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Compatible and Complementary Fuzzy Partitions

  • Slavka Bodjanova
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

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.

Keywords

Compatibility Complementarity Decision Making Fuzzy Partitions α-Cuts Aggregation 

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References

  1. 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.Google Scholar
  2. Bodjanova, S. (1997). Aggregation Operations on Fuzzy Partitions, in: IFSA’97 Proceedings, Mares et al. (Eds.), Academia, Prague, 181–186.Google Scholar
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  5. Zadeh, L. A. (1965). Fuzzy Sets, Information and Control, 8, 3, 338–353.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • Slavka Bodjanova
    • 1
  1. 1.Department of MathematicsTexas A&M University-KingsvilleKingsvilleUSA

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