Context: Routing algorithms play a crucial role in the performance of Network-on-Chip (NoC)based Multi-Processor Systems-on-Chip (MPSoC). However, the selection of appropriate and effective routing algorithms poses a challenge for designers, given the multitude of assessment criteria, data fluctuations, and varying criteria importance. Objective: In this study, we propose a comprehensive assessment of various routing algorithms, aiming to identify the most suitable and effective routing algorithm that satisfies designers' systemlevel requirements and assessment criteria. Method: This research integrates the Fuzzy-Weighted Zero-Inconsistency (FWZIC) method and the Fuzzy Decision by Opinion Score Method (FDOSM). The utilisation of the Z-Cloud Rough Numbers (ZCRNs) environment addresses the challenge of two types of uncertainty, providing a framework for managing ambiguity in the data and achieving a higher level of data freedom. Our methodology consists of two main phases. Firstly, the decision matrix is constructed based on the performance assessment criteria and routing algorithms. Secondly, we employ the ZCR-FWZIC method to derive the weights for each criterion and subsequently employ the ZCR-FDOSM-BM approach to rank the routing algorithms. Result: The analysis reveals that Adaptive Dimensional Bubble Routing (ADBR), Message-based Congestion-Aware Routing (MCAR), and Dynamic and Adaptive Routing Algorithm (DyAd) are ranked as the top three routing algorithms, respectively. Conclusion: This research presents essential implications for designers and system engineers involved in NoCbased MPSoC, offering insights to enhance decision-making processes and facilitate the selection of an appropriate routing algorithm.