An Expanded Concept and Graph of Zadeh’s Algebraic Operations for 3-Dimensional Generalized Triangular Fuzzy Sets

Abstract

Algebraic operators for fuzzy sets have been studied in 2-dimensional space. We define the algebraic operators between two 3-dimensional fuzzy sets and calculate the operators for the generalized 3-dimensional triangular fuzzy sets. To facilitate an understanding of the results in 3D, the values of membership function are displayed in graphs using color density. We give various types of graphs of $\alpha$ -cuts.