Frequent Itemsets ◽  
Formal Concept ◽  
Rule Mining

In the form of background in the form of concept partial relation to the corresponding concept lattice, concept lattice is the core data structure of formal concept analysis. Association rule mining process includes two phases: first find all the frequent itemsets in data collection, Second it is by these frequent itemsets to generate association rules. This paper analyzes the association rule mining algorithms, such as Apriori and FP-Growth. The paper presents the construction search engine based on formal concept analysis and association rule mining. Experimental results show that the proposed algorithm has high efficiency.

scholarly journals Efficient Closure Operators for FCA-Based Classification

2020 ◽  
Vol 10 (2) ◽  
pp. 79-98
Author(s):  
Nida Meddouri ◽  
Mondher Maddouri
Keyword(s):  
Data Mining ◽  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Nearest Neighbor Search ◽  
Knowledge Discovery In Databases ◽  
Support Vector ◽  
Formal Concept ◽  
Closure Operators ◽  
Nominal Data

Knowledge discovery in databases (KDD) aims to exploit the large amounts of data collected every day in various fields of computing application. The idea is to extract hidden knowledge from a set of data. It gathers several tasks that constitute a process, such as: data selection, pre-processing, transformation, data mining, visualization, etc. Data mining techniques include supervised classification and unsupervised classification. Classification consists of predicting the class of new instances with a classifier built on learning data of labeled instances. Several approaches were proposed such as: the induction of decision trees, Bayes, nearest neighbor search, neural networks, support vector machines, and formal concept analysis. Learning formal concepts always refers to the mathematical structure of concept lattice. This article presents a state of the art on formal concept analysis classifier. The authors present different ways to calculate the closure operators from nominal data and also present new approach to build only a part of the lattice including the best concepts. This approach is based on Dagging (ensemble method) that generates an ensemble of classifiers, each one represents a formal concept, and combines them by a voting rule. Experimental results are given to prove the efficiency of the proposed method.

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.

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.

Rough-set-driven approach for attribute reduction in fuzzy formal concept analysis

2020 ◽  
Vol 391 ◽  
pp. 117-138 ◽  
Author(s):  
M. José Benítez-Caballero ◽  
Jesús Medina ◽  
Eloísa Ramírez-Poussa ◽  
Dominik Ślȩzak
Keyword(s):  
Rough Set ◽  
Formal Concept Analysis ◽  
Attribute Reduction ◽  
Concept Analysis ◽  
Formal Concept ◽  
Fuzzy Formal Concept ◽  
Fuzzy Formal Concept Analysis
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