Reduction method for concept lattices based on rough set theory and its application

Liu, Min; Shao, Mingwen; Zhang, Wenxiu; Wu, Cheng

doi:10.1016/j.camwa.2006.03.040

Cited by 130 publications

(46 citation statements)

References 13 publications

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“…Then inspired by rough set theory 22 , two kinds of attribute reduction methods and object reduction methods for concept lattices were developed, respectively 14 . After that, based on irreducible elements in the object and property oriented concept lattices, a new approach to attribute reduction was presented 27 .…”

Section: Co-published By Atlantis Press and Taylor And Francismentioning

confidence: 99%

“…After eliminating the superfluous attributes, the formal context becomes simpler and the discovery of the initial knowledge hidden in the formal context becomes easier, thus it is a key problem in knowledge discovery. In recent years, many scholars have studied attribute reduction extensively from various perspectives and each of them aims at some basic requirements 14,16,19,27,32,36 . In 2005, a method to attribute reduction was proposed in concept lattices via the discernibility matrix and Boolean function 36 .…”

Section: Introductionmentioning

confidence: 99%

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Attribute reduction based on maximal rules in decision formal context

Li¹,

Mi²,

Xie³

2014

IJCIS

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One of the key issues in the theory of concept lattices is to extract the useful rules from the decision formal context. The maximal rules implicate the others, thus people are interested in them. This paper proposes two new kinds of attribute reduction in the decision formal context based on maximal rules. The reducts preserve all the condition extensions and the decision extensions related to the original maximal rules. The internal relationship between the original maximal rules and the maximal rules in the reduced decision formal context is derived. The reducts can make the maximal rules more concise and accurate. The mathematical property of the proposed attribute reduction is investigated and we construct the discernibility matrix and function to compute all the reducts. Finally, all the attributes are classified into three types based on the maximal rules. The characteristics of these types of attributes are also analyzed.

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Section: Co-published By Atlantis Press and Taylor And Francismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Attribute reduction based on maximal rules in decision formal context

Li¹,

Mi²,

Xie³

2014

IJCIS

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“…Such approaches include ice-berg lattices [1], nesting lattices [2], creating sub-contexts [3], fault-tolerance [4,5], expandable concept trees [6], rough concepts [7] and approximation [8]. However, there will always be the need for faster performance of the fundamental operations in FCA, such as the computation of formal concepts.…”

Section: Introductionmentioning

confidence: 99%

Making Use of Empty Intersections to Improve the Performance of CbO-Type Algorithms

Andrews

2017

Lecture Notes in Computer Science

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Abstract. This paper describes how improvements in the performance of Close-by-One type algorithms can be achieved by making use of empty intersections in the computation of formal concepts. During the computation, if the intersection between the current concept extent and the next attribute-extent is empty, this fact can be simply inherited by subsequent children of the current concept. Thus subsequent intersections with the same attribute-extent can be skipped. Because these intersections require the testing of each object in the current extent, significant time savings can be made by avoiding them. The paper also shows how further time savings can be made by forgoing the traditional canonicity test for new extents, if the intersection is empty. Finally, the paper describes how, because of typical optimizations made in the implementation of CbO-type algorithms, even more time can be saved by amalgamating inherited attributes with inherited empty intersections into a single, simple test.

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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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Reduction method for concept lattices based on rough set theory and its application

Cited by 130 publications

References 13 publications

Attribute reduction based on maximal rules in decision formal context

Attribute reduction based on maximal rules in decision formal context

Making Use of Empty Intersections to Improve the Performance of CbO-Type Algorithms

Building multi-adjoint concept lattices

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