## 1 Introduction  
In the past, maritime transportation research focused on ship safety [1; 2] as it is closely related to real-world events involving ship navigation, and meteorological and marine environments have a significant influence in this regard. Recent maritime accidents include the following: in April 2014, the Sewol ferry capsized in strong winds and waves, killing about 300 people; in December 2014, the Norman Atlantic ferry faced strong winds and waves in the Adriatic Sea, resulting in 11 deaths; in October 2015, the cargo ship El Faro went missing in a hurricane, killing all 33 crew members; in March 2021, strong winds pushed the Ever Given off course in Egypt's Suez Canal and it ran aground; and in November 2020, a container ship stack collapse occurred after the ONE Apus encountered adverse weather and sea conditions in the North Pacific Ocean. Moreover, the loss rate of ships, of which bulk carriers account for the majority, is increasing amidst changes in wave patterns in recent years [3]. Consequently, research on optimal route planning to help ships avoid dangerous regions is crucial for ship safety. At present, route planning is the main topic of research in this field, but many studies have concentrated on weather and ocean conditions and have not quantitatively studied the risk-bearing capacity of ships when assessing risk values. For example, [PERSON] et al. [4] calculated the sailing cost associated with weather conditions by using weather data and terrain data for each section, but they did not factor in ship vulnerability. Absolute danger, hazard factors, and influential factors were used for risk contour mapping as the structure of their route planning technique [5]. [PERSON] et al. [6] provided a model to optimize routes with the maximum property values according to weather forecast maps and studied the effect of ship speed on these optimal routes. Ship information including the under keel clearance (UKC) and draft was calculated for safety contours that were used to assess the probability of ships running aground [7]. Although these risk evaluation methods mentioned the ship parameters during navigation, they did not quantitatively analyze the ship vulnerability. [PERSON] et al. [8] only qualitatively constructed the risk field of ships needed to plan optimal routes, without calculating the risk values of sailing ships in depth. Therefore, this study proposes a multi-layer fuzzy comprehensive evaluation method to integrate the external environment of weather and marine factors with ship vulnerability. The multi-layer fuzzy comprehensive evaluation method can effectively synthesize different evaluation indicators from different criteria. When sailing in harsh weather conditions, ships may encounter a variety of dangerous situations including wind-induced waves and heavy swells. To assist ship captains in handling such situations, the International Maritime Organization (IMO) [9] set guidelines which apply to all types of ships. Weather routing has captured researchers' attention in many studies, but only a few of them have taken the IMO guidelines into account. For example, a voyage optimization approach aimed to minimize fuel consumption and air emissions was tested in a harsh sea environment to prove that the approach was effective in avoiding storms [10]. [PERSON] and [PERSON] [11] qualitatively used available weather forecast information when selecting the optimal routes via a data-driven decision support framework. Penalty costs were added to the fitness function of the algorithm for finding an optimal route with the minimum travel time and fuel consumption when the wave height was greater than the maximum acceptable wave height [12]. [PERSON] [PERSON] et al. [13] used a real-coded genetic algorithm to investigate how to plan minimum sailing time routes for ocean going vessels to avoid weather hazards such as wind and waves. if the wave height was significantly exceeded for the area.