A Cooperative Neutrosophic Sets with Dual Rough Set and Entropy Enhanced Multi-Similarity Measures Based Decision Making for Sustainable Transportation

Abstract

Sustainable transportation helps address environmental, social and urban mobility 
challenges in modern cities and campuses. The present work highlights a cooperative decision
making framework that integrates Dual Rough Sets (RS), Real Interval Order Relations and 
Neutrosophic Sets (NS) within a Multi-Criteria Decision-Making (MCDM) approach. Shannon 
Entropy serves to determine objective weights and multiple similarity measures such as Jaccard 
Similarity, Hamming Distance and Cosine Similarity improve robustness in evaluation. The 
three NS’s are Single-Valued (SVNS), Interval-Valued (IVNS) and Pythagorean (PNS), all of 
which are systematically applied and compared. The framework is validated by real-time data 
on sustainability criteria (for example, population, modes of transport, trip length and vehicle 
density) from twelve metropolitan Indian cities. Delhi is consistently recognized as the most 
sustainable city, followed by Bangalore and Ahmedabad, while the worst-performing cities were 
Bhopal and Indore. The stability of rankings across different neutrosophic environments is 
confirmed through sensitivity analysis of the metropolis. The framework represents a consistent 
and flexible decision-making tool for sustainable transportation planning in the face of 
uncertainty, considering the combination of cutting-edge similarity measures, composite 
entropy-based weighting and neutrosophic reasoning, it provides decision-making support for 
transparency and adaptive decision-making processes at both campus and urban levels. 

DOI 10.5281/zenodo.17420080