基于结构元模糊值函数的Newton-Leibniz公式

Newton-leibniz formulas of fuzy-valued function based on structuring element

模糊值函数与经典函数之间存在着一种必然的联系,因此研究模糊值函数的Newton-Leibniz公式也就具有了很重要的价值,原有的模糊值函数的Newton-Leibniz公式是在标准算子下给出的,其表现形式及实际应用不够灵活。为了体现该公式的灵活性,本文在受限算子下,利用模糊结构元理论给出了模糊值函数的Newton-Leibniz公式的一种新的表现形式,这种形式摒弃了对原函数的限制,使得该公式运用起来更加灵活简便,而且具有一定的实际应用价值,同时也体现了模糊结构元理论在简化模糊分析计算方面的优越性,整个公式的给出和证明过程及文章中的实例也说明了这一点。

Fuzzy-valued function has a certain relation to classical function, so it will be very important to study the Newton-Leibniz formula of fuzzy-valued function, the previous formula was given on the condition that the arithmetic operator was standard fuzzy arithmetic, its expression wasn't simple. In order to make the expression of the formulas become simple, this paper gives a new kind of expression of the Newton-Leibniz formula by using the method of fuzzy structuring element on the condition that the arithmetic operator is constrain fuzzy arithmetic, this new kind of expression avoids the limit of image function, so the expression of the formula becomes simpler, and it also has a certain value both in theory research and practical application, at the same time the advantage of fuzzy structuring element theory in fuzzy analysis and calculation is represented ,the expression of formula and the proof of formula and the example all illustrate it.