李娜;包玉娥;

• 1:内蒙古民族大学数学学院

摘要(Abstract)：

首先给出了区间数空间子集的有界性及确界等概念,并给出了确界的存在性定理;然后讨论了区间值映射的半连续性问题,给出了区间值映射的半连续性概念及相关性质;最后讨论了半连续区间值映射的凸性问题,给出了半连续区间值映射为凸区间值映射的两个充分条件.

关键词(KeyWords)： 区间数;区间值映射;半连续性;凸性

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(11461052);; 内蒙古自然科学基金(2018MS01010);; 内蒙古民族大学研究生科研基金(NMDSS1874)

作者(Authors): 李娜;包玉娥;

参考文献(References)：

• [1] Wu H C. The Karush-Kuhn-Tucker optimality conditions in multi-objective programming problems with interval-valued objective functions[J]. European Journal of Operational Research, 2009,196:49-60.
• [2] Osuna-Gomez R, Chalco-Cano Y, Hernandez-Jimenez B, et al. Optimality conditions for generalized differentiable interval-valued functions[J]. Information Sciences, 2015,321:136-146.
• [3] Chalco-Cano Y, Rufian-Lizan A, Roman-Flores H, et al. Calculus for interval-valued functions using generalized Hukuhara derivative and applications[J]. Fuzzy Sets and Systems, 2013,219:49-67.
• [4] VanHoa N, Lupulescu V, RegandLe D. Solving interval-valued fractional initial value problems under Caputo gH-fractional differentiability[J]. Fuzzy Sets and Systems, 2017,309:1-34.
• [5] Craven B D. Invex functions and constrained local minima[J]. Bull. Austral. Math. Soc., 1981,24(3):357-366.
• [6] Zhang P. An interval mean-average absolute deviation model for multipored portfolio selection with risk control and cardinality constraints[J]. Soft Comput., 2016,20:1203-1212.
• [7] Wu H C. On interval valued nonlinear programming problems[J]. Journal of Mathematical Analysis and Applications, 2008,338:299-316.
• [8] Singh D, Dar B A, Kim D S. KKT optimality conditions in interval valued multi-objective programming with generalized differentiable functions[J]. European Journal of Operational Research,2016,254:29-39.
• [9] Bao Y E, Zhao B, Bai E D. Directional differentiability of interval valued functions[J]. J. Math.Computer Sci., 2016,16:507-515.
• [10] Bao Y E, Li J J, Bai E D. Study on differentiability problems of interval-valued functions[J]. J.Nonlinear Sci. Appl., 2017,10:5677-5689.
• [11]代兵,包玉娥.区间数的绝对值与区间值函数的极限[J].纯粹数学与应用数学, 2016,32(6):583-590.
• [12] Ying X M, Teo K L, Yang X Q. A characterization of convex function[J]. J. Math. Letters, 2000,13:27-30.