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  1.  58
    Fuzzy Galois Connections.Radim Bêlohlávek - 1999 - Mathematical Logic Quarterly 45 (4):497-504.
    The concept of Galois connection between power sets is generalized from the point of view of fuzzy logic. Studied is the case where the structure of truth values forms a complete residuated lattice. It is proved that fuzzy Galois connections are in one-to-one correspondence with binary fuzzy relations. A representation of fuzzy Galois connections by Galois connections is provided.
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  2.  13
    Concept Lattices and Order in Fuzzy Logic.Radim Bĕlohlávek - 2004 - Annals of Pure and Applied Logic 128 (1-3):277-298.
    The theory of concept lattices is approached from the point of view of fuzzy logic. The notions of partial order, lattice order, and formal concept are generalized for fuzzy setting. Presented is a theorem characterizing the hierarchical structure of formal fuzzy concepts arising in a given formal fuzzy context. Also, as an application of the present approach, Dedekind–MacNeille completion of a partial fuzzy order is described. The approach and results provide foundations for formal concept analysis of vague data—the propositions “object (...)
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  3.  21
    Fuzzy Equational Logic.Radim Bělohlávek - 2002 - Archive for Mathematical Logic 41 (1):83-90.
  4.  58
    Lattices of Fixed Points of Fuzzy Galois Connections.Radim Bělohlávek - 2001 - Mathematical Logic Quarterly 47 (1):111-116.
    We give a characterization of the fixed points and of the lattices of fixed points of fuzzy Galois connections. It is shown that fixed points are naturally interpreted as concepts in the sense of traditional logic.
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  5.  38
    Birkhoff Variety Theorem and Fuzzy Logic.Radim Bělohlávek - 2003 - Archive for Mathematical Logic 42 (8):781-790.
    An algebra with fuzzy equality is a set with operations on it that is equipped with similarity ≈, i.e. a fuzzy equivalence relation, such that each operation f is compatible with ≈. Described verbally, compatibility says that each f yields similar results if applied to pairwise similar arguments. On the one hand, algebras with fuzzy equalities are structures for the equational fragment of fuzzy logic. On the other hand, they are the formal counterpart to the intuitive idea of having functions (...)
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  6.  18
    A Logic of Graded Attributes.Radim Belohlavek & Vilem Vychodil - 2015 - Archive for Mathematical Logic 54 (7-8):785-802.
    We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ⇒ B and can be interpreted in two ways: first, in data tables with entries representing degrees to which objects have attributes ; second, in database tables where each domain is equipped with a similarity relation. We assume that the degrees form (...)
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  7.  19
    Concepts and Fuzzy Logic.Radim Belohlavek & George J. Klir (eds.) - 2011 - MIT Press.
    In this work - both psychologists working on concepts and mathematicians working on fuzzy logic - reassess the usefulness of fuzzy logic for the psychology of concepts.
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  8.  42
    Fuzzy Horn Logic I.Radim Bělohlávek & Vilém Vychodil - 2006 - Archive for Mathematical Logic 45 (1):3-51.
    The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style completeness theorem (degree of provability equals degree (...)
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  9.  27
    Fuzzy Horn Logic II.Radim Bělohlávek & Vilém Vychodil - 2006 - Archive for Mathematical Logic 45 (2):149-177.
    The paper studies closure properties of classes of fuzzy structures defined by fuzzy implicational theories, i.e. theories whose formulas are implications between fuzzy identities. We present generalizations of results from the bivalent case. Namely, we characterize model classes of general implicational theories, finitary implicational theories, and Horn theories by means of closedness under suitable algebraic constructions.
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