A Study of Watershed Hydrodynamical System using Advanced Weighted Correlation Measure of Pythagorean Neutrosophic Cubic Set

Abstract

The principal objective of this study is for analyzing how Pythagorean Neutrosophic Cubic Sets (PNCS), a hybrid framework that combines interval-valued and crisp Pythagorean Neutrosophic information, might be used to resolve complex uncertainty in hydrodynamic decisions. Although current models, such as Cubic Intuitionistic Fuzzy Sets (CIFS), offer a basis for making decisions, they frequently fall short in capturing higher-order uncertainty and independent degrees of indeterminacy. We provide a sophisticated weighted correlation measure created especially for the PNCS context in order to get over these restrictions, and we thoroughly characterize its basic mathematical characteristics. To guarantee computational accuracy and reproducibility, a multi-criteria decision-making (MCDM) algorithm has been deployed and carried out in behavior via Python using the developed correlation measures and a comparison analysis is made for CIFS and PNCS an explanation is given for choosing the PNCSs for this case study. A case study of a watershed management system that assesses four possible locations based on socioeconomic and environmental factors demonstrates the approach's practical usefulness. Policymakers and environmental engineers can use this study's insightful findings to create sustainable watershed management plans.