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Compatibility of Fuzzy Relations.

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Title: Compatibility of Fuzzy Relations.
Authors: Kheniche, A.1, Baets, B.2, Zedam, L.1
Source: International Journal of Intelligent Systems. Mar2016, Vol. 31 Issue 3, p240-256. 17p.
Subjects: Fuzzy relational calculus, Fuzzy sets, Lattice theory, Representations of algebras, Mathematical symmetry
Abstract: The notion of extensionality, introduced by Höhle and Blanchard, and the notion of compatibility, as coined by Bělohlávek, of a fuzzy relation with respect to a fuzzy equality are trivially equivalent. Here, this compatibility property is dissected into left and right compatibility, mimicking the original twofold definition of extensionality, and studied in detail in the context of arbitrary fuzzy relations. Relying on the notions of left and right traces of a fuzzy relation, it is shown that compatibility can be characterized in terms of inclusions, shedding another light on the matter. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Intelligent Systems is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Compatibility of Fuzzy Relations.
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Intelligent+Systems%22">International Journal of Intelligent Systems</searchLink>. Mar2016, Vol. 31 Issue 3, p240-256. 17p.
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  Data: <searchLink fieldCode="DE" term="%22Fuzzy+relational+calculus%22">Fuzzy relational calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Fuzzy+sets%22">Fuzzy sets</searchLink><br /><searchLink fieldCode="DE" term="%22Lattice+theory%22">Lattice theory</searchLink><br /><searchLink fieldCode="DE" term="%22Representations+of+algebras%22">Representations of algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+symmetry%22">Mathematical symmetry</searchLink>
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  Data: The notion of extensionality, introduced by Höhle and Blanchard, and the notion of compatibility, as coined by Bělohlávek, of a fuzzy relation with respect to a fuzzy equality are trivially equivalent. Here, this compatibility property is dissected into left and right compatibility, mimicking the original twofold definition of extensionality, and studied in detail in the context of arbitrary fuzzy relations. Relying on the notions of left and right traces of a fuzzy relation, it is shown that compatibility can be characterized in terms of inclusions, shedding another light on the matter. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of International Journal of Intelligent Systems is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1002/int.21783
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      – SubjectFull: Fuzzy relational calculus
        Type: general
      – SubjectFull: Fuzzy sets
        Type: general
      – SubjectFull: Lattice theory
        Type: general
      – SubjectFull: Representations of algebras
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      – SubjectFull: Mathematical symmetry
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      – TitleFull: Compatibility of Fuzzy Relations.
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              Text: Mar2016
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