Generalizations of Information Granules

  • Andrzej Bargiela
  • Witold Pedrycz
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 717)


In this chapter, we discuss various extensions of the fundamental formal environments of granular computing and elaborate on a series of synergistic interactions arising between them. The first trend is motivated by the complexity and diversity of the granular aspect of information. The second category of developments is motivated by a multifaceted nature of information granularity that usually embraces several dimensions of such concept.


Membership Function Fuzzy Relation Membership Grade Information Granule Granular Computing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Atanassov, K. (1986), Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87–96.MathSciNetMATHCrossRefGoogle Scholar
  2. Atanassov, K. (1994), New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61, 137–142.MathSciNetMATHCrossRefGoogle Scholar
  3. Chen, S.M., Hsiao, W.H., Jong, W.T. (1997), Bidirectional approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems, 91, 339–353.MathSciNetMATHCrossRefGoogle Scholar
  4. Dubois, D., Prade, H.(1992), Rough fuzzy sets and fuzzy rough sets, Int. J. General Systems, 17, 203–232.MathSciNetGoogle Scholar
  5. Gorzalczany, M.B. (1987), A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems, 21, 1–17.MathSciNetMATHCrossRefGoogle Scholar
  6. Hirota, H. (1981), Concepts of probabilistic sets, Fuzzy Sets & Systems, 5, 31–46.MathSciNetMATHCrossRefGoogle Scholar
  7. Karnik, N.N., Mendel, J.M. (2001), Operations on type-2 fuzzy sets, Fuzzy Sets and Systems, 12, 327–348.MathSciNetCrossRefGoogle Scholar
  8. Mendel, J.M., John, R.I.B. (2002), Type-2 fuzzy sets made simple, IEEE Trans, on Fuzzy Systems, 10(2), 117–127.CrossRefGoogle Scholar
  9. Pawlak, Z. (1982), Rough sets, Int. J. Inform. Comp. Sci., 11(5), 341–356.MathSciNetMATHCrossRefGoogle Scholar
  10. Pedrycz, W. (1998), Shadowed sets: representing and processing fuzzy sets, IEEE Trans, on Systems, Man, and Cybernetics, part B, 28, 103–109.Google Scholar
  11. Pedrycz, W. (1999), Shadowed sets: bridging fuzzy and rough sets, In: Pal, S. K., Skowron A.(eds.), Rough Fuzzy Hybridization. A New Trend in Decision-Making, Springer Verlag, Singapore, pp. 179–199.Google Scholar
  12. Szmidt, E., Kacprzyk, J. (2000), Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, 114, 505–518MathSciNetMATHCrossRefGoogle Scholar
  13. Zadeh, L.A. (1968), Probability of fuzzy events, J. Math. Anal and Appl., 22, 421–427.MathSciNetCrossRefGoogle Scholar
  14. Zimmermann, H.J. (2001), Fuzzy Set Theory and Its Applications, 4th Edition, Kluwer Academic Publishers, Boston, Dordercht.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Andrzej Bargiela
    • 1
  • Witold Pedrycz
    • 2
  1. 1.The Nottingham Trent UniversityNottinghamUK
  2. 2.University of AlbertaEdmontonCanada

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