Rough Set Approximations in Formal Concept Analysis

Yao, Yiyu; Chen, Yaohua

doi:10.1007/11847465_14

Cited by 76 publications

(37 citation statements)

References 36 publications

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“…Clearly, the set R ∆ (S) is the contrary of the (standard) extent of R ∆ (S), as outlined in the FCA cube. In several studies, it has been pointed out that the basic operators in the two theories are the four modal-like operators of the FCA square of oppositions and that the basic FCA operator is a sufficiency-like operator [12,13,48]. This fits well with our setting where it is possible to see that R ∆ (the sufficiency on FCA) and (X)) a "property oriented concept" [12].…”

Section: Related Worksupporting

confidence: 86%

“…Several authors have investigated the possibility of mixing the two theories or finding common points (see [25,48]), e.g. relating concept lattices and partitions [20], or the place of Galois connections in RST [43], or computing rough concepts [19].…”

Section: Related Workmentioning

confidence: 99%

“…In the attempt at mixing the two theories, several authors considered rough approximations of concepts in the FCA settings [16,25,37,48]. The basic idea is (see for instance p.205 of [25]) that given any set of objects T , the lower and upper approximations are…”

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

The Structure of Oppositions in Rough Set Theory and Formal Concept Analysis - Toward a New Bridge between the Two Settings

Ciucci

Dubois

Prade

2014

Lecture Notes in Computer Science

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Section: Related Worksupporting

confidence: 86%

Section: Related Workmentioning

confidence: 99%

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The Structure of Oppositions in Rough Set Theory and Formal Concept Analysis - Toward a New Bridge between the Two Settings

Ciucci

Dubois

Prade

2014

Lecture Notes in Computer Science

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“…The crisp rough set-based feature selection (RSFS) process described previously can only operate effectively with datasets containing discrete values [34]. As most data contain real-valued features, it is necessary to perform a discretization step beforehand to use RSFS.…”

Section: Fuzzy-rough Feature Selectionmentioning

confidence: 99%

Approximation-based feature selection and application for algae population estimation

Shen

Jensen

2007

Appl Intell

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This paper presents a data-driven approach for feature selection to address the common problem of dealing with high-dimensional data. This approach is able to handle the real-valued nature of the domain features, unlike many existing approaches. This is accomplished through the use of fuzzy-rough approximations. The paper demonstrates the effectiveness of this research by proposing an estimator of algae populations, a system that approximates, given certain water characteristics, the size of algae populations. This estimator significantly reduces computer time and space requirements, decreases the cost of obtaining measurements and increases runtime efficiency, making itself more viable economically. By retaining only information required for the estimation task, the system offers higher accuracy than conventional estimators. Finally, the system does not alter the domain semantics, making any distilled knowledge human-readable. The paper describes the problem domain, architecture and operation of the system, and provides and discusses detailed experimentation. The results show that algae estimators using a fuzzy-rough feature selection step produce more accurate predictions of algae populations in general.

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“…Düntsch et al [26,27] calls R △ a sufficiency operator, and its representation capabilities are studied in the theory of Boolean algebras. Taking inspiration as the previous authors from rough sets [40], Yao [45,46] also considers these four subsets. In both cases, the four operators were introduced.…”

Section: Formal Context Settingmentioning

confidence: 99%

Formal Concept Analysis from the Standpoint of Possibility Theory

Dubois

Prade

2015

Formal Concept Analysis

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15496The contribution was presented at : http://www.matap.uma.es/icfca2015/files/a61b70b0124cd72ef5b1442c0223db4a-0.html Abstract. Formal concept analysis (FCA) and possibility theory (PoTh) have been developed independently. They address different concerns in information processing: while FCA exploits relations linking objects and properties, and has applications in data mining and clustering, PoTh deals with the modeling of (graded) epistemic uncertainty. However, making a formal parallel between FCA and PoTh is fruitful. The four set-functions at work in PoTh have meaningful counterparts in FCA; this leads to consider operators neglected in FCA, and thus new fixed point equations. One of these pairs of equations, paralleling the one defining formal concepts in FCA, defines independent sub-contexts of objects and properties that have nothing in common. The similarity of the structures underlying FCA and PoTh is still more striking, using a cube of opposition (a device extending the traditional square of opposition in logic). Beyond the parallel between FCA and PoTh, this invited contribution, which largely relies on several past publications by the authors, also addresses issues pertaining to the possible meanings, degree of satisfaction vs. degree of certainty, of graded object-property links, which calls for distinct manners of handling the degrees. Other lines of interest for further research are briefly mentioned.

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Rough Set Approximations in Formal Concept Analysis

Cited by 76 publications

References 36 publications

The Structure of Oppositions in Rough Set Theory and Formal Concept Analysis - Toward a New Bridge between the Two Settings

The Structure of Oppositions in Rough Set Theory and Formal Concept Analysis - Toward a New Bridge between the Two Settings

Approximation-based feature selection and application for algae population estimation

Formal Concept Analysis from the Standpoint of Possibility Theory

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