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PARAMETRIC OPERATIONS FOR TWO FUZZY NUMBERS

  • Byun, Jisoo (Department of Mathematics Education Kyungnam University) ;
  • Yun, Yong Sik (Department of Mathematics and Research Institute for Basic Sciences Jeju National University)
  • Received : 2012.07.20
  • Published : 2013.07.31

Abstract

There are many results on the extended operations of two fuzzy numbers based on the Zadeh's extension principle. For the calculation, we have to use existing operations between two ${\alpha}$-cuts. In this paper, we define parametric operations between two ${\alpha}$-cuts which are different from the existing operations. But we have the same results as the extended operations of Zadeh's principle.

Acknowledgement

Supported by : Kyungnam University

References

  1. A. Kaufmann and M. M. Gupta, Introduction To Fuzzy Arithmetic, Theory and Applications, Van Nostrand Reinhold Co., New York, 1985.
  2. Y. S. Yun, S. U. Ryu, and J. W. Park, The generalized triangular fuzzy sets, J. Chungcheong Math. Soc. 22 (2009), no. 2, 161-170. https://doi.org/10.5391/JKIIS.2012.22.2.212
  3. L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning. I, Inform. Sci. 8 (1975), 199-249. https://doi.org/10.1016/0020-0255(75)90036-5
  4. H. J. Zimmermann, Fuzzy Set Theory-and Its Applications, Kluwer-Nijhoff Publishing, 1985.

Cited by

  1. Zadeh's extension principle for 2-dimensional triangular fuzzy numbers vol.25, pp.2, 2015, https://doi.org/10.5391/JKIIS.2015.25.2.197