Real formal concept analysis based on grey-rough set theory

Wu, Qiang; Liu, Zongtian

doi:10.1016/j.knosys.2008.06.001

Cited by 74 publications

(25 citation statements)

References 10 publications

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“…Due to the adoption of interval representation for grey numbers, however, grey sets have been considered the same as interval-valued fuzzy sets [15,16]. Some recent publications have reported work on the combination of grey sets with rough sets [40,42]. However, in their work, grey sets are still defined using interval grey numbers which makes them equivalent to interval-valued fuzzy sets.…”

Section: A Fuzzy Set With Interval Values As Its Membership Values Ismentioning

confidence: 99%

“…Grey numbers and intervals have some similarity and grey sets are considered to be the same as interval-valued fuzzy sets [15]. With the increasing applications of grey systems, the combination of grey sets with fuzzy sets and rough sets have been investigated recently [40,42]. However, all these research works considered grey sets using interval grey numbers only, and such a restriction makes grey sets and interval-valued fuzzy sets equivalent.…”

Section: Introductionmentioning

confidence: 99%

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Grey sets and greyness

Yang

John

2012

Information Sciences

109

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This paper discusses the application of grey numbers for uncertainty representation. It highlights the difference between grey sets and interval-valued fuzzy sets, and investigates the degree of greyness for grey sets. It facilitates the representation of uncertainty not only for elements of a set, but also the set itself as a whole. Our results show that a grey set could be specified for interval-valued fuzzy sets or rough sets under special conditions. With the notion of grey sets and their associated degrees of greyness, various set operations between grey sets are discussed.

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Section: A Fuzzy Set With Interval Values As Its Membership Values Ismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Grey sets and greyness

Yang

John

2012

Information Sciences

109

View full text Add to dashboard Cite

show abstract

“…However, grey numbers and intervals have some similarity and grey sets are considered to be equivalent to interval-valued fuzzy sets [8], [10]. With the increasing applications of grey systems, the combination of grey sets with fuzzy sets and rough sets have been investigated recently [22], [23]. However, all these research works considered grey sets using interval grey numbers only, and such a restriction does indeed make grey sets and interval-valued fuzzy sets equivalent.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Representation of Grey Numbers and Grey Sets

Yang

Liu

John

2014

IEEE Trans. Cybern.

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Abstract-In the literature there is a presumption that a grey set and an interval-valued fuzzy set are equivalent. This presumption ignores the existence of discrete components in a grey number. In this paper new measurements of uncertainties of grey numbers and grey sets, consisting of both absolute and relative uncertainties, are defined to give a comprehensive representation of uncertainties in a grey number and a grey set. Some simple examples are provided to illustrate that the proposed uncertainty measurement can give an effective representation of both absolute and relative uncertainties in a grey number and a grey set. The relationships between grey sets and interval-valued fuzzy sets are also analysed from the point of view of the proposed uncertainty representation. The analysis demonstrates that grey sets and intervalvalued fuzzy sets provide different but overlapping models for uncertainty representation in sets.

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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

Mei

Wang

et al. 2014

International Journal of Computational Intelligence Systems

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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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Real formal concept analysis based on grey-rough set theory

Cited by 74 publications

References 10 publications

Grey sets and greyness

Grey sets and greyness

Uncertainty Representation of Grey Numbers and Grey Sets

On inference rules in decision formal contexts

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