Graphical Representation of Zadeh's Max-Min Composition Operator for Two 3-Dimensional Quadratic Fuzzy Numbers (European Journal of Pure and Applied Mathematics, 2025)
We computed the extended operations for generalized quadratic fuzzy sets and extended quadratic fuzzy numbers from R to R2. By defining parametric operations between two a-cuts, which are regions, we derived the parametric operations for two quadratic fuzzy numbers defined on R2. The outcomes of these parametric operations serve as a generalization of Zadeh's extended algebraic operations. We demonstrated that the results obtained from the parametric operations represent an extension of Zadeh's extended algebraic operations. Additionally, we expanded quadratic fuzzy numbers initially defined in two dimensions to three dimensions and calculated Zadeh's max-min composition operator for two extended three-dimensional quadratic fuzzy numbers. We presented an illustrative example of three-dimensional results along with corresponding graphs.
Keywords: graphic representation; parametric operation; 3-dimensional quadraric fuzzy number