Negative Attributes and Implications in Formal Concept Analysis

Rodríguez‐Jiménez, Jose Manuel; Cordero, Pablo; Enciso, Manuel; Mora, Ángel

doi:10.1016/j.procs.2014.05.325

Cited by 30 publications

(20 citation statements)

References 10 publications

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“…If we want to calculate both, mixed implicational system and set of mixed concepts, we can extend algorithm 2 [8]. We know that we only have to modify a few lines because it works with closures.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Optimization in Engine Design via Formal Concept Analysis Using Negative Attributes

Rodríguez‐Jiménez

Enciso

Mora

2016

Computer Science &Amp; Information Technology ( CS &Amp; IT )

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Section: Discussionmentioning

confidence: 99%

“…The algorithm for calculating the implicational system that we propose in [8] uses the axiomatic system and, considering the full consistent sets, the dataset have to be checked 3 |M| -2 |M| times in the worst case.…”

Section: Our Approach For Extending Formal Concept Analysis With Negamentioning

confidence: 99%

Optimization in Engine Design via Formal Concept Analysis Using Negative Attributes

Rodríguez‐Jiménez

Enciso

Mora

2016

Computer Science &Amp; Information Technology ( CS &Amp; IT )

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“…Concept lattice uses positive attributes to characterize a target set. However, many studies have shown that positive attributes and negative attributes are of equal importance in describing a target [25][26][27][28]. By taking both positive and negative attributes into consideration, Qi et al [8,9] proposed three-way concept analysis (3WCA), which has become a hot topic in FCA [10,20,23].…”

Section: Three-way Concept Analysismentioning

confidence: 99%

Three-Way Concept Analysis for Incomplete Formal Contexts

Huang

Hao

2018

Mathematical Problems in Engineering

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Recently, incomplete formal contexts have received more and more attention from the communities of formal concept analysis. Different from a complete context where the binary relations between all the objects and attribute are known, an incomplete formal context has at least a pair of object and attribute with a completely unknown binary relation. Partially known formal concepts use interval sets to indicate the incompleteness. Three-way formal concept analysis is capable of characterizing a target set by combining positive and negative attributes. However, how to describe target set, by pointing out what attributes it has with certainty and what attributes it has with possibility and what attributes it does not has with certainty and what attributes it does not has with possibility, is still an open problem. This paper combines the ideas of three-way formal concept analysis and partially known formal concepts and presents a framework of approximate three-way concept analysis. At first, approximate object-induced and attribute-induced three-way concept lattices are introduced, respectively. And then, the relationship between approximate three-way concept lattice and classical three-way concept lattice are investigated. Finally, examples are presented to demonstrate and verify the obtained results.

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“…Some starting approaches in this line can be found in [16,14,15] and applications in [17,11,12]. In [18], we tackled this issue focusing on the problem of mining implications with positive and negative attributes from formal contexts. As a conclusion of that work, we emphasized the necessity of a full development of the algebraic framework, which is the aim of this paper.…”

Section: Negative Attributesmentioning

confidence: 99%

“…In [18,19], we chose this new term to avoid confusion with other notions where the adjective "complete" is used: complete axiomatic system and complete implicational system.…”

Section: Mixed Concept Latticesmentioning

confidence: 99%