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Three‐Dimensional Expansion and Graphical Concept of Generalized Triangular Fuzzy Set

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  • Yong Sik Yun

Abstract

We have studied the extended algebraic operations between two fuzzy numbers and calculated Zadeh’s max‐min composition operator for two generalized triangular fuzzy sets in ℝ2. And we generalized the triangular fuzzy numbers from ℝ2 to ℝ3. We prove that the result of the three‐dimensional case is an extension of two‐dimensional case and presented it in a graph. The extension is proved by showing that the result obtained by restricting the three‐dimensional result to two‐dimensional result is consistent with the existing two‐dimensional result.

Suggested Citation

  • Yong Sik Yun, 2022. "Three‐Dimensional Expansion and Graphical Concept of Generalized Triangular Fuzzy Set," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:3248127
    DOI: 10.1155/2022/3248127
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    References listed on IDEAS

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    1. Pattrawut Chansangiam, 2015. "A Survey on Operator Monotonicity, Operator Convexity, and Operator Means," International Journal of Analysis, Hindawi, vol. 2015, pages 1-8, November.
    2. Yong Sik Yun & Qingkai Zhao, 2021. "Graphic Representation of a Dimensional Expansion of Triangular Fuzzy Number," Journal of Mathematics, Hindawi, vol. 2021, pages 1-11, July.
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