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Modalities Based on Double Negation

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New Trends in Aggregation Theory (AGOP 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 981))

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Abstract

Modal operators play an important role in fuzzy theory, and in recent years researchers have devoted more effort on this topic. Here we concentrate on continuous strictly monotonously increasing Archimedian t-norms. In our study, we will construct modal operators related to negation operators and we introduce graded modal operators.

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References

  1. Cintula, P., Klement, E.P., Mesiar, R., Navara, M.: Fuzzy logics with an additional involutive negation. Fuzzy Sets Syst. 161, 390–411 (2010)

    Article  MathSciNet  Google Scholar 

  2. Dombi, J.: Towards a general class of operators for fuzzy systems. IEEE Trans. Fuzzy Syst. 16, 477–484 (2008)

    Article  Google Scholar 

  3. Dombi, J.: De Morgan systems with an infinitely many negations in the strict monotone operator case. Inf. Sci. 181, 1440–1453 (2011)

    Article  Google Scholar 

  4. Dombi, J.: On a certain class of aggregative operators. Inf. Sci. 245(1), 313–328 (2013)

    Article  MathSciNet  Google Scholar 

  5. Esteva, F., Godo, L., Hájek, P., Navara, M.: Residuated fuzzy logics with an involutive negation. Arch. Math. Log. 39(2), 103–124 (2000)

    Article  MathSciNet  Google Scholar 

  6. Esteva, F., Godo, L., Noguera, C.: A logical approach to fuzzy truth hedges. Inf. Sci. 232, 366–385 (2013)

    Article  MathSciNet  Google Scholar 

  7. Gottwald, S., Hájek, P.: Triangular norm-based mathematical fuzzy logics. Logical Algebraic, Analytic and Probabilistic Aspects of Triangular Norms, pp. 275–299 (2005)

    Google Scholar 

  8. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)

    Book  Google Scholar 

  9. Łukasiewicz, J.: Two-valued logic. Przeglad Filozoficzny 13, 189–205 (1921)

    MATH  Google Scholar 

  10. Flaminio, T., Marchioni, E.: T-norm-based logics with an independent involutive negation. Fuzzy Sets Syst. 157(24), 3125–3144 (2006)

    Article  MathSciNet  Google Scholar 

  11. Orlowska, E.: A logic of indiscernibility relations. LNCS, vol. 208, pp. 177–186. Springer, Berlin (1985)

    Google Scholar 

  12. Pavelka, J.: On fuzzy logic I. Many-valued rules of inference. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25, 45–52 (1979)

    Article  MathSciNet  Google Scholar 

  13. Trillas, E.: Sobre functiones de negacion en la teoria de conjuntas difusos. Stochastica 3, 47–60 (1979)

    MathSciNet  Google Scholar 

  14. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning, part 1. Inf. Sci. 8, 199–249 (1975)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Szeged, Szeged, Hungary

    József Dombi

Authors
  1. József Dombi
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Correspondence to József Dombi .

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Editors and Affiliations

  1. Faculty of Science, Palacký University, Olomouc, Czech Republic

    Radomír Halaš

  2. Systems Research Institute, Polish Academy of Science, Warsaw, Poland

    Marek Gagolewski

  3. Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

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Dombi, J. (2019). Modalities Based on Double Negation. In: Halaš, R., Gagolewski, M., Mesiar, R. (eds) New Trends in Aggregation Theory. AGOP 2019. Advances in Intelligent Systems and Computing, vol 981. Springer, Cham. https://doi.org/10.1007/978-3-030-19494-9_30

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