模糊数关于紧承下方图度量的线性性质

Linearity of sendograph metric of fuzzy numbers

证明了紧承下方图度量不是平移不变的.对紧承下方图度量的代数运算的连续性进行了讨论.证明了关于紧承下方图度量,模糊数空间只能是嵌入到拓扑向量空间当中,但不嵌入赋范线性空间当中.并与关于上确界度量的结果进行了比较.最后,给出了一个紧承下方图度量的下界.

It is shown that the sendograph metric is not translation invariant.Basic properties of the sendograph metric under algebraic operations,as well as the continuity of the operations are discussed.It follows that with respect to the sendograph metric,the fuzzy number space can only be embedded into a topological vector space,but not into a normed linear space,as compared with the result about the supremum metric.Finally,a lower bound for the sendograph metric under translation is given.