Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Soft Computing
Erschienen in: Soft Computing 12/2011

01.12.2011 | Original Paper

On a generalization of the concept of state property system

verfasst von: Sergey A. Solovyov

Erschienen in: Soft Computing | Ausgabe 12/2011

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Based in the notions of topological system of S. Vickers and lattice-valued topological space of S.E. Rodabaugh, the paper introduces a generalization of the concepts of state property system of D. Aerts and closure space (used by many authors in the literature), showing that the categories of the new structures are equivalent.
Vorheriger Artikel Fuzzy XNOR connectives in fuzzy logic
Nächster Artikel Lattice pseudoeffect algebras as double residuated structures

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
Adámek J, Herrlich H, Strecker GE (2006) Abstract and concrete categories: the joy of cats. Repr Theory Appl Categ 17:1–507
Aerts D (1981) The One and the Many. Ph.D. thesis, Free University of Brussels, Brussels
Aerts D (1982) Description of many physical entities without the paradoxes encountered in quantum mechanics. Found Phys 12:1131–1170MathSciNetCrossRef
Aerts D (1983) Classical theories and non classical theories as a special case of a more general theory. J Math Phys 24:2441–2454MathSciNetCrossRef
Aerts D (1999) Foundations of quantum physics: a general realistic and operational approach. Int J Theor Phys 38(1):289–358MathSciNetMATHCrossRef
Aerts D, Colebunders E, van der Voorde A, van Steirteghem B (1999) State property systems and closure spaces: a study of categorical equivalence. Int J Theor Phys 38(1):359–385MATHCrossRef
Aerts D, Colebunders E, van der Voorde A, van Steirteghem B (2002) On the amnestic modification of the category of state property systems. Appl Categ Struct 10(5):469–480MATHCrossRef
Barr M (1979) *-Autonomous categories. Springer, Berlin
Birkhoff G (1935) On the structure of abstract algebras. Proc Camb Philos Soc 31:433–454CrossRef
Cohn PM (1981) Universal algebra. D Reidel Publishing Company, Dordrecht
Denniston JT, Rodabaugh SE (2009) Functorial relationships between lattice-valued topology and topological systems. Quaest Math 32(2):139–186MathSciNetMATHCrossRef
Denniston JT, Melton A, Rodabaugh SE (2009) Lattice-valued topological systems. In: Bodenhofer U, De Baets B, Klement EP, Saminger-Platz S (eds) Abstracts of the 30th Linz seminar on fuzzy set theory. Johannes Kepler Universität, Linz, pp 24–31
Dikranjan D, Giuli E, Toi A (1988) Topological categories and closure operators. Quaest Math 11(3):323–337MATHCrossRef
Eklund P (1986a) A comparison of lattice-theoretic approaches to fuzzy topology. Fuzzy Sets Syst 19:81–87MathSciNetMATH
Eklund P (1986b) Categorical fuzzy topology. Ph.D. thesis, ÅboAkademi
Erné M (1984) Lattice representations for categories of closure spaces. In: Proceedings of the international conference on categorical topology, Toledo/Ohio 1983. Sigma Ser Pure Math, vol 5, pp 197–222
Faure CA (1994) Categories of closure spaces and corresponding lattices. Cah Topologie Géom Différ Catég 35(4):309–319MathSciNetMATH
Ganter B, Wille R (1996) Formale Begriffsanalyse. Mathematische Grundlagen. Springer, BerlinMATH
Guido C (2009) Attachment between fuzzy points and fuzzy sets. In: Bodenhofer U, De Baets B, Klement EP, Saminger-Platz S (eds) Abstracts of the 30th Linz seminar on fuzzy set theory. Johannes Kepler Universität, Linz, pp 52–54
Höhle U, Šostak AP (1999) Axiomatic foundations of fixed-basis fuzzy topology. In: Höhle U, Rodabaugh SE (eds) Mathematics of fuzzy sets: logic, topology and measure theory, The handbooks of fuzzy sets series, vol 3. Kluwer, Dordrecht, pp 123–272
Jauch JM (1968) Foundations of quantum mechanics. Addison-Wesley, Reading
Johnstone PT (1982) Stone spaces. Cambridge University Press, Cambridge
Kelley JL (1975) General topology. Springer, Berlin
Kruml D, Paseka J (2008) Algebraic and Categorical Aspects of Quantales. In: Hazewinkel M (ed) Handbook of Algebra, vol 5. Elsevier, Amsterdam, pp. 323–362
Linton FEJ (1966) Some aspects of equational categories. Proc Conf Categor Algebra La Jolla 1965:84–94MathSciNet
Mac Lane S (1998) Categories for the working mathematician 2nd edn. Springer, Berlin
Manes EG (1976) Algebraic theories. Springer, Berlin
Moore DJ (1995) Categories of representations of physical systems. Helv Phys Acta 68:658–678MathSciNetMATH
Moore DJ (1999) On state spaces and property lattices. Stud Hist Phil Mod Phys 30:61–83MATHCrossRef
