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On Extensional Fuzzy Sets Generated by Factoraggregation

  • Conference paper
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 444))

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Abstract

We develop the concept of a general factoraggregation operator introduced by the authors on the basis of an equivalence relation and applied in two recent papers for analysis of bilevel linear programming solving parameters. In the paper this concept is generalized by using a fuzzy equivalence relation instead of the crisp one. We show how the generalized factoraggregation can be used for construction of extensional fuzzy sets and consider approximations of arbitrary fuzzy sets by extensional ones.

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References

  1. Calvo, T., Mayor, G., Mesiar, R.: Aggregation Operators. Physical-Verlag, Heidelberg (2002)

    Book  MATH  Google Scholar 

  2. Detyniecki, M.: Fundamentals on Aggregation Operators, Berkeley (2001)

    Google Scholar 

  3. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press (2009)

    Google Scholar 

  4. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000)

    Book  MATH  Google Scholar 

  5. Mattioli, G., Recasens, J.: Comparison of different algorithms of approximation by extensional fuzzy subsets. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds.) Aggregation Functions in Theory and in Practise. AISC, vol. 228, pp. 307–317. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  6. Morsi, N.N., Yakout, M.M.: Axiomatics for fuzzy rough sets. Fuzzy Sets and Systems 100, 327–342 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Orlovs, P., Montvida, O., Asmuss, S.: A choice of bilevel linear programming solving parameters: factoraggregation approach. In: Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology. Advances in Intelligent Systems Research, vol. 32, pp. 489–496 (2013)

    Google Scholar 

  8. Orlovs, P., Montvida, O., Asmuss, S.: An analysis of bilevel linear programming solving parameters based on factoraggregation approach. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds.) Aggregation Functions in Theory and in Practise. AISC, vol. 228, pp. 345–354. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  9. Takaci, A.: General aggregation operators acting on fuzzy numbers induced by ordinary aggregation operators. Novi Sad J. Math. 33(2), 67–76 (2003)

    MATH  MathSciNet  Google Scholar 

  10. Zadeh, L.: Similarity relations and fuzzy ordering. Inform. Sci. 3(2), 177–200 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  11. Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems 1, 45–55 (1978)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, University of Latvia, Raina blvd. 29, Riga, LV-1459, Latvia

    Pavels Orlovs & Svetlana Asmuss

Authors
  1. Pavels Orlovs
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  2. Svetlana Asmuss
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Editor information

Editors and Affiliations

  1. University Montpellier 2, LIRMM - CNRS UMR 5506, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Anne Laurent

  2. Institute for Human Factors and Technology Management, IAT, University of Stuttgart, Nobelstraße 12, 70569, Stuttgart, Germany

    Oliver Strauss

  3. LIP6, UPMC Univ. Paris 06, CNRS UMR 7606, F-75005, Paris, France

    Bernadette Bouchon-Meunier

  4. Dept. of Information Systems, Iona College, 710 North Ave, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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Orlovs, P., Asmuss, S. (2014). On Extensional Fuzzy Sets Generated by Factoraggregation. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 444. Springer, Cham. https://doi.org/10.1007/978-3-319-08852-5_33

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  • DOI: https://doi.org/10.1007/978-3-319-08852-5_33

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08851-8

  • Online ISBN: 978-3-319-08852-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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