With the increasing relevance of web mining and content analysis in uncovering mobility patterns from large-scale online data, traffic flow prediction plays a crucial role in proactive urban planning and enhancing the responsiveness of intelligent transportation systems. However, existing traffic flow prediction methods often fail to explicitly capture correlations in continuous multivariate sequences that are naturally suited for trend and periodic pattern extraction by vision models and rely on fixed spatial graphs that neglect the cognitive advantages of granular-ball structures, which limits their ability to model interactions and strengthen spatiotemporal dependencies. To address these challenges, this paper proposes a Cross-domain Mamba framework that integrates Multi-scale Imaging and Granular-ball Computing for traffic flow prediction (MIGC-CMamba). First, a multi-scale sequence imaging method is presented, which converts the original time series into image modality and leverages MambaVision to capture both local and global dependencies. Second, a multi-granularity spatial graph is constructed via granular-ball clustering, which balances global trend representation and local detail preservation. Third, a cross-domain enhancement mechanism adaptively integrates temporal and spatial domains, strengthening spatiotemporal dependencies. Lastly, extensive experiments demonstrate superior performance over state-of-the-art baselines, highlighting how vision-based imaging, cognition-inspired granular-ball modeling, and content-aware mining jointly advance the modeling of spatiotemporal dependencies in traffic flow prediction.

Metro flow prediction is a critical application in smart city and Web of Things infrastructures, essential for optimizing urban mobility. However, building such predictive systems faces three key challenges: (1) the fragmentation of multimodal spatiotemporal data, (2) the inefficiency of existing models in capturing long-range dependencies, and (3) the data silos and privacy concerns inherent in distributed station infrastructures. To address these challenges, a multimodal federated learning framework named MF3 (Mamba-Transformer-Federated Metro Flow Prediction) is proposed. First, a multimodal alignment (MA) module is designed, where cross-modal alignment attention bridges visual and spatiotemporal features, thereby enhancing feature complementarity and alignment. Second, a dual-path Mamba-Transformer (DMT) module is designed, in which Mamba's linear long-range memory and the Transformer's global perception operate in parallel, reducing information loss. Third, a blockchain-based federated reputation (BFR) module is established to perform personalized federated learning, thereby enhancing privacy protection. Finally, extensive experiments on real metro datasets from Hangzhou and Shanghai demonstrate that MF3 achieves superior performance in terms of prediction accuracy. In summary, the proposed MF3 framework provides a new feasible paradigm for metro flow prediction, supporting urban traffic optimization, metro operation and scheduling, and the development of smart city and Web of Things infrastructures.

Pythagorean fuzzy set, an extension form of intuitionistic fuzzy set, which owns many advantages for dealing with uncertainties, and it has been developed to deal with various complex decision-making problems. Furthermore, based on lower and upper approximations induced by multiple binary relations, the multigranulation rough set has become one of the most promising directions in rough set theory. To combine the two ideas and explore the practical decision-making problems, we develop a new multigranulation rough set model, called Pythagorean fuzzy multigranulation rough set over two universes. In the framework of our study, we introduce the models of Pythagorean fuzzy rough set over two universes and Pythagorean fuzzy multigranulation rough set over two universes, respectively. Both the definition and basic properties are explored. Finally, we give a general algorithm, which is applied to a decision-making problem in merger and acquisition, and the effectiveness of the algorithm is demonstrated by a numerical example.