A New Neutrosophic Spherical Framework for Evaluating the High-Quality Economic Development at the Provincial Level

Abstract

High-quality economic development (HQED) is a modern goal for provinces 
and nations. It includes not only economic growth but also innovation, environmental 
protection, fairness, and openness. Measuring HQED is complex because it involves many 
indicators, different opinions, and uncertain data. This paper presents a new 
mathematical framework using Neutrosophic Spherical Sets (NSS). Our model introduces 
three powerful ideas: Bipolar NSS to include both positive and negative effects of 
indicators, Multi-Granular NSS to combine multiple expert views, and Hyper NSS to treat 
each province as a structured system. We define each concept clearly with equations and 
examples. Then, we apply the model to evaluate HQED for different provinces using real
world indicators. Our results show that this method gives deeper insights and handles 
uncertainty better than traditional models.

DOI: 10.5281/zenodo.16496769