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Good fuzzy preorders on fuzzy power structures

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This paper deals with good fuzzy preorders on fuzzy power structures. It is shown that a fuzzy preorder R on an algebra \({(X,\mathbb{F})}\) is compatible if and only if it is Hoare good, if and only if it is Smyth good.

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References

  1. Bělohlávek R.: Fuzzy Relational Systems, Foundations and Principles. Kluwer/Plenum Publishers, New York (2002)

    MATH  Google Scholar 

  2. Bělohlávek R., Vychodil V.: Algebras with fuzzy equalities. Fuzzy Sets Syst. 157, 161–201 (2006)

    Article  MATH  Google Scholar 

  3. Bošnjak I., Madaráz R.: Good quotient algebras and power algebras. Novi Sad J. Math. 29, 71–84 (1999)

    MathSciNet  Google Scholar 

  4. Bošnjak I., Madaráz R.: Power algebras and generalized quotient algebras. Algebra Univers. 45, 179–189 (2001)

    MATH  Google Scholar 

  5. Bošnjak I., Madaráz R.: On some classes of good quotient relations. Novi Sad J. Math. 32, 131–140 (2002)

    MATH  MathSciNet  Google Scholar 

  6. Bošnjak I., Madaráz R., Vojvodić G.: Algebras of fuzzy sets. Fuzzy Sets Syst. 160, 2979–2988 (2009)

    Article  MATH  Google Scholar 

  7. Brink C.: Power structures. Algebra Univers. 30, 177–216 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Brink C., Rewitzki I.: A Paradigm for Program Semantics, Power Structures and Duality. CSLI Publications, Stanford (2001)

    Google Scholar 

  9. Georgescu G.: Fuzzy power structures. Arch. Math. Logic 47, 233–261 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Hájek P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)

    MATH  Google Scholar 

  11. Höhle U.: Commutative, residuated l-monoids. In: Höhle, U., Klement, E.P. (eds) Non-classical Logics and Their Applications to Fuzzy Subsets: A Handbook on the Mathematical Foundations of Fuzzy Set Theory, pp. 53–105. Kluwer, Dordrecht (1995)

    Google Scholar 

  12. Kelly, G. M.: Basic Concepts of Enriched Category Theory, London Mathematical Soceity Lecture Notes Series 64, Cambridge University Press (1982)

  13. Lai H., Zhang D.: Complete and directed complete Ω-categories. Theor. Comput. Sci. 388, 1–25 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  14. Lawvere F.W.: Metric spaces, generalized logic, and closed categories. Rendiconti del Seminario Matématico e Fisico di Milano 43, 135–166 (1973)

    Article  MathSciNet  Google Scholar 

  15. Madaráz R.: Remarks on power structures. Algebra Univers. 34, 179–184 (1995)

    Article  Google Scholar 

  16. Valverde L.: On the structure of F-indistinguishability operators. Fuzzy Sets Syst. 17, 313–328 (1985)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Hongliang Lai.

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Lai, H., Zhang, D. Good fuzzy preorders on fuzzy power structures. Arch. Math. Logic 49, 469–489 (2010). https://doi.org/10.1007/s00153-010-0181-z

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  • DOI: https://doi.org/10.1007/s00153-010-0181-z

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