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Towards Fuzzy Partial Set Theory

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 611))

Abstract

We sketch a simple theory of fuzzy partial sets, i.e., fuzzy sets that can have undefined membership degrees. The theory is developed in the semantic framework of a first-order extension of the recently proposed fuzzy partial propositional logic. We introduce a selection of basic notions of fuzzy partial set theory, discuss their variants, and present a few initial results on the properties of fuzzy partial class operations and relations.

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References

  1. Běhounek, L., Cintula, P.: Fuzzy class theory. Fuzzy Sets Syst. 154(1), 34–55 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Běhounek, L., Cintula, P., Hájek, P.: Introduction to mathematical fuzzy logic. In: Cintula, P., Hájek, P., Noguera, C. (eds.) Handbook of Mathematical Fuzzy Logic, pp. 1–101. College Publications (2011)

    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. IEEE (2015)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. Dubois, D.: Reasoning about ignorance and contradiction: many-valued logics versus epistemic logic. Soft Comput. 16, 1817–1831 (2012)

    Article  MATH  Google Scholar 

  6. Gottwald, S.: A Treatise on Many-Valued Logics. Research Studies Press, Baldock (2001)

    MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  8. Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Boston (1999)

    Book  MATH  Google Scholar 

  9. Rasiowa, H.: An Algebraic Approach to Non-Classical Logics. North-Holland, Amsterdam (1974)

    MATH  Google Scholar 

  10. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

The work was supported by grant No. 16–191705 “Fuzzy partial logic” of GA ČR and project LQ1602 “IT4I XS” of MŠMT ČR.

Author information

Authors and Affiliations

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

    Libor Běhounek & Martina Daňková

Authors
  1. Libor Běhounek
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  2. Martina Daňková
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Corresponding author

Correspondence to Martina Daňková .

Editor information

Editors and Affiliations

  1. INESC-ID,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Joao Paulo Carvalho

  2. LIP 6, Université Pierre et Marie Curie, Paris, France

    Marie-Jeanne Lesot

  3. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  4. IDMEC,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Susana Vieira

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Iona College, Machine Intelligence Institute, New Rochelle, New York, USA

    Ronald R. Yager

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© 2016 Springer International Publishing Switzerland

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Běhounek, L., Daňková, M. (2016). Towards Fuzzy Partial Set Theory. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 611. Springer, Cham. https://doi.org/10.1007/978-3-319-40581-0_39

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  • DOI: https://doi.org/10.1007/978-3-319-40581-0_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40580-3

  • Online ISBN: 978-3-319-40581-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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