충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제31권4호
  • /
  • Pages.379-386
  • /
  • 2018
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

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)
  • 투고 : 2018.06.27
  • 심사 : 2018.09.10
  • 발행 : 2018.11.15
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

  1. J. Byun and Y. S. Yun, Parametric operations for two fuzzy numbers, Communications of Korean Mathematical Society, 28 (2013), no. 3, 635-642. https://doi.org/10.4134/CKMS.2013.28.3.635
  2. C. Kang and Y. S. Yun, An extension of Zadehs max-min composition operator, International Journal of Mathematical Analysis, 9 (2015), no. 41, 2029-2035. https://doi.org/10.12988/ijma.2015.55154
  3. C. Kang and Y. S. Yun, A Zadehs max-min composition operator for two 2- dimensional quadratic fuzzy numbers, Far East Journal of Mathematical Sciences, 101 (2017), no. 10, 2185-2193. https://doi.org/10.17654/MS101102185
  4. C. Kim and Y. S. Yun, Zadeh's extension principle for 2-dimensional triangular fuzzy numbers, Journal of The Korean Institute of Intelligent Systems, 25 (2015), no. 2, 197-202. https://doi.org/10.5391/JKIIS.2015.25.2.197
  5. H. S. Ko and Y. S. Yun, An extension of algebraic operations for 2-dimensional quadratic fuzzy number, Far East Journal of Mathematical Sciences, 103 (2018), no. 12, 2007-2015. https://doi.org/10.17654/MS103122007
  6. B. J. Lee and Y. S. Yun, The generalized trapezoidal fuzzy sets, Journal of the Chungcheong Mathematical Society, 24 (2011), no. 2, 253-266.
  7. Y. S. Yun and B. J. Lee, The one-sided quadrangular fuzzy sets, Journal of the Chungcheong Mathematical Society, 26 (2013), no. 2, 297-308. https://doi.org/10.14403/jcms.2013.26.2.297
  8. H. J. Zimmermann, Fuzzy set Theory - and Its Applications, Kluwer-Nijhoff Publishing, Boston-Dordrecht-Lancaster, 1985.

피인용 문헌

  1. A Zadeh′s max-min composition operator for 3-dimensional triangular fuzzy number vol.39, pp.3, 2018, https://doi.org/10.3233/jifs-192095
  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