A Zadeh^′s max-min composition operator for 3-dimensional triangular fuzzy number

Article type: Research Article

Authors: Yun, Yong Sik^*;

Affiliations: Department of Mathematics and Research Institute for Basic Sciences, Jeju National University, Jeju, Korea

Correspondence: [*] Corresponding author. Yong Sik Yun, Department of Mathematics and Research Institute for Basic Sciences,Jeju National University, Jeju 63243, Korea E-mail: [email protected].

Abstract: We generalized triangular fuzzy numbers from ℝ to ℝ2 . By defining parametric operations between two α-cuts, which are regions, we obtained parametric operations for two triangular fuzzy numbers defined on ℝ2 . We also generalized triangular fuzzy numbers from ℝ2 to ℝ3 . By defining parametric operations between two α-cuts, which are subsets of ℝ3 , we derived parametric operations for two triangular fuzzy numbers defined on ℝ3 . For the calculation of Zadeh’s principle operators, the definition of parametric operations between two α-cuts, which are subsets of ℝ3 , is critical.

Keywords: Zadeh’s max-min composition operator, 3-dimensional triangular fuzzy number

Keywords: 47N99

DOI: 10.3233/JIFS-192095

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 3, pp. 3783-3793, 2020