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Undefined Values in Fuzzy Logic

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Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 642))

Abstract

The main objective of this paper is to propose an extended algebra of truth values by special truth values which may have several interpretations, such as “undefined”, “non-applicative” “overdetermined”, “undetermined”, etc. In this paper, we will analyze several situations, where the non-existent data may come from, and show within a fuzzy sets framework that different cases of non-existence have to be carefully treated and interpreted in a different way.

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Notes

  1. 1.

    By \(\mathcal {M}\) we denote a structure which interprets formulas.

References

  1. Lukasiewicz, J.: O logice trojwartosciowej. Ruch filozoficzny 5, 170–171 (1920)

    Google Scholar 

  2. Malinowski, G.: The Many Valued and Nonmonotonic Turn in Logic. North-Holland, Amsterdam (2007)

    Google Scholar 

  3. Běhounek, L., Novák, V.: Towards fuzzy partial logic. In: Proceedings of the IEEE 45th International Symposium on Multiple-Valued Logics (ISMVL 2015), pp. 139–144 (2015)

    Google Scholar 

  4. Běhounek, L., Daňková, M.: Towards fuzzy partial set theory. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016), pp. 482–494 (2016)

    Google Scholar 

  5. Esteva, F., Garcia-Calvés, P., Godo, L.: Enriched interval bilattices and partial many-valued logics: an approach to deal with graded truth and imprecision. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 02, 37–54 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gasse, B.V., Cornelis, C., Deschrijver, G., Kerre, E.: A characterization of interval-valued residuated lattices. Int. J. Approx. Reasoning 49, 478–487 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hájek, P.: On vagueness, truth values and fuzzy logic. Studia Logica 91, 367–382 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  9. Ciucci, D., Dubois, D.: A map of dependencies among three-valued logics. Inf. Sci. 250, 162–177 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  Google Scholar 

  11. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning - I. Inf. Sci. 8(3), 199–249 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  12. Grattan-Guiness, I.: Fuzzy membership mapped onto interval and many-valued quantities. Z. Math. Logik. Grundladen Math. 22, 149–160 (1975)

    Article  MathSciNet  Google Scholar 

  13. Jahn, K.U.: Intervall-wertige mengen. Math. Nach. 68, 115–132 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  14. Murinová, P., Burda, M.: Linguistic characterization of natural data by applying intermediate quantifiers on fuzzy association rules. J. Fuzzy Set Valued Anal. (2017). Accepted

    Google Scholar 

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Acknowledgements

Authors acknowledge support by project “LQ1602 IT4Innovations excellence in science” and by GAČR 16-19170S.

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Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modeling, CE IT4Innovations, Division University of Ostrava, 30. Dubna 22, 701 03, Ostrava, Czech Republic

    Petra Murinová, Michal Burda & Viktor Pavliska

Authors
  1. Petra Murinová
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  2. Michal Burda
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  3. Viktor Pavliska
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Corresponding author

Correspondence to Petra Murinová .

Editor information

Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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

    Eulalia Szmidt

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Slawomir Zadrożny

  4. Department of Telecommunications and Information Processing, Bulgarian Academy of Sciences, Sofia, Bulgaria

    K. T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

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Murinová, P., Burda, M., Pavliska, V. (2018). Undefined Values in Fuzzy Logic. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 642. Springer, Cham. https://doi.org/10.1007/978-3-319-66824-6_53

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  • DOI: https://doi.org/10.1007/978-3-319-66824-6_53

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66823-9

  • Online ISBN: 978-3-319-66824-6

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