What is a Fuzzy Concept Lattice? II

Bělohlávek, Radim

doi:10.1007/978-3-642-21881-1_4

Cited by 60 publications

(79 citation statements)

References 33 publications

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“…However, the development of a fuzzy formal concept analysis theory requires an appropriate algebra of fuzzy sets [6,8]. While many theoretical studies have been developed, the different gradual interpretations of a fuzzy formal context have not been much discussed.…”

Section: Graded Links Between a Property And An Objectmentioning

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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Section: Graded Links Between a Property And An Objectmentioning

confidence: 99%

Formal Concept Analysis from the Standpoint of Possibility Theory

Dubois

Prade

2015

Formal Concept Analysis

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“…A fuzzy formal context is a triplet K = (G, M, R  ) where G is set of formal objects, M is a set of formal attributes, and R  is a fuzzy relation between G and M [4,5]. The fuzzy relation ( , ) R g m  represents that the object gG has a membership value ( , ) g m   with the attributes mM.…”

Section: Formal Concept Analysis In the Fuzzy Settingmentioning

confidence: 99%

“…Vychodil [5] Belohlavek [29,30] Hu et al [14] Djouadi [24] Ghosh et al [7] Kandasamy and Smarandache [23] Aswani Kumar [10,11,45,46,53,54] Zhang et al [32] Li and Zhang [16] Dubois and…”

Section: Formal Concept Analysis In the Fuzzy Settingmentioning

confidence: 99%

“…Prade [25] Aswani Kumar Bartl et al [41] Skowron et al [44] For detailed illustrations about generating the formal concepts from a given formal context, readers can refer to references including [1][2][3][4][5][6][7][8]13,16,[24][25][26][27][29][30][31][32][33][34][35][36][37][38][39][40]. Reducing the number of formal concepts and the size of the lattice structure are open issues for researchers as knowledge reduction problems.…”

Section: Formal Concept Analysis In the Fuzzy Settingmentioning

confidence: 99%

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A Note on Computing the Crisp Order Context of a Fuzzy Formal Context for Knowledge Reduction

Singh¹,

Cherukuri²

2014

J Inf Process Syst

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Fuzzy Formal Concept Analysis (FCA) is a mathematical tool for the effective representation of imprecise and vague knowledge. However, with a large number of formal concepts from a fuzzy context, the task of knowledge representation becomes complex. Hence, knowledge reduction is an important issue in FCA with a fuzzy setting. The purpose of this current study is to address this issue by proposing a method that computes the corresponding crisp order for the fuzzy relation in a given fuzzy formal context. The obtained formal context using the proposed method provides a fewer number of concepts when compared to original fuzzy context. The resultant lattice structure is a reduced form of its corresponding fuzzy concept lattice and preserves the specialized and generalized concepts, as well as stability. This study also shows a step-by-step demonstration of the proposed method and its application.

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“…Denote the set of all the -fuzzy subsets on According to [20][21][22], we can give the following theorem. The form of the two mappings in Theorem 3.1 is the same with the one in [20][21][22], but the operators are derived from the lattice implication algebra, which is not the same.…”

Section: Lattice-valued Concept Latticementioning

confidence: 99%

A Combination Algorithm of Multiple Lattice-Valued Concept Lattices

Wang

2013

IJCIS

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With the rapid development of network technology, especially in the internet area, distributed computation and parallel processing of data are urgently needed. This paper studies the combination operation of the lattice-valued concept lattices to realize its distributed computation and parallel processing. The proposal of its corresponding combination algorithm is mainly according to the conjunction properties of incomparable attribute values. Firstly, we define a homotypic lattice-valued concept lattice and a combined concept lattice; secondly, we analyze some relations between the lattice-valued formal concepts under two conditions and prove the isomorphism of the combination theory; finally, we present the combination algorithm of multiple lattice-valued concept lattices and analyze the algorithm complexity and employ an example to show the application of this combination algorithm.

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What is a Fuzzy Concept Lattice? II

Cited by 60 publications

References 33 publications

Formal Concept Analysis from the Standpoint of Possibility Theory

Formal Concept Analysis from the Standpoint of Possibility Theory

A Note on Computing the Crisp Order Context of a Fuzzy Formal Context for Knowledge Reduction

A Combination Algorithm of Multiple Lattice-Valued Concept Lattices

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