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The Formal Construction of Fuzzy Numbers Cover

The Formal Construction of Fuzzy Numbers

Formalized Mathematics
Volume 22 (2014): Issue 4 (December 2014)
By: Adam Grabowski  
Open Access
|Dec 2014

References

  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
    Search in Google Scholar
  2. [2] Józef Białas. Properties of the intervals of real numbers. Formalized Mathematics, 3(2): 263-269, 1992.
    Search in Google Scholar
  3. [3] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
    Search in Google Scholar
  4. [4] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
    Search in Google Scholar
  5. [5] Czesław Bylinski. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521-527, 1990.
    Search in Google Scholar
  6. [6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
    Search in Google Scholar
  7. [7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
    Search in Google Scholar
  8. [8] Didier Dubois and Henri Prade. Operations on fuzzy numbers. International Journal of System Sciences, 9(6):613-626, 1978.10.1080/00207727808941724
    Search in Google Scholar
  9. [9] Didier Dubois and Henri Prade. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980.
    Search in Google Scholar
  10. [10] Didier Dubois and Henri Prade. Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems, 17(2-3):191-209, 1990.10.1080/03081079008935107
    Search in Google Scholar
  11. [11] Adam Grabowski. Efficient rough set theory merging. Fundamenta Informaticae, 135(4): 371-385, 2014. doi:10.3233/FI-2014-1129.10.3233/FI-2014-1129
    Search in Google Scholar
  12. [12] Adam Grabowski. On the computer certification of fuzzy numbers. In M. Ganzha, L. Maciaszek, and M. Paprzycki, editors, 2013 Federated Conference on Computer Science and Information Systems (FedCSIS), Federated Conference on Computer Science and Information Systems, pages 51-54, 2013.
    Search in Google Scholar
  13. [13] Adam Grabowski. Basic properties of rough sets and rough membership function. Formalized Mathematics, 12(1):21-28, 2004.
    Search in Google Scholar
  14. [14] Takashi Mitsuishi, Noboru Endou, and Yasunari Shidama. The concept of fuzzy set and membership function and basic properties of fuzzy set operation. Formalized Mathematics, 9(2):351-356, 2001.
    Search in Google Scholar
  15. [15] Takashi Mitsuishi, Katsumi Wasaki, and Yasunari Shidama. Basic properties of fuzzy set operation and membership function. Formalized Mathematics, 9(2):357-362, 2001.
    Search in Google Scholar
  16. [16] Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990.
    Search in Google Scholar
  17. [17] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
    Search in Google Scholar
  18. [18] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990.
    Search in Google Scholar
  19. [19] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.
    Search in Google Scholar
  20. [20] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
    Search in Google Scholar
  21. [21] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
    Search in Google Scholar
  22. [22] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
    Search in Google Scholar
  23. [23] Lotfi Zadeh. Fuzzy sets. Information and Control, 8(3):338-353, 1965. 10.1016/S0019-9958(65)90241-X
    Search in Google Scholar
DOI: https://doi.org/10.2478/forma-2014-0032 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
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Language: English
Page range: 321 - 327
Submitted on: Dec 31, 2014
|
Published on: Dec 31, 2014
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
fuzzy sets,
formal models of fuzzy sets,
triangular fuzzy numbers
Related subjects:
Computer sciences,
Computer sciences, other,
Mathematics,
General mathematics

© 2014 Adam Grabowski, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

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