Three-Dimensional Expansion and Graphical Concept of Generalized Triangular Fuzzy Set - Yong Sik Yun (Journal of Mathematics)
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.