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2-Dimensional Expansion of Quadratic Fuzzy Numbers through Calculation and Graph

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주제분류수학

초록

We compute the extended four operations of the 2-dimensional quadratic fuzzy numbers. Then we calculate the intersection between a plane perpendicular to the x-axis, which passes through each vertex, and the resulting 2-dimensional quadratic fuzzy number. We confirm that the equations of the two intersections acquired in this way and the graphs are actually identical, respectively.

Abstract

We compute the extended four operations of the 2-dimensional quadratic fuzzy numbers. Then we calculate the intersection between a plane perpendicular to the x-axis, which passes through each vertex, and the resulting 2-dimensional quadratic fuzzy number. We confirm that the equations of the two intersections acquired in this way and the graphs are actually identical, respectively.

참고문헌 (9)

  1. 변지수, "Parametric operations for two fuzzy numbers", 대한수학회논문집, 28(3), pp.635~642 (2013), 대한수학회
  2. C. Kang, "A Zadehs max-min composition operator for two 2-dimensional quadratic fuzzy numbers", Far East Journal of Mathematical Sciences, 101(10), pp.2185~2193 (2017)
  3. C. Kang, "An extension of Zadeh's max-min composition operator", Inter-national Journal of Mathematical Analysis, 9(41), pp.2029~2035 (2015)
  4. C. Kim, "Parametric operations for generalized 2-dimensional triangular fuzzy sets", International Journal of Mathematical Analysis, 11(4), pp.189~197 (2017)
  5. 김창일, "Zadeh's extension principle for 2-dimensional triangular fuzzy numbers", 한국지능시스템학회 논문지, 25(2), pp.197~202 (2015), 한국지능시스템학회
  6. H. S. Ko, "An extension of algebraic operations for 2-dimensional quadratic fuzzy number", Far East Journal of Mathematical Sciences, 103(12), pp.2007~2015 (2018)
  7. 송재충, "Normal fuzzy probability and exponential fuzzy probability for various fuzzy numbers", 박사, 수학, pp.2006
  8. 윤용식, "The Extended Operations for Generalized Quadratic Fuzzy Sets", 한국지능시스템학회 논문지, 20(4), pp.592~595 (2010), 한국지능시스템학회
  9. L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-I", Information Sciences, 8, pp.199~249 (1975)

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