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The optimization of sustainable smart cities is an essential endeavor in modern urban development, aiming to enhance the quality of life for citizens while minimizing environmental impacts. Big data plays a critical role in achieving these goals by enabling the collection, analysis, and utilization of vast amounts of information to make informed decisions. However, implementing big data in smart cities faces significant barriers, including data-sharing challenges, technical limitations, and organizational non-cooperation. Addressing these barriers is crucial for the successful deployment of smart city initiatives. We propose a novel approach to tackle these challenges using the Improved Zero-Sum Grey Game (IZSGG) theory and the Grey Best-Worst Method (G-BWM). This method comprehensively analyzes the risks and uncertainties associated with big data implementation in smart cities. By modeling the interactions between different stakeholders and their competing interests, IZSGG theory provides a framework to identify optimal strategies for data management. The G-BWM further refines these strategies by evaluating and prioritizing the various factors influencing big data utilization. Our findings reveal that the worst-case scenario for a smart city involves the simultaneous occurrence of several risks, all of which have positive values, indicating their potential to significantly disrupt smart city operations. The specific risks identified include: the sharing of data and information, the collection and recording of data, technical limitations and challenges associated with technology, the non-cooperation of organizations, and issues related to the interpretation of complex information. The technical barrier is the most significant with a weight of w(T)=0.6152, indicating its critical role compared to other barriers. Within this category, the sub-barrier of technical and technological constraints is particularly critical, with a weight of 0.39267375.