[1]刘晨玉,吴健荣.集值单调测度的自连续与伪自连续性[J].南京师范大学学报(自然科学版),2017,40(03):21.[doi:10.3969/j.issn.1001-4616.2017.03.004]
　Liu Chenyu,Wu Jianrong.Autocontinuity and Pseudo-Autocontinuity of Set-Valued Monotone Measures[J].Journal of Nanjing Normal University(Natural Science Edition),2017,40(03):21.[doi:10.3969/j.issn.1001-4616.2017.03.004]
点击复制

集值单调测度的自连续与伪自连续性()
分享到：

《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第40卷
期数:
2017年03期
页码:
21
栏目:
·数学·
出版日期:
2017-09-30

文章信息/Info

Title:
Autocontinuity and Pseudo-Autocontinuity of Set-Valued Monotone Measures
文章编号:
1001-4616(2017)03-0021-08
作者:
刘晨玉; 吴健荣
苏州科技大学数理学院,江苏 苏州 215009
Author(s):
Liu Chenyu; Wu Jianrong
College of Mathematics and Physics,Suzhou University of Science and Technology,Suzhou 215009,China
关键词:
集值分析; 单调测度; 自连续; 伪自连续
Keywords:
set-valued analysis; monotone measure; autocontinuity; pseudo-autocontinuity
分类号:
O159
DOI:
10.3969/j.issn.1001-4616.2017.03.004
文献标志码:
A
摘要:
在集值单调测度空间上,给出了集值单调测度的集值零可加、集值自连续、集值一致自连续、集值伪零可加、集值伪自连续和集值伪一致自连续等性质,并讨论了它们之间的蕴涵关系.
Abstract:
On monotone set-valued measure space,set-valued null-additive,set-valued autocontinuity,set-valued uniformly autocontinuity,set-valued pseudo-null-additive,set-valued pseudo-autocontinuity,set-valued uniformly pseudo-autocontinuity and so on,are defined. And some relationships among them are further discussed.

参考文献/References:

[1] CHOQUET G. Theory of capacities[J]. Annales de l’institute Fourier,1954,5:131-295.
[2]DEMPSTER A P. Upper and lower probabilities induced by multi-valued mapping[J]. Ann Math Statist,1967,38:325-339.
[3]SUGENO M. Theory of fuzzy integrals and its applications[D]. Tokyo:Tