基于结构元的模糊值函数曲面积分

Fuzzy Value Functions Surface Integral Base on the Fuzzy Structured Element

针对扩张原理在模糊值函数曲面积分中的遍历性问题,结合实际应用背景给出了模糊值函数第一型曲面积分的概念及其结构元表示.通过将二维模糊点和模糊结构元的定义推广到三维空间中,给出了模糊值函数第二型曲面积分的定义及其结构元表示.研究结果不仅丰富了模糊分析学理论,而且为具有不确定性因素的工程实践提供了方法依据.

For the expansion principle has crisp arguments on the surface integral of fuzzy- valued functions, this paper presents the definition of the fuzzy-valued function＇s first form surface and the expression by the fuzzy structured element,with the background of engineering practice. Then, it gives the definition and some properties of the fuzzy-valued fimction＇s second form surface integral by discussing the projection of three-dimensional fuzzy vectors and generating the definitions of two-dimensional fuzzy numbers and two-dimensional fuzzy structured element. The result not only enriches theories on fuzzy analysis, but also provides a basis for engineering practice with uncertain factors.