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International Conference on Flexible Query Answering Systems

FQAS 2017: Flexible Query Answering Systems pp 201–208Cite as

Multiplicative Type of Operations over Intuitionistic Fuzzy Pairs

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10333))

Abstract

Intuitionistic Fuzzy Sets (IFSs) are an extension of fuzzy sets. Each element x of the IFS A has degrees of a membership (\(\mu _A(x)\)) and of a non-membership (\(\nu _A(x)\)) so that \(0 \le \mu _A(x) + \nu _A(x) \le 1\). The pair \(\langle \mu _A(x), \nu _A(x) \rangle \) is called an Intuitionistic Fuzzy Pair (IFP). A lot of operations, relations and operators are defined over IFPs. In the paper, novel operations over IFPs are introduced and some of their basic properties are studied. Geometrical interpretations of these operations are given. Open problems are formulated.

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References

  1. Atanassov, K.: Intuitionistic Fuzzy Logics. Springer, Cham (2017)

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  2. Atanassov, K., Szmidt, E., Kacprzyk, J.: On intuitionistic fuzzy pairs. Notes Intuitionistic Fuzzy Sets 19(3), 1–13 (2013)

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  3. Buhaescu, T.: Some observations on intuitionistic fuzzy relations. Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj- Napoca, pp. 111- 118 (1989)

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Acknowledgments

The first author is thankful for the support provided by the Bulgarian National Science Fund under Grant Ref. No. DFNI-I-02-5.

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Authors and Affiliations

  1. Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., 1113, Sofia, Bulgaria

    Krassimir Atanassov

  2. Intelligent Systems Laboratory Prof. Asen Zlatarov University, 8010, Burgas, Bulgaria

    Krassimir Atanassov

  3. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Eulalia Szmidt & Janusz Kacprzyk

  4. Warsaw School of Information Technology, ul. Newelska 6, 01-447, Warsaw, Poland

    Eulalia Szmidt & Janusz Kacprzyk

Authors
  1. Krassimir Atanassov
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  2. Eulalia Szmidt
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  3. Janusz Kacprzyk
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Corresponding authors

Correspondence to Krassimir Atanassov , Eulalia Szmidt or Janusz Kacprzyk .

Editor information

Editors and Affiliations

  1. Roskilde University, Roskilde, Denmark

    Henning Christiansen

  2. ENSSAT-IRISA, Lannion Cedex, France

    Hélène Jaudoin

  3. University of Westminster, London, United Kingdom

    Panagiotis Chountas

  4. Roskilde University, Roskilde, Denmark

    Troels Andreasen

  5. Aalborg University, Esbjerg, Denmark

    Henrik Legind Larsen

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© 2017 Springer International Publishing AG

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Atanassov, K., Szmidt, E., Kacprzyk, J. (2017). Multiplicative Type of Operations over Intuitionistic Fuzzy Pairs. In: Christiansen, H., Jaudoin, H., Chountas, P., Andreasen, T., Legind Larsen, H. (eds) Flexible Query Answering Systems. FQAS 2017. Lecture Notes in Computer Science(), vol 10333. Springer, Cham. https://doi.org/10.1007/978-3-319-59692-1_17

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  • DOI: https://doi.org/10.1007/978-3-319-59692-1_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59691-4

  • Online ISBN: 978-3-319-59692-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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