Fifth Order Butchers RK Methods in MAGDM using Square Root Fuzzy Sets

In the realm of fuzzy set theory, the concept of a square root fuzzy set introduces a novel approach to handling uncertainty and imprecision in data representation. Traditional fuzzy sets use membership functions to quantify the degree of truth or belonging, typically ranging from 0 to 1. The square root fuzzy set extends this framework by applying the square root transformation to the membership values, resulting in a new set of membership degrees that are more sensitive to lower values and less sensitive to higher values. The Square Root Fuzzy Matrices are used as the dataset, and the weights are calculated employing Runge-Kutta methods.The Square root Fuzzy Hybrid Geometric operator and the Square root Fuzzy Weighted Geometric operator both supply solutions that we must use in the decision-making process. This paper presents examples showing the efficiency and usefulness of the Canberra Distance calculation, which is used for ranking Keywords: Square Root Fuzzy Set, Square Root Fuzzy Weighted Geometric, Square Root Fuzzy Hybrid Geometric, Butcher ‘s Fifth Order Runge-Kutta Method.