O型模糊数及其结构元表示方法

O-fuzzy-number and the Method of Circular Fuzzy Structured Element

为研究平面或空间模糊几何问题的需要,在平面或空间模糊点的背景下,给出了O型模糊数的概念,它是一类二维实数域上的模糊集,同时给出了O型模糊数的二维模糊结构元表示方法。二维模糊数的结构元方法,可以使O型模糊数的运算变成普通实数与模糊结构元之间的运算,使得过去必须依赖扩张原理和表现定理来刻画的模糊数运算变得更加简单与直观,不仅仅为模糊分析计算的简化提供了工具,也为二维实数域上模糊分析理论与应用的研究开创了一条新的途径。

For the need of studing the fuzzy plane or space geometry, under the background of plane or space fuzzy points, this paper presents the definition of the fuzzy number in R2, and defines two- dimensional fuzzy number. In order to realize the expression of two-dimensional fuzzy real number~ s membership function, the paper defines o-fuzzy-number that is a special fuzzy set in Rz. What＂s more, we provide the circular structured element representation theorem of o-fuzzy-number and study some of its fundamental properties. The operations of fuzzy sets are easier with the new represented theorem than those based on the extension principle. The method of circular fuzzy structured element not only provides a tool for the fuzzy calculations, but also paves a new way for studying the fuzzy number in R2.