模糊分析中的结构元方法(Ⅱ)

Method of structuring element in fuzzy analysis(Ⅱ)

在模糊数学中,模糊值函数的导数和模糊值函数的积分通常分别是利用区间值函数导数和区间值函数积分模糊集的表现定理给出的。在文献[1]中提出的模糊结构元概念基础上, 给出了模糊结构函数和模糊值函数的结构元表示方法。利用模糊数和模糊值函数的结构元表现形式,给出了模糊值函数的微分和模糊值函数的积分(黎曼意义下)运算的等价形式。模糊结构元理论与技术不仅仅为模糊分析计算的简化提供了工具,同时也为模糊分析理论与应用的研究开创了一条新的途径。

Fuzzy number and fuzzy-valued functions are the basic concepts in fuzzy analysis. Generally, the operations of fuzzy numbers and fuzzy-valued functions are provided with the form based on the extension principle. In paper [1], presented the concept of fuzzy structuring element, and discussed some of its useful properties, proved the structuring element representation theorem of fuzzy number and fuzzy-valued function. In this paper, gave the differential and integral calculate method of fuzzy-valued functions using fuzzy structuring element method. The theory of fuzzy structuring element not only provides a simple and effective tool for the fuzzy analysis and calculations, but also makes a new path to study the theory and application of fuzzy analysis.