赋Γ收敛结构的模糊数空间上的两个基本定理

Two basic theorem on fuzzy number space equipped with Γ-convergence

首先介绍关于模糊数和Γ收敛的相关概念和结论,然后给出具有小于等于关系的模糊数之间的Hausdorff距离的一个不等式。设u,v,w∈E,若uvw,则dH(endu,endv)≤dH(endu,endw)。在此基础上证明了在赋Γ收敛结构的模糊数空间上成立单调收敛定理和闭区间套定理。这一结论推广了实数理论的相关结果。

Some notions and results related to fuzzy numbers and Г convergence are firstly introduce. Then, it give an inequality on the Hausdorff distances between the fuzzy numbers which have the equal or lesser than relation： Suppose that u,v,w∈E. If u≤v≤w, then dH（end u,end v） ≤dH（end u,end w）. From which, it is shown that the monotone convergence theorem and the nested intervals theorem both hold on fuzzy number space equipped with the Г-convergence. These conclusions generalize the corresponding results for real number space.