Dimensional extension of Zadeh’s max-min composition operator on generalized quadratic fuzzy sets: from 2D to 3D with structural consistency

we show that the parametric operations for two generalized quadratic fuzzy sets defined on ℝ³ is a generalization of a Zadeh’s max-min composition operations for two generalized quadratic fuzzy sets defined on ℝ². We formally define 3D quadratic fuzzy numbers and their multidimensional membership representation. This work lays a theoretical foundation for the development of high-dimensional fuzzy systems, particularly in applications where reasoning occurs over multi-input spatial domains.