模糊数关于紧承下方图度量的线性性质(英文)Linearity of sendograph metric of fuzzy numbers
樊太和;李洋;
摘要(Abstract):
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.
关键词(KeyWords): 模糊数;紧承下方图度量;平移不变性
基金项目(Foundation): 国家自然科学基金(61379018)
作者(Authors): 樊太和;李洋;
参考文献(References):
- [1] Diamond P, Kloeden P. Metric Spaces of Fuzzy Sets[M]. Singapore:World Scientific, 1994.
- [2] Fan T H. Equivalence of weak convergence and endograph metric convergence for fuzzy number spaces, fuzzy logic, soft computing and computational intelligence[C]//Proceedings of the 11th international Fuzzy Systems Association World Congress, Beijing, 2005:41-49.
- [3] Goetschel R, Voxman W. Topological properties of fuzzy numbers[J]. Fuzzy Sets and Systems,1983,10(1):87-99.
- [4] Huang H. Characterizations of compact sets in fuzzy sets with Lp metric[J]. Fuzzy Sets and Systems, 2018,330(1):16-40.
- [5] Huang H. Characterizations of endograph metric andΓ-convergence on fuzzy sets[J]. Fuzzy Sets and Systems, 2018,350(1):55-84.
- [6] Kim D S, Kim Y K. Some properties of a new metric on the space of fuzzy numbers[J]. Fuzzy Sets and Systems, 2005,145(3):395-410.
- [7] Trutschnig W. Characterization of the sendograph-convergence of fuzzy sets by means of their Lpand levelwise convergence[J]. Fuzzy Sets and Systems, 2010,161(8):1064-1077.
- [8] Wang H M, Fan T H. On the Equivalence of Convergence of Fuzzy Number Series with Respect to Different Metrics[M]//Quantitative Logic and Soft Computing, Cham:Springer, 2016:465-475.
- [9] Wu C X, Ma M. An embedding operator of fuzzy numbers and its application for fuzzy integrals[J].System Science and Mathematical Science, 1990,3(3):193-199.
- [10] Puri M L, Ralescu D A. Differential for fuzzy functions[J]. Journal of Mathematical Analysis and its Applications, 1983,91(2):552-558.
- [11] Kloeden P. Compact supported endographs and fuzzy sets[J]. Fuzzy Sets and Systems, 1980,4(2):193-201.
- [12] Kloeden P. Fuzzy dynamic systems[J]. Fuzzy Sets and Systems, 1982,7(1):275-296.
- [13] Rudin W. Functional Analysis[M]. New York:McGraw-Hill Education Pvt Ltd, 2006.
- [14] Coroianu L. Trapezoidal approximations of fuzzy numbers using quadratic programs[J]. Fuzzy Sets and Systems, 2021,417(1):71-92.
- [15] Fan T H, Wang G J. Endographic approach on supremum and infimum of fuzzy numbers[J].Information Sciences, 2004,159(3):221-231.
- [16] Wu C X, Zhao Z T, Ren X K. Fuzzy Analysis and Special Functional Spaces[M]. Harbin:Harbin Institute of Science and Technology Press, 2013.