A Combination Algorithm of Multiple Lattice-Valued Concept Lattices

Li, Yang; Wang, Yuhui; Xu, Yang

doi:10.1080/18756891.2013.807109

Cited by 6 publications

(4 citation statements)

References 18 publications

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“…Wille 1 introduced a hierarchical order for formal concepts of a formal context and proved that the set of all formal concepts together with the hierarchical order forms a complete lattice, called the concept lattice of the formal context. In FCA, concept lattices are the basic tool used to analyze relational databases and have been applied to a variety of areas such as machine learning 9,10,11,12,13,14 , knowledge discovery 15,16,17,18,19 , software engineering 20 and other aspects 21,22,23 .…”

Section: Introductionmentioning

confidence: 99%

On inference rules in decision formal contexts

Li¹,

Mei²,

Wang³

et al. 2015

IJCIS

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Rule acquisition is one of the main purposes in the analysis of decision formal contexts. In general, the number of implications in a decision formal context is an exponential increase to the scale of the database. So, it is important to introduce effective inference rules between implications for eliminating as many superfluous implications as possible. This study puts forward a criterion called 'strongness' to assess the effectiveness of inference rules in terms of eliminating superfluous implications. We define a new inference rule in decision formal contexts and prove that the proposed inference rule is stronger than the existing one. Furthermore, we figure out the exact number of the superfluous implications that we can additionally remove by using the proposed inference rule compared with the existing one.

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Section: Introductionmentioning

confidence: 99%

On inference rules in decision formal contexts

Li¹,

Mei²,

Wang³

et al. 2015

IJCIS

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“…All the formal concepts are constructed from the formal context and form a concept lattice which reflects the relationship of generalization and the specialization among concepts. It has been studied from various perspectives, such as its mathematical property 4,8,13,17,18,25 and the applications in knowledge discovery 3,5,6,26,33,35 .…”

Section: Introductionmentioning

confidence: 99%

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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“…Computing all formal concepts and the concept lattice is the most basic issue that has been investigated by many domestic and foreign researchers from different angles. Various forms of algorithms in concepts computing and concept lattice generation can be generally divided into three categories: batch processing algorithm [ 10 – 14 ], progressive algorithm [ 15 , 16 ], and parallel algorithms [ 17 , 18 ]. The basic idea of batch processing algorithm is to form the edges according to the presubsequent relationship among all concepts generated and then constructs the concept lattice.…”

Section: Introductionmentioning

confidence: 99%

Deep First Formal Concept Search

Zhang

Wang

et al. 2014

The Scientific World Journal

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The calculation of formal concepts is a very important part in the theory of formal concept analysis (FCA); however, within the framework of FCA, computing all formal concepts is the main challenge because of its exponential complexity and difficulty in visualizing the calculating process. With the basic idea of Depth First Search, this paper presents a visualization algorithm by the attribute topology of formal context. Limited by the constraints and calculation rules, all concepts are achieved by the visualization global formal concepts searching, based on the topology degenerated with the fixed start and end points, without repetition and omission. This method makes the calculation of formal concepts precise and easy to operate and reflects the integrity of the algorithm, which enables it to be suitable for visualization analysis.

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A Combination Algorithm of Multiple Lattice-Valued Concept Lattices

Cited by 6 publications

References 18 publications

On inference rules in decision formal contexts

On inference rules in decision formal contexts

Attribute reduction based on maximal rules in decision formal context

Deep First Formal Concept Search

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