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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 many practical problems, such as fuzzy control and fuzzy programming, it is often necessary to find a comprehensive cut-off of fuzzy numbers at different levels for some arithmetic rules. Based on the analysis of the intrinsic mechanism of such operations, Method, the rules for determining the total number of intercepts of the fuzzy numbers at different intercept levels are given. Based on the Lebesgue measure of the symmetric difference sets of the horizontal intercepts, the concept of the clearness level of the fuzzy numbers is introduced, A method of objectively integrating different cutoff levels gives the formula of trigonometric fuzzy numbers on different levels. These discussions will provide an effective way for the integration of different levels of information and the problems of fuzzy programming and fuzzy optimization at different levels.