模糊值函数分析学的结构元方法简介(Ⅰ)——结构元与模糊数运算

Brief Introduction of Fuzzy-valued Function Analytics Base on Fuzzy Structured Element Method(Ⅰ)

简述了模糊值函数分析学在具体工程实践应用中存在的困难和障碍,系统地介绍了模糊结构元方法在模糊值函数分析学中的应用,包括模糊结构元的概念、模糊数的模糊结构元表示形式、基于结构元表达形式的模糊数运算与隶属函数确定.模糊结构元方法将复杂的模糊数运算转化为一类单调有界函数的运算,不仅仅为模糊分析计算的简化提供了工具,同时也为模糊值函数分析学应用的研究开创了一条新的途径.

This paper systematic introduced the application of fuzzy structured element method in the fuzzy-valued function analysis. It include the concept of fuzzy structured element, the structured element representation theorem of fuzzy number and the four operations of fuzzy numbers base on fuzzy structured element forms. The theory of fuzzy structuring element not only provide a simple and effective tool for the fuzzy-valued function analysis and calculations, but also break a new path to study the theory and application of fuzzy analysis.