A Zadeh’s Max-Min Composition Operator for Two Generalized 3-Dimensional Quadratic Fuzzy Sets

A. We extended the scope to consider operations between general quadratic fuzzy sets, whose maximum membership values are not necessarily equal to 1.We have proven that the max-min composition between two fuzzy sets with peak values h1 and h2, where 0 < h1 < h2 < 1, yields a result with a maximum value equal to h1.Furthermore, we demonstrated that the result of such an operation does not preserve the form of a quadratic fuzzy set, highlighting a significant structural distinction when extending beyond normalized fuzzy numbers.The study of general quadratic fuzzy sets-rather than traditional quadratic fuzzy numbers-opens avenues for broader applications.In particular, our results are expected to contribute significantly to fields requiring high precision and flexibility, such as fuzzy decision-making systems, high-dimensional fuzzy control systems, information fusion and sensor data integration, and fuzzy image processing and segmentation.