模糊结构元诱导的两类加权模糊数度量

Two Types of Weighted Fuzzy Number Metrics Induced by Fuzzy Structured Element

针对模糊数度量中不同隶属程度对度量的贡献程度应不同的客观事实,给出两类模糊数的结构元加权度量。首先,在区间[-1,1]上的同序标准单调有界函数类B[-1,1]上定义两类结构元加权度量dH、dp,分别讨论了这两类度量空间的完备性和可分性;其次,利用正则模糊结构元导出的模糊泛函,给出一种由B[-1,1]上度量诱导有界闭模糊数全体上的度量方法,进而给出由dH、dp诱导的两类模糊数结构元加权度量dNH、dNp,并分析了两类诱导的模糊数度量空间的完备性和可分性;最后,给出了dNH、dNp与传统方法定义的模糊数度量的区别与联系。

For the objective fact that elements with different membership degrees should have different contribution to the metric measure between fuzzy numbers, this paper presents two types of fuzzy number metrics weighted by structured element. Firstly, we define two kinds of metrics weighted by structured element dH,dp on the family （B [-1, 1]） of all the same monotone and standard bounded functions on closed interval [-1,1], and discuss the completeness and separability of those two metric spaces. Next, using the fuzzy functional induced by normal fuzzy structured element, we give out a method that the metric of the closed bounded fuzzy number space is induced by the metric on function space B[-1,1]. Furthermore, two types of fuzzy number metrics dNH,dNp weighted by structured element which both are induced by dNH,dNp are presented, and analyze completeness and separability of the two induced fuzzy number metric spaces. Lastly, the difference and relationship between dNH,dNp and the metrics defined by traditional method are shown.