Class Theory

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Tomáš Kroupa - One of the best experts on this subject based on the ideXlab platform.

  • Filters in fuzzy Class Theory
    Fuzzy Sets and Systems, 2008
    Co-Authors: Tomáš Kroupa
    Abstract:

    A concept of filter is introduced in fuzzy Class Theory. Graded properties of filters, prime filters, and related constructions are investigated. In particular, the properties of filters relativized with respect to the three basic t-norms (Godel, product, and Lukasiewicz) are studied. A naturally arising example of a graded filter is constructed and it is shown that the models of filters include well-known families of set functions.

  • EUSFLAT Conf. (1) - Interior-Based Topology in Fuzzy Class Theory.
    2007
    Co-Authors: Libor Behounek, Tomáš Kroupa
    Abstract:

    Fuzzy topology based on interior operators is studied in the fully graded framework of Fuzzy Class Theory. Its relation to graded notions of fuzzy topology given by open sets and neighborhoods is shown.

  • IFSA (1) - Topology in Fuzzy Class Theory: Basic Notions
    Lecture Notes in Computer Science, 1
    Co-Authors: Libor Běhounek, Tomáš Kroupa
    Abstract:

    In the formal and fully graded setting of Fuzzy Class Theory (or higher-order fuzzy logic) we make an initial investigation into basic notions of fuzzy topology. In particular we study graded notions of fuzzy topology regarded as a fuzzy system of open or closed fuzzy sets and as a fuzzy system of fuzzy neighborhoods. We show their basic graded properties and mutual relationships provable in Fuzzy Class Theory and give some links to the traditional notions of fuzzy topology.

Raju J. Das - One of the best experts on this subject based on the ideXlab platform.

Paul William Kingston - One of the best experts on this subject based on the ideXlab platform.

  • The Implications of Intergenerational Class Mobility for Class Theory: A Comment on Western
    Social Forces, 1996
    Co-Authors: Paul William Kingston
    Abstract:

    Focusing on the relative permeability of particular Class boundaries (defined by Wright's Class schema), Western's (1994) analysis does not draw out the most critical implications of mobility patterns for Class Theory - namely, whether Classes actually exist as relatively cohesive social entities with common life experiences. Wright's Class system is not even remotely marked by intergenerational social closure, nor are presumed Class advantages commonly transmitted across generations. The lack of intergenerational Class structuration undermines a key tenet of Class Theory

Libor Běhounek - One of the best experts on this subject based on the ideXlab platform.

  • relational compositions in fuzzy Class Theory
    Fuzzy Sets and Systems, 2009
    Co-Authors: Libor Běhounek, Martina Daňkova
    Abstract:

    We present a method for mass proofs of theorems of certain forms in a formal Theory of fuzzy relations and Classes. The method is based on formal identification of fuzzy Classes and inner truth values with certain fuzzy relations, which allows transferring basic properties of sup-T and inf-R compositions to a family of more than 30 composition-related operations, including sup-T and inf-R images, pre-images, Cartesian products, domains, ranges, resizes, inclusion, height, plinth, etc. Besides yielding a large number of theorems on fuzzy relations as simple corollaries of a few basic principles, the method provides a systematization of the family of relational notions and generates a simple equational calculus for proving elementary identities between them, thus trivializing a large part of the Theory of fuzzy relations.

  • Relations in Fuzzy Class Theory
    Fuzzy Sets and Systems, 2008
    Co-Authors: Libor Běhounek, Ulrich Bodenhofer, Petr Cintula
    Abstract:

    This paper studies fuzzy relations in the graded framework of Fuzzy Class Theory (FCT). This includes (i) rephrasing existing work on graded properties of binary fuzzy relations in the framework of Fuzzy Class Theory and (ii) generalizing existing crisp results on fuzzy relations to the graded framework. Our particular aim is to demonstrate that Fuzzy Class Theory is a powerful and easy-to-use instrument for handling fuzzified properties of fuzzy relations. This paper does not rephrase the whole Theory of (fuzzy) relations; instead, it provides an illustrative introduction showing some representative results, with a strong emphasis on fuzzy preorders and fuzzy equivalence relations.

  • Fuzzy Class Theory
    Fuzzy Sets and Systems, 2005
    Co-Authors: Libor Běhounek, Petr Cintula
    Abstract:

    The paper introduces a simple, yet powerful axiomatization of Zadeh's notion of fuzzy set, based on formal fuzzy logic. The presented formalism is strong enough to serve as foundations of a large part of fuzzy mathematics. Its essence is elementary fuzzy set Theory, cast as two-sorted first-order Theory over fuzzy logic, which is generalized to simple type Theory. We show a reduction of the elementary fuzzy set Theory to fuzzy propositional calculus and a general method of fuzzification of Classical mathematical theories within this formalism. In this paper we restrict ourselves to set relations and operations that are definable without any structure on the universe of objects presupposed; however, we also demonstrate how to add structure to the universe of discourse within our framework.

  • IFSA (1) - Topology in Fuzzy Class Theory: Basic Notions
    Lecture Notes in Computer Science, 1
    Co-Authors: Libor Běhounek, Tomáš Kroupa
    Abstract:

    In the formal and fully graded setting of Fuzzy Class Theory (or higher-order fuzzy logic) we make an initial investigation into basic notions of fuzzy topology. In particular we study graded notions of fuzzy topology regarded as a fuzzy system of open or closed fuzzy sets and as a fuzzy system of fuzzy neighborhoods. We show their basic graded properties and mutual relationships provable in Fuzzy Class Theory and give some links to the traditional notions of fuzzy topology.

Michał Lenartowicz - One of the best experts on this subject based on the ideXlab platform.