Set approximations in fuzzy formal concept analysis

Shao, Mingwen; Liu, Min; Zhang, Wenxiu

doi:10.1016/j.fss.2007.05.002

Cited by 55 publications

(31 citation statements)

References 27 publications

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“…This observation has a significant role in analyzing the human reasoning of relational informational systems [1][2][3][20][21][22][23]38,42]. Also, the proposed method can be applied in various fields like knowledge discovery and representation [1][2][3]14,39,41,[42][43][44][45]53,54]; information retrieval [2,3,24,45,54]; knowledge reduction [7,10,12,15,[17][18][19]25,29,31,32,35,39,40,48,51,52]; and association rule mining [1][2][3]6,16,46,…”

Section: Discussionmentioning

confidence: 99%

“…The operator ( , )   is known as a fuzzy Galois connection for extensive study readers can refer to [24,25,[29][30][31][32][33][34][35]. When the operator () is applied to a set of objects, it provides a set of attributes that are covered by these objects.…”

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%

See 2 more Smart Citations

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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Section: Discussionmentioning

confidence: 99%

Section: Formal Concept Analysis In the Fuzzy Settingmentioning

confidence: 99%

Section: Formal Concept Analysis In the Fuzzy Settingmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Formal concept analysis (FCA) has been extended with ideas from fuzzy set theory [1,2,3], fuzzy logic reasoning [4,5,6], rough set theory [7,8,9], some integrated approaches such as fuzzy and rough [10], or rough and domain theory [11].…”

Section: Introductionmentioning

confidence: 99%

Building multi-adjoint concept lattices

Díaz¹,

Garcia²,

Medina³

et al. 2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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In Formal Concept Analysis it is very important to study fast algorithms to compute concept lattices. This paper introduces an algorithm on the multiadjoint concept lattice framework, in order to compute the whole concept lattice. This fuzzy framework is very general and provides more flexibility in relational systems. This has been theoretically studied and, now, we need an algorithm to compute the concept lattice for each frame and context.

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“…These four operators are also used for achieving rough approximations of crisp formal concepts (Yao and Chen 2006;Lei and Luo 2009), or even for knowledge reduction (Wang and Zhang 2008). Whereas in Lai andZhang (2009), Fan et al (2006), Shao et al (2007), rough approximations are generalized to fuzzy formal concepts using a residuated algebra.…”

Section: Introductionmentioning

confidence: 99%

Possibility-theoretic extension of derivation operators in formal concept analysis over fuzzy lattices

Djouadi

Prade

2011

Fuzzy Optim Decis Making

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Formal concept analysis (FCA) associates a binary relation between a set of objects and a set of properties to a lattice of formal concepts defined through a Galois connection. This relation is called a formal context, and a formal concept is then defined by a pair made of a subset of objects and a subset of properties that are put in mutual correspondence by the connection. Several fuzzy logic approaches have been proposed for inducing fuzzy formal concepts from L-contexts based on antitone L−Galois connections. Besides, a possibility-theoretic reading of FCA which has been recently proposed allows us to consider four derivation powerset operators, namely sufficiency, possibility, necessity and dual sufficiency (rather than one in standard FCA). Classically, fuzzy FCA uses a residuated algebra for maintaining the closure property of the composition of sufficiency operators. In this paper, we enlarge this framework and provide sound minimal requirements of a fuzzy algebra w.r.t. the closure and opening properties of antitone L−Galois connections as well as the closure and opening properties of isotone L−Galois connections. We apply these results to particular compositions of the four derivation operators. We also give some noticeable properties which may be useful for building the corresponding associated lattices.

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Set approximations in fuzzy formal concept analysis

Cited by 55 publications

References 27 publications

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

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

Building multi-adjoint concept lattices

Possibility-theoretic extension of derivation operators in formal concept analysis over fuzzy lattices

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