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Describing fuzzy sets using a new concept: fuzzify functor

  • Optoelectronics Letters
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Abstract

This paper proposed a fuzzify functor as an extension of the concept of fuzzy sets. The fuzzify functor and the first-order operated fuzzy set are defined. From the theory analysis, it can be observed that when the fuzzify functor acts on a simple crisp set, we get the first order fuzzy set or type-1 fuzzy set. By operating the fuzzify functor on fuzzy sets, we get the higher order fuzzy sets or higher type fuzzy sets and their membership functions. Using the fuzzify functor we can exactly describe the type-1 fuzzy sets, type-2 fuzzy sets and higher type or higher order fuzzy sets. The fuzzify functor makes type-1, type-2 and any fuzzy sets much more accessible to all readers.

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References

  1. L. A. Zadeh, Information and Control, 8 (1965), 338.

    Article  MATH  MathSciNet  Google Scholar 

  2. L. A. zadeh, Information Science, 8 (1975),199.

    Article  MathSciNet  Google Scholar 

  3. J. M. Mendel, IEEE Computational Intelligence Magazine, 2 (2007), 29.

    Article  Google Scholar 

  4. J. M. Mendel, IEEE connections, 1 (2003),10.

    Google Scholar 

  5. F. Masulli, S. Mitra, G. Pasi, Applications of fuzzy sets theory: 7th International Workshop on Fuzzy Logic and Application, WILF 2007, Camogli, Italy, Berlin: Springer, 2007.

    Google Scholar 

  6. J.M. Mendel, Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Upper Saddle River, NJ: Prentice-Hall, 2001.

    MATH  Google Scholar 

  7. W. Pedrycz and F. Gomide, An introduction to fuzzy set: analysis and design, Imprint Cambridge, Mass.: MIT Press, London, 1998.

    Google Scholar 

  8. ZX Wang, YG Sun, ZY Wang, J Qin, XW Sun, HY Shen, Optoelectronics Letters, 2 (2006), 0373.

  9. GR Chen, T.T. Pham, Introduction to fuzzy systems, Boca Raton, FL, Chapman & Hall/CRC, c2006.

  10. N. N. Karnik, J. M. Mendel, and QL Liang, IEEE Transactions On Fuzzy Systems, 7 (1999), 643.

    Article  Google Scholar 

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Authors and Affiliations

  1. Tianjin Key Laboratory of Control Theory & Applications in Complicated Systems, Tianjin University of Technology, Tianjin, 300191, China

    Ke-xin Wei  (魏克新), Zhao-xia Wang  (王兆霞) & Quan Wang  (王权)

  2. Department of Electrical and Computer Engineering, National University of Singapore, Singapore, 119260, Singapore

    Zhao-xia Wang  (王兆霞)

Authors
  1. Ke-xin Wei  (魏克新)
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  2. Zhao-xia Wang  (王兆霞)
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  3. Quan Wang  (王权)
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Corresponding author

Correspondence to Zhao-xia Wang  (王兆霞).

Additional information

This work has been supported in part by the Project of Tianjin Key Laboratory of Control Theory & Applications in Complicated Systems and the Key Project of Tianjin Natural Science Foundation (Grant No. 06YFJMJC01)

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Wei, Kx., Wang, Zx. & Wang, Q. Describing fuzzy sets using a new concept: fuzzify functor. Optoelectron. Lett. 5, 69–72 (2009). https://doi.org/10.1007/s11801-009-8132-9

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  • DOI: https://doi.org/10.1007/s11801-009-8132-9

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