Binarization and Validation in Formal Concept Analysis

2012 ◽  
Vol 1 (4) ◽  
pp. 16-27 ◽  
Author(s):  
Mostafa A. Salama ◽  
Aboul Ella Hassanien
Keyword(s):  
Formal Concept Analysis ◽  
Real Life ◽  
Numerical Data ◽  
Concept Analysis ◽  
Formal Concept ◽  
Data Sets ◽  
Medical Field ◽  
Data Set ◽  
Cancer Data ◽  
Scaling Procedure

Representation and visualization of continuous data using the Formal Concept Analysis (FCA) became an important requirement in real-life fields. Application of formal concept analysis (FCA) model on numerical data, a scaling or Discretization / binarization procedures should be applied as preprocessing stage. The Scaling procedure increases the complexity of computation of the FCA, while the binarization process leads to a distortion in the internal structure of the input data set. The proposed approach uses a binarization procedure prior to applying FCA model, and then applies a validation process to the generated lattice to measure or ensure its degree of accuracy. The introduced approach is based on the evaluation of each attribute according to the objects of its extent set. To prove the validity of the introduced approach, the technique is applied on two data sets in the medical field which are the Indian Diabetes and the Breast Cancer data sets. Both data sets show the generation of a valid lattice.

Discovering Knowledge in Data Using Formal Concept Analysis

2013 ◽  
Vol 4 (2) ◽  
pp. 31-50 ◽  
Author(s):  
Simon Andrews ◽  
Constantinos Orphanides
Keyword(s):  
Formal Concept Analysis ◽  
Ad Hoc ◽  
Semantic Analysis ◽  
Large Data ◽  
Real Data ◽  
Concept Analysis ◽  
Formal Concept ◽  
Data Sets ◽  
Domain Experts ◽  
Tools And Techniques

Formal Concept Analysis (FCA) has been successfully applied to data in a number of problem domains. However, its use has tended to be on an ad hoc, bespoke basis, relying on FCA experts working closely with domain experts and requiring the production of specialised FCA software for the data analysis. The availability of generalised tools and techniques, that might allow FCA to be applied to data more widely, is limited. Two important issues provide barriers: raw data is not normally in a form suitable for FCA and requires undergoing a process of transformation to make it suitable, and even when converted into a suitable form for FCA, real data sets tend to produce a large number of results that can be difficult to manage and interpret. This article describes how some open-source tools and techniques have been developed and used to address these issues and make FCA more widely available and applicable. Three examples of real data sets, and real problems related to them, are used to illustrate the application of the tools and techniques and demonstrate how FCA can be used as a semantic technology to discover knowledge. Furthermore, it is shown how these tools and techniques enable FCA to deliver a visual and intuitive means of mining large data sets for association and implication rules that complements the semantic analysis. In fact, it transpires that FCA reveals hidden meaning in data that can then be examined in more detail using an FCA approach to traditional data mining methods.

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.

scholarly journals Continuous Domains in Formal Concept Analysis*

2021 ◽  
Vol 179 (3) ◽  
pp. 295-319
Author(s):  
Longchun Wang ◽  
Lankun Guo ◽  
Qingguo Li
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Continuous Functions ◽  
Formal Context ◽  
Formal Concept ◽  
Contractive Mappings ◽  
Continuous Domains ◽  
Algebraic Domains ◽  
Scott Continuous ◽  
Continuous Domain

Formal Concept Analysis (FCA) has been proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notion of contractive mappings over formal contexts is proposed, which can be viewed as a generalization of interior operators on sets into the framework of FCA. Then, by considering subset-selections consistent with contractive mappings, the notions of attribute continuous formal contexts and continuous concepts are introduced. It is shown that the set of continuous concepts of an attribute continuous formal context forms a continuous domain, and every continuous domain can be restructured in this way. Moreover, the notion of F-morphisms is identified to produce a category equivalent to that of continuous domains with Scott continuous functions. The paper also investigates the representations of various subclasses of continuous domains including algebraic domains and stably continuous semilattices.

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.

Set approximations in fuzzy formal concept analysis

2007 ◽  
Vol 158 (23) ◽  
pp. 2627-2640 ◽  
Author(s):  
Ming-Wen Shao ◽  
Min Liu ◽  
Wen-Xiu Zhang
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Formal Concept ◽  
Fuzzy Formal Concept ◽  
Fuzzy Formal Concept Analysis
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