摘要
本文针对Goerschel和Voxman意义度量下模糊数度量空间的七大基本定理进行了讨论,四个定理仍然成立。对不成立的定理,分别给出了使它们成立的充分条件,并给与了证明。
This paper discusses the basic theorem in fuzzy number space with supremum metric. Four theorems remain holds in fuzzy number space. Separately, the sufficient conditions are shown to hold the other theorems.
引文
[1] Diamond P,Kloeden P E.Metric space of fuzzy sets-Theory and applications[M].Singapore:World Scientific,1994.
[2] 吴从炘,马明.模糊分析学基础[M].国防工业出版社,1991.
[3] 李洪亮,裴慧丽,吴从炘.Zadeh扩张原理下模糊数空间的代数结构[J].模糊系统与数学,2014,28(1):84~87.
[4] Wu C X,Wu C.The supremum and infimum of the set of fuzzy numbers and its application[J].Journal of Mathematic Analysis and Application,1997,210:49~511.
[5] Wu C X,Wu C.Some note on the supremum and infimum of the set of fuzzy numbers[J].Fuzzy Sets and Systems,1999,103:183~187.
[6] Fang J X,Huang H.On the level convergence of sequence of fuzzy numbers[J].Fuzzy Sets and Systems,2004,147:417~435.
[7] Wu C X,Li H L,Ren X K.A note on the sendograph metric of fuzzy numbers[J].Information Sciences,2009,179:3410~3417.
[8] Pedraza T.Convergence of fuzzy sets with respect to the supremum metric[J].Fuzzy Sets and Systems,2014,245:83~100.
[9] 吴从炘,李洪亮.两个基本定理在模糊数度量空间的推广[J].黑龙江大学自然科学学报,2008,25(2):141~143.