Note on generating fuzzy concept lattices via Galois connections

Pócs, Jozef

doi:10.1016/j.ins.2011.09.021

Cited by 69 publications

(36 citation statements)

References 16 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%

“…Together with this ordering, in the complete lattice an infimum (0, 0, …, 0) and a supremum (1,1,…,1) exist for some formal concepts [30,31]: Hu et al [14] Gely [12] Nguyen et al [9] Ganter 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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Section: Discussionmentioning

confidence: 99%

Section: Formal Concept Analysis In the Fuzzy Settingmentioning

confidence: 99%

Section: Formal Concept Analysis In the Fuzzy Settingmentioning

confidence: 99%

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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“…This is the reason why we call this new approach heterogeneous. Another answer to the problem of data heterogeneity was given by Pócs in [28] and [29]. This approach also works with different lattices for every object and every attribute, but it gives a Galois connection to the table fields.…”

Section: Introductionmentioning

confidence: 99%

On Different Types of Heterogeneous Formal Contexts

Antoni¹,

Kraj²,

Krídlo³

2013

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

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We provide a generalization of Formal Concept Analysis that works with different types of the values in a heterogeneous formal context. An appropriate counterpart of the basic theorem on concept lattices is formulated. We suggest the transformation of the heterogeneous formal context to Galois connectional approach. Illustration on an example is included. Moreover, we show that this approach is a generalization of the multi-adjoint concept lattices proposed by Medina and Ojeda-Aciego. Finally, links between the proposed environment and related studies are stated.

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