Flexible robotic fish are emerging as a promising class of deep-sea exploration platforms because they combine compliant bodies, low-disturbance fish-like propulsion, and the potential for distributed sensing and autonomy. Unlike conventional biomimetic robotic fish developed mainly for shallow or moderate-depth environments, deep-sea flexible robotic fish must simultaneously address high hydrostatic pressure, low temperature, darkness, limited communication, constrained power supply, and complex near-bottom terrain. This review synthesizes research at the intersection of deep-sea soft robotics, bio-inspired robotic fish, smart-material actuation, pressure-adaptive packaging, multimodal sensing, and autonomous control. The literature is organized around a system-level design chain: biological mechanisms that inspire pressure adaptation and perception, body architectures that distribute pressure and protect electronics, soft actuators that generate fish-like propulsion, and control strategies that enable near-bottom and long-duration tasks. The review highlights that the central challenge is not any single actuator or material, but the co-design of pressure-adaptive bodies, hybrid soft actuation, reliable interfaces, multimodal perception, energy management, and autonomy. To strengthen engineering translation, this revised review further adds design-principle abstraction, actuator-selection guidance, prototype-level comparison, failure-mode analysis, and a computational design workflow. Future research should prioritize long-term reliability tests, standardized deep-sea evaluation protocols, physics-informed modeling, and integrated prototype demonstrations under realistic mission conditions.

Fish-like biomimetic robots increasingly combine compliant structures, soft and variable-stiffness actuation, distributed sensing, and autonomous control, but cross-study comparison remains difficult because biological inspiration, robotic embodiment, test boundaries, and mission definitions are heterogeneous. We synthesize the field through a mechanism-to-evidence framework that links biological mechanisms to measurable descriptors, robotic embodiment, controlled interventions, task-oriented evidence, and conditional design principles. Across the literature, the transferable unit is not external resemblance but a functional mechanism whose advantage remains measurable after robotic integration. Three conclusions recur: dynamic performance depends on matching stiffness, actuation frequency, damping, and fluid loading within the intended operating range; morphology, sensing, control, power, and payload must be co-designed; and component, free-swimming, controlled-task, and field studies support different scopes of inference. We translate these findings into nine evidence-informed conditional design principles with explicit applicability limits and discriminating validation tests. Major gaps remain in wet-state dynamic characterization, complete reporting of power boundaries and kinematics, uncertainty and failures, matched task-level comparisons, and long-duration field validation. The resulting framework shifts evaluation from peak metrics and taxonomic labels toward task-conditioned, evidence-bounded design decisions.

Ship safety assessment must accommodate aleatory variability, epistemic incompleteness, and heterogeneous representations of uncertainty. This study develops a generalized probability theory (GPT) as an extended probabilistic framework that interfaces with classical probability, fuzzy theory, grey system theory, and Dempster-Shafer (D-S) evidence theory while preserving their distinct semantics. Generalized random numbers (GRNs) represent information at different levels of precision; the degree of overlap (DOO) characterizes shared information structures; and the residual event W retains probability mass outside the currently identified factor set. Generalized total probability and generalized Bayesian inference enable forward propagation and backward diagnostic updating, respectively. Using multi-factor coupling data from complex waters, the framework distinguishes empirical co-occurrence from information overlap, corrects double counting among coupled factors, and supports higher-order propagation and posterior updating. The case study is limited to real-valued coupling data. Within this validation boundary, the generalized probability theory provides a consistent and interpretable interface for uncertainty representation and probabilistic inference in ship safety assessment.