不同层次模糊信息的加权综合方法

Weighted operation method of fuzzy information at different levels

在模糊控制与模糊规划等许多实际问题中,常常需要针对某种运算规则求模糊数在不同水平下的综合截集,该文在分析了这种运算的内在机理的基础上,采用水平加权的方法,给出了确定模糊数的在不同截集水平下的综合截集的规则,并从水平截集的对称差集合的Lebesgue测度出发,引入了模糊数关于水平的清晰程度概念,进而建立了一种客观地综合不同截集水平的方法,给出了三角模糊数关于不同层次水平的运算公式。这些讨论将为不同层次信息的综合以及不同层次水平的模糊规划和模糊优化问题提供一种有效的途径。

In fuzzy control and programming problems, the synthetic cutset of the fuzzy numbers is calculated for different cutset levels based on operation rules. This paper establishes a synthetic rule for fuzzy numbers in different cutset levels using the level weighted method. Then the Lebesgue measure of the symmetric difference between level cutsets is used to define the clearness of a fuzzy number within a level, to synthesize different levels of a cutset, and to define the synthetic level of a cutset for triangular fuzzy numbers. The results provide a synthesis of fuzzy information for different levels for fuzzy programming and optimization problems.