## 1 Introduction  
Recently, the possibility of maritime collision accidents has been increasing due to the emergence of large ships, high speed, and the growth of maritime transportation and international trade. Thus, the scale of maritime accidents becomes larger and it causes serious marine pollution, huge economic losses, and loss of life at sea. According to statistic investigation presented by Korean Maritime Safety Tribunal (KMRT) [1] over the past five years, collision accidents among entire accidents at sea have reported approximately 13.5%. In particular, more than approximately 90% out of collision accidents was due to human errors. Most of these human errors were a \"lack of recognition of collision risk\". According to \"Rule 7: Risk of Collision\" in the International Regulations for Preventing Collision at the Sea (COLREGs) [2], the collision risk must be assessed by all available means appropriate to the prevailing circumstance using predictive technology. In particular, the radar having the Automatic Radar Plotting Aid (ARPA) function, which can obtain plots of detected objects, equivalent systematic observations, Distance to Closest Point of Approach (\(D_{CPA}\)), and Time to Closest Point of Approach (\(T_{CPA}\)), was referred to as an appropriate equipment to obtain early warning of the collision risk in the COLREGs. Therefore, while nearly four decades since the radar appeared, representative two types of static and dynamic assessment methods on the collision risk have been actively utilizing. As for static assessment methods, the term of a ship safety domain was first proposed by [PERSON] and [PERSON] [3] to deal with the safe navigation ships. At this time, safe boundary taking into consideration the distance from the center ship must keep the area of evasion from the overlapping of other ship's safety domain. This concept of similar definitions can be found in [3; 4; 5; 6; 7; 8; 9; 10] applying a different size and shape of the safe boundary. Strength is that the navigator may feel intuitional and comfortable analyzing what spacing around an approaching ship via a graphical shape [11]. However, weakness is that the ship safety domain would not only require complex and frequent reconfiguration according to different types of water areas, but also could not quick computational collision risk and decision-making in dynamic changing circumstances due to only taking account of the ship's length as a parameter [11]. Hence, a number of researches assessing the collision risk via Collision Risk Index (_CRI_) have been conducted [12; 13; 14; 15; 16; 17; 18; 19]. The _CRI_ is to aggregate dynamic parameters into just one number, and in terms of computational time and quick decision-making, it is faster than ship safety domain. In particular, [PERSON] [15] developed the Fuzzy Inference System (FIS) for computing the _CRI_ based on type-1 fuzzy logic. For this, navigator interviews were used to connect \(D_{CPA}\) and \(T_{CPA}\) to the _CRI_. In [16; 18], on the basis of [15], fuzzy membership functions using \(D_{CPA}\) and \(T_{CPA}\) were created by using dimensionless values with the ship length and velocity or adding another input parameter. However, the Fuzzy Inference System based on the type-1 fuzzy logic (T1 FIS) was pointed out that membership functions only depended on empirical factor due to navigator interviews [17; 19]. Thus, membership functions of \(D_{CPA}\) and \(T_{CPA}\) were determined on the basis of virtual navigation situation resulting from the maneuverability of the Own-Ship (OS) using K-T (i.e., index of turning ability and index of responsiveness to the helm) equations [17] and near-collision situation data using the ship safety domain [19]. Nonetheless, the T1 FIS has the following significant limitations. The membership functions of \(D_{CPA}\) and \(T_{CPA}\) were created as a crisp degree according to the linguistic variables obtained average values via navigator interviews, ship maneuverability, and near-collision data.