A general approach to fuzzy concepts

Popescu, Andrei

doi:10.1002/malq.200310098

Cited by 76 publications

(43 citation statements)

References 27 publications

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“…In both cases, the four operators were introduced. See also (Popescu 2004;Georgescu and Popescu 2004). The interest of the bridge between possibility theory and FCA is that it enables a systematic investigation of alternative connections between objects and properties to be carried out; they differ from the standard Galois connection of FCA.…”

Section: Application To the Formal Context Settingmentioning

confidence: 99%

“…This approach has mathematical roots in category theory and Heyting algebras (Higgs 1973), whereby a multivalued notion of equality is used. As we are going to see, although defined in a different algebraic setting and on the basis of a completely different intuition, it is also closely related to the gradual version of formal concept analysis (Bělohlávek 1999(Bělohlávek , 2002Popescu 2004;Georgescu and Popescu 2004).…”

Section: Extensional Fuzzy Sets and Fuzzy Contextsmentioning

confidence: 99%

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Bridging gaps between several forms of granular computing

2016

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Two important ideas at the core of Zadeh's seminal contributions to fuzzy logic and approximate reasoning are the notions of granulation and that of possibilistic uncertainty. In this paper, elaborating on the basis of some formal analogy, recently laid bare by the authors, between possibility theory and formal concept analysis, we suggest other bridges between theories for which the concept of granulation is central. We highlight the common features between the notion of extensional fuzzy set with respect to a similarity relation and the notion of formal concept. We also discuss the case of fuzzy rough sets. Thus, we point out some fruitful cross-fertilizations between the possibilistic representation of information and several views of granulation emphasizing the idea of clusters of points that can be identified respectively on the basis of their closeness, or of their common labeling in terms of properties.

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Section: Application To the Formal Context Settingmentioning

confidence: 99%

Section: Extensional Fuzzy Sets and Fuzzy Contextsmentioning

confidence: 99%

Bridging gaps between several forms of granular computing

2016

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“…It was proposed by Popescu [41] and studied in a general setting of residuated algebras, but not in the usual Boolean setting. Namely, let us consider pairs (X, Y ) s.t.…”

Section: Formal Context Decompositionmentioning

confidence: 99%

Formal Concept Analysis from the Standpoint of Possibility Theory

Dubois

Prade

2015

Formal Concept Analysis

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15496The contribution was presented at : http://www.matap.uma.es/icfca2015/files/a61b70b0124cd72ef5b1442c0223db4a-0.html Abstract. Formal concept analysis (FCA) and possibility theory (PoTh) have been developed independently. They address different concerns in information processing: while FCA exploits relations linking objects and properties, and has applications in data mining and clustering, PoTh deals with the modeling of (graded) epistemic uncertainty. However, making a formal parallel between FCA and PoTh is fruitful. The four set-functions at work in PoTh have meaningful counterparts in FCA; this leads to consider operators neglected in FCA, and thus new fixed point equations. One of these pairs of equations, paralleling the one defining formal concepts in FCA, defines independent sub-contexts of objects and properties that have nothing in common. The similarity of the structures underlying FCA and PoTh is still more striking, using a cube of opposition (a device extending the traditional square of opposition in logic). Beyond the parallel between FCA and PoTh, this invited contribution, which largely relies on several past publications by the authors, also addresses issues pertaining to the possible meanings, degree of satisfaction vs. degree of certainty, of graded object-property links, which calls for distinct manners of handling the degrees. Other lines of interest for further research are briefly mentioned.

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“…The main aim of this section is to recall the shortened definitions and results of approach from [28], [29] which is inspired by the (homogeneous) approach from [32].…”

Section: Galois Connectional Formal Contextmentioning

confidence: 99%

On Different Types of Heterogeneous Formal Contexts

Antoni¹,

Kraj²,

Krídlo³

2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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We provide a generalization of Formal Concept Analysis that works with different types of the values in a heterogeneous formal context. An appropriate counterpart of the basic theorem on concept lattices is formulated. We suggest the transformation of the heterogeneous formal context to Galois connectional approach. Illustration on an example is included. Moreover, we show that this approach is a generalization of the multi-adjoint concept lattices proposed by Medina and Ojeda-Aciego. Finally, links between the proposed environment and related studies are stated.

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A general approach to fuzzy concepts

Cited by 76 publications

References 27 publications

Bridging gaps between several forms of granular computing

Bridging gaps between several forms of granular computing

Formal Concept Analysis from the Standpoint of Possibility Theory

On Different Types of Heterogeneous Formal Contexts

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