Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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AN ALGEBRAIC OPERATIONS FOR TWO GENERALIZED 2-DIMENSIONAL QUADRATIC FUZZY SETS

  • Yun, Yong Sik (Department of Mathematics and Research Institute for Basic Sciences Jeju National University)
  • Received : 2018.06.27
  • Accepted : 2018.09.10
  • Published : 2018.11.15
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Abstract

We generalized the quadratic fuzzy numbers on ${\mathbb{R}}$ to ${\mathbb{R}}_2$. By defining parametric operations between two regions valued ${\alpha}-cuts$, we got the parametric operations for two triangular fuzzy numbers defined on ${\mathbb{R}}_2$. The results for the parametric operations are the generalization of Zadeh's extended algebraic operations. We generalize the 2-dimensional quadratic fuzzy numbers on ${\mathbb{R}}_2$ that may have maximum value h < 1. We calculate the algebraic operations for two generalized 2-dimensional quadratic fuzzy sets.

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References

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  2. A Zadeh's max-min composition operator for two triangular fuzzy numbers defined on ℝ vol.33, pp.5, 2018, https://doi.org/10.14477/jhm.2020.33.5.277