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Compatible and Complementary Fuzzy Partitions

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Advances in Data Science and Classification

Abstract

Fuzzy partitions with large (small) coefficients at the same locations are considered to be compatible. We investigate to what extent two or more fuzzy partitions are compatible and to what extent two fuzzy partitions are complementary. Linguistic expressions large and small are defined by comparison with a threshold α ∈ (0, 1). We discuss how to find α at which two or more fuzzy partitions are compatible and how to find α at which two fuzzy partitions are complementary. Then we explain how α-compatibility and α-complementarity can be used in decision making.

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References

  • Bezdek, J. C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York. Bodjanova, S. (1997). Aggregation Operations on Fuzzy Partitions, in: IFSA’97 Proceedings, Mares et al. (Eds.), Academia, Prague, 181–186.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX, 78363, USA

    Slavka Bodjanova

Authors
  1. Slavka Bodjanova
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Editor information

Editors and Affiliations

  1. Dipartimento di Statisticà, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185, Roma, Italia

    Alfredo Rizzi

  2. Dipartimento di Metodi Quantitativi e Teoria Economica, Università “G. D’Annunzio” di Chieti, Viale Pindaro 42, I-65127, Pescara, Italia

    Maurizio Vichi

  3. Institut für Statistik und Wirtschaftsmathematik, Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen, Wüllnerstraße 3, D-52056, Aachen, Germany

    Hans-Hermann Bock

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© 1998 Springer-Verlag Berlin · Heidelberg

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Bodjanova, S. (1998). Compatible and Complementary Fuzzy Partitions. In: Rizzi, A., Vichi, M., Bock, HH. (eds) Advances in Data Science and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72253-0_13

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  • DOI: https://doi.org/10.1007/978-3-642-72253-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64641-9

  • Online ISBN: 978-3-642-72253-0

  • eBook Packages: Springer Book Archive

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