Papert D, Papert S (1959) Sur les treillis des ouverts et les paratopologies. Semin. de Topologie et de Geometrie differentielle Ch. Ehresmann 1 (1957/58), vol 1, pp 1–9
Paseka J (1999) Quantale Modules. Habilitation Thesis, Department of Mathematics, Faculty of Science, Masaryk University Brno
Piron C (1976) Foundations of quantum physics. W. A. Benjamin, Inc, New York
Piron C (1988) Recent developments in quantum mechanics. Helv Phys Acta 62(1):82–90MathSciNet
Piron C (1990) Mécanique Quantique: Bases et Applications. Presses Polytechniques et Universitaires Romandes, LausanneMATH
Pratt V (1999) Chu spaces. School on category theory and applications. In: Lecture notes of courses, Coimbra, Portugal, July 13–17, 1999. Textos Mat., Sér. B. vol 21. Universidade de Coimbra, Departamento de Matemática, Coimbra, pp 39–100
Resende P (1995) Observational system specification. In: Wieringa R, Feenstra R (eds) Selected papers of ISCORE’94. World Scientific, Singapore, pp 135–151
Rodabaugh SE (1997) Powerset operator based foundation for point-set lattice-theoretic (poslat) fuzzy set theories and topologies. Quaest Math 20(3):463–530MathSciNetMATHCrossRef
Rodabaugh SE (1999a) Categorical foundations of variable-basis fuzzy topology. In: Höhle U, Rodabaugh SE (eds) Mathematics of fuzzy sets: logic, topology and measure theory. The handbooks of fuzzy sets series, vol 3. Kluwer, Dordrecht, pp 273–388
Rodabaugh SE (1999b) Powerset operator foundations for poslat fuzzy set theories and topologies. In: Höhle U, Rodabaugh SE (eds) Mathematics of fuzzy sets: logic, topology and measure theory, The Handbooks of fuzzy sets series, vol 3. Kluwer, Dordrecht, pp 91–116
Rodabaugh SE (2007) Relationship of algebraic theories to powerset theories and fuzzy topological theories for lattice-valued mathematics. Int J Math Math Sci 2007:1–71MathSciNetCrossRef
Rosenthal KI (1990) Quantales and their applications. In: Pitman research notes in mathematics series, vol 234. Longman, London
Rosický J (1981) Equational categories. Cah Topol Géom Différ 22:85–95MATH
Solovjovs S (2008) On a categorical generalization of the concept of fuzzy set: basic definitions, properties, examples. VDM Publishing, Germany
Solovjovs S (2009a) On a coalgebraic category of variety-based topological systems. In: Abstracts of the 4th international conference on topology, algebra and categories in logic. Inst. for Logic, Language and Computation, Amsterdam
Solovjovs S (2009b) Embedding topology into algebra. In: Bodenhofer U, De Baets B, Klement EP, Saminger-Platz S (eds) Abstracts of the 30th Linz seminar on fuzzy set theory. Johannes Kepler Universität, Linz, pp 106–110
Solovjovs S (2009c) Limits and colimits of variable-basis topological systems. In: Abstracts of applications of algebra XIII. Institute of Mathematics and Computer Science of Jan Długosz University, pp 38–41
Solovyov S (2008a) Categorical frameworks for variable-basis sobriety and spatiality. Math Stud (Tartu) 4:89–103MathSciNet
Solovyov S (2010) Variable-basis topological systems versus variable-basis topological spaces. Soft Comput 14(10):1059–1068MATHCrossRef
Solovyov S (2011a) Localification of variable-basis topological systems. Quaest Math (in press)
Solovyov S (2011b) On algebraic and coalgebraic categories of variety-based topological systems. Iran J Fuzzy Syst (in press)
Van der Voorde A (2000) A categorical approach to T 1 separation and the product of state property systems. Int J Theor Phys 39(3):947–953MathSciNetMATHCrossRef
Vickers S (1989) Topology via logic. Cambridge University Press, Cambridge
Metadaten
Titel
On a generalization of the concept of state property system
verfasst von
Sergey A. Solovyov
Publikationsdatum
01.12.2011
Verlag
Springer-Verlag
Erschienen in
Soft Computing / Ausgabe 12/2011
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-011-0709-0

Weitere Artikel der Ausgabe 12/2011

Soft Computing 12/2011 Zur Ausgabe

Focus

Learning knowledge bases of multi-objective evolutionary fuzzy systems by simultaneously optimizing accuracy, complexity and partition integrity

Original Paper

Lattice pseudoeffect algebras as double residuated structures

Original Paper

Torsion elements in effect algebras

Focus

Special issue on evolutionary fuzzy systems

Focus

Evolutionary fuzzy rule extraction for subgroup discovery in a psychiatric emergency department

Original Paper

Fuzzy XNOR connectives in fuzzy logic

Premium Partner

    Bildnachweise