使用可拓集合论确定海上船舶碰撞危险度的模型

The Mathematical Model for Determiation of Collision Risk of Ships at Sea Using the Theory of Extension Set

船舶碰撞危险度可以分为宏观碰撞危险度和微观碰撞危险度,本文所进行的研究,是微观碰撞危险度的研究。在这方面,日本和西欧的许多专家学者多年来进行了大量研究,取得了一定成绩,但又都存在一定的问题。本文运用可拓集合这一新的数学工具,综合各种因素的影响,建立了船舶碰撞危险度和采取避让行动时机的数学模型。

There are two ways to study the collision risk of ships,the macroscopic one is to study the probability of collisionsin a certain area at a certain period of time, the microscopicone is to study the degree of collision risk between two shipsin the course of avoiding collision. The authors devote at thelatter study in this paper. A lot of studies in this aspect havebeen conducted by many specialists in recent years and someprogresses have been made, but certain problems still exist asfollows in the whole:1) The influential factors adopted are not sufficient orproper;2) The synthetical influence of relevant factors is notconsidered; 3) The expostition of the influence of each factor over thecollision risk has not been made theoretically;4) The mathematical method used for founding the modelis not reasonable;5) The model founded exist certain problems in the theoryof avoiding collision. This new mathematical method using the Theory of Exten-sion Set in this paper tries to consider all the influentialfactors involved for estatablishing the math model of ships'collision risk and the action time for avoiding collision. Themain advantages of this model are as follows:1) The concept of fuzzy boundary of ship's domain(FBD);2) The concept of the time of maximum risk(TMR):3) The consideration of influence from the variation ofDCPA over the collision risk;4) Enunciating the difference between collision risk andaction time; The calculating result of this model is quite consistentwith the values obtained from observation or the data fromspecialists.