A Zadeh’s Max-Min Composition Operator for Two Generalized 3-Dimensional Quadratic Fuzzy Sets
Year: 2025
Type: article
Abstract: 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.
DOI: 10.28924/apjm/12-72
Language: English
Topic: Fuzzy and Soft Set Theory
Field: Decision Sciences
Domain: Social Sciences
Open Access status: diamond
Funder: Jeju National University
OpenAlex ID: W4413025606