# Dynamic Multi-Attribute Decision-Making Method for Risk-Based Ship Design
###### Abstract
[14] presented guidelines for the development of risk criteria for dams in developing countries, using China as an example, and proposed a targeted analytical method for selecting relevant parameters based on the ALARP principle and F-N curves showing the relationship between cumulative frequency and the number of potential fatalities. The ALARP principle reflects the risk aversion of decision-makers, that is, decision-makers have different attitudes towards risk control as the size of the risk varies. Thus, to consider the changes in risk aversion with risk level, a dynamic multi-attribute index system is used in this study, which involves the selection of the multi-attribute set depending on the acceptable risk level. For example, a CEA multi-attribute set is selected in a medium-risk condition and a performance multi-attribute set without cost indices is selected in a high-risk condition. In recent years, in the research of risk control decision models, [PERSON] et al. [15] performed an environmental risk analysis of the oil and gas industry and created a multidisciplinary assessment model based on a probabilistic risk analysis approach. [PERSON] and [PERSON] [16] introduced a fuzzy set-based risk analysis method, which is useful for improving the safety of the investment process in the railroad traffic control industry. [PERSON] et al. [17] provided an innovative approach that combines cost-benefit analysis with STPA-BN-Influence diagrams for risk-based decision-making. [PERSON] et al. [18] introduced an enhanced risk model, combining event tree analysis and a Bayesian network for ship evacuation processes in order to help understand the actual risk of fire and flood events during evacuation and assess various risk control measures and mitigation strategies. This paper establishes a GRA model for RCO-level assessment based on multi-attribute evaluation, as the indicators for ship FSA and risk control decision-making are diverse and complex. It is difficult to quantify the impact of each indicator as some belong to grey areas. The GRA method can overcome issues such as incomplete data, high uncertainty, and difficulty in quantification. By calculating the grey relational degree (GRD) of indicator data, it can identify the degree of correlation between each indicator, thereby helping decision-makers to clarify the relationships between various indicators and assist in multi-attribute evaluation and decision-making for risk control measures. Therefore, using the grey relational analysis method for multi-attribute evaluation of risk control measures is a more suitable approach. The grey system theory was first proposed by [PERSON] in 1989 [19] and, since then, it has been an important topic of discussion in multiple-attribute decision-making applications in engineering, e.g., in [PERSON] et al. [20], [PERSON] et al. [21], [PERSON] et al. [22], [PERSON] et al. [23], and [PERSON] et al. [24]. In an FSA study of a ship, [PERSON] and [PERSON] [25] initially ranked the RCOs by using a GRD-based multi-attribute assessment. The results of the multi-attribute assessment depend significantly on the attribute weights. Currently, the commonly used methods for determining attribute weights can be categorized into three types according to the source of raw data. The first category is the subjective weighting method, i.e., determining the weights by taking into account the subjective preferences or experiences of the decision-making experts. Traditional subjective methods include the analytic hierarchy process (AHP) [26] and Delphi methods [27]. The second category is the objective weighting method, in which weights are set by a specific algorithm applied to the raw data without taking into account expert preferences. Conventional objective weighting methods include the entropy weighting method [28], the maximizing deviation method [29], and the linear programming method [30]. The third category integrates subjective preference and objective importance.