Multi-criteria decision-making (MCDM) methods have been extensively employed by researchers in the public transport (PT) sector. While many studies utilize a single MCDM method, employing multiple MCDM methods can achieve more robust results. Furthermore, integrated MCDM methods have the potential to address the weaknesses and limitations inherent in single MCDM method. In this study, we address the limitations of single MCDM methods by integrating the analytic hierarchy process (AHP) with the analytic network process (ANP) to evaluate public transport networks performance. Based on the established public transport criteria matrix AHP model, we identify interdependencies among criteria. The AHP-ANP method is then applied to assess public transport networks in three case study cities in Australia. The sensitivity analysis conducted on both the AHP and integrated AHP-ANP approaches highlights the influence of criteria interdependency. This research contributes to mitigating the limitations of AHP method and applies AHP-ANP model to provide decision-makers with insights to enhance PT network performance and achieve smart PT network management.

This paper proposes a new optimization algorithm for backpropagation (BP) neural networks by fusing integer-order differentiation and fractional-order differentiation, while fractional-order differentiation has significant advantages in describing complex phenomena with long-term memory effects and nonlocality, its application in neural networks is often limited by a lack of physical interpretability and inconsistencies with traditional models. To address these challenges, we propose a mixed integer-fractional (MIF) gradient descent algorithm for the training of neural networks. Furthermore, a detailed convergence analysis of the proposed algorithm is provided. Finally, numerical experiments illustrate that the new gradient descent algorithm not only speeds up the convergence of the BP neural networks but also increases their classification accuracy.