广义直觉模糊数在集装箱堆场选择中的应用

Yard allocation decision making in container terminals with generalized intuitionistic fuzzy numbers

基于经典直觉模糊数的定义,通过对隶属度函数的正规性和非隶属度函数最小点取值位置的讨论,改进了与模糊数定义更为贴近的三角直觉模糊数.基于上述三角直觉模糊数的修改,拓展了直觉模糊数的概念,引入了更具有一般性的广义直觉模糊数定义,并探讨了广义直觉模糊数同传统直觉模糊数之间的对应关系.依据扩展原理,得到广义直觉模糊数的运算规则,其中将数乘运算进行了重新设计,使之既服从经典模糊集理论体系,又满足运算有界性.通过使用广义直觉模糊数多属性决策方法,根据集装箱港口装卸集装箱的类型、时间节点、装船和卸船的倒箱率,给出了落场集装箱对应堆场选择的决策流程.通过与基于经典直觉模糊数的排序方法进行比较,由于采用广义直觉模糊数求解此类问题时考虑了方案对于评判标准的不满足程度,证实了所提出方法产生的排序结果较经典方法更为精细.

Based on the definitions of traditional intuitionistic fuzzy numbers （IFN）, a series of discussions and modifications were conducted concerning the triangular intuitionistic fuzzy numbers （TIFN）, which approximate more closely to the original definition of fuzzy numbers （FN）. Then extensions of the traditional FNs and TIFNs were implemented to introduce the generalized intuitionistic fuzzy numbers （GIFN）. The relationships between the GIFNs and the traditional IFNs were revealed, via transformation of GIFNs into IFNs by assigning specific x values. Meanwhile, the arithmetic rules of the GIFNs were deduced by the extension principle. Furthermore, in contrast with the traditional scalar multiply arithmetic, a novel type of multiplication was proposed so as to obey the extension principle, and at the same time the new method keeps the closeness of the multiply arithmetics. Thereafter, the general steps in ranking with GFNs were shown. Finally, the ranking methods of GIFNs were applied in the real fuzzy multi-attribute decision making problems, such as a numerical example of the yard allocation decision making in container terminals. In order to validate the proposed method, a comparison study was performed to illustrate the differences between the introduced methods and the traditional decision making approach. The comparison reveals that the proposed approach is more precise in ranking alternatives, since the memberships of the negative and positive evaluations are integrated simultaneously into the decision making process.