A novel arithmetic operation function utilizing height of interval type-2 fuzzy sets to express risk preference: case study of remotely controlled autonomous ship

Risk analysis for maritime emerging technology relies on subjective data derived from the knowledge, experiences, and individual characteristics of seafarers or experts. Risk preference is a key indicator in maritime emergencies, playing a significant role in risk analysis. This study uses interval type-2 fuzzy sets (IT2FSs) to represent risk preference and focuses on the associated arithmetic operation performed on the reference points and heights. Therefore, a function is proposed to integrate the reciprocal influences of the height of IT2FS for three types of risk preferences; namely, caution, impartiality, and adventurousness, with uncertainty. The proposed function is used to define arithmetic operations for the IT2FSs, including addition, subtraction, multiplication, division, multiplication by a crisp number, and exponentiation operations. Furthermore, case studies are conducted to validate and demonstrate that the proposed arithmetic operations apply to the fuzzy risk analysis and risk criteria design processes. The results of a case study reveal that a conservative expert increases the assessed risk and lowers its uncertainty. By contrast, the more radical the expert, the less important the consequence of the autonomous ship. Finally, this study discusses various functions, evaluating their computational time and performance, and recommends the most suitable options.