Fuzzy inference based on fuzzy concept lattice

Fan, Shiqing; Zhang, Wenxiu; Xu, Wei

doi:10.1016/j.fss.2006.07.011

Cited by 64 publications

(24 citation statements)

References 21 publications

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“…The idea to extend FCA to a fuzzy formal context, which enables us to express that an object satisfies a property to an intermediary degree, has been initially proposed by Burusco and Fuentes-Gonzalez [12] before being considerably developed by Belohlavek [5][6][7], and by a number of other authors, as in particular [30,26,32,33]. For a discussion of different meaningful gradual extensions of FCA, the reader is referred to [14,16].…”

Section: Concluding Remarks: the Gradual Casementioning

confidence: 99%

A Formal Concept View of Abstract Argumentation

Amgoud

Prade

2013

Lecture Notes in Computer Science

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Abstract. The paper presents a parallel between two important theories for the treatment of information which address questions that are apparently unrelated and that are studied by different research communities: an enriched view of formal concept analysis and abstract argumentation. Both theories exploit a binary relation (expressing object-property links, attacks between arguments). We show that when an argumentation framework rather considers the complementary relation does not attack, then its stable extensions can be seen as the exact counterparts of formal concepts. This leads to a cube of oppositions, a generalization of the well-known square of oppositions, between eight remarkable sets of arguments. This provides a richer view for argumentation in cases of bi-valued attack relations and fuzzy ones.

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Section: Concluding Remarks: the Gradual Casementioning

confidence: 99%

A Formal Concept View of Abstract Argumentation

Amgoud

Prade

2013

Lecture Notes in Computer Science

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“…Burusco and Bělohlávek [16][17][18][19][20][21] extended the concept lattices to fuzzy concept lattices in fuzzy formal context. Fan et al [22] studied various fuzzy concept lattices and discussed fuzzy inference methods. Ma et al [23] built the relations between fuzzy concept lattices and granular computing.…”

Section: Introductionmentioning

confidence: 99%

A mathematical model for concept granular computing systems

Qiu¹,

Ma²,

Yang³

et al. 2010

Sci. China Inf. Sci.

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Extent-intent and intent-extent operators are introduced between two complete lattices in this paper and a mathematical model for concept granular computing system is established. We proved that the set of all concepts in this system is a lattice with the greatest element and the least element. This framework includes formal concept lattices from formal contexts, L fuzzy concept lattices from L fuzzy formal contexts and three kinds of variable threshold concept lattices, i.e. the extension and the intension of a concept are a crisp set and a crisp set, a crisp set and a fuzzy set, a fuzzy set and a crisp set, respectively. Finally, some iterative algorithms for constructing concepts are proposed and they are proved to be optimal concepts under some conditions in this system. CitationQiu G F, Ma J M, Yang H Z, et al. A mathematical model for concept granular computing systems.

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“…The theory of formal concept analysis (FCA), originally proposed by Wille 1 in 1982, is oriented towards the discovery of formal concepts and their hierarchical structure at its early stage of development, but nowadays it has shown a trend of multidisciplinary intersection and fusion 2,3,4,5,6,7 . This theory is based on mathematical order theory, in particular the theory of complete lattice, and it has been considered to be an effective tool for conceptual data analysis and knowledge processing 8 .…”

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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Fuzzy inference based on fuzzy concept lattice

Cited by 64 publications

References 21 publications

A Formal Concept View of Abstract Argumentation

A Formal Concept View of Abstract Argumentation

A mathematical model for concept granular computing systems

On inference rules in decision formal contexts

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