基于结构元的模糊矢量研究

Study on Fuzzy Vectors Based on the Fuzzy Structured Element

在给出n维实空间Rn上模糊点的结构元表示基础上,提出了分量为模糊实数的模糊矢量概念,研究了其运算性质,并将模糊矢量的运算转化为其相应坐标分量间的运算。最后,给出了两种特殊的模糊矢量内积的定义。研究结果不仅丰富了模糊分析学的研究内容,也为进一步研究模糊解析几何学提供了方法和工具。

Based on the represent method of fuzzy points in the n-dimensional real space Rn given by the fuzzy structured element, this paper presents the concept of fuzzy vectors whose coordinate components are fuzzy real numbers, then this article not only discusses some operations of fuzzy vectors, but also transform the operations of fuzzy vectors into the operations of their coordinate components. At last, we come up with two special kinds of the inner product of fuzzy vectors. The results not only enrich the research contents of the fuzzy ana[ytics, hut also provide an analysis tool for the study on the fuzzy geometry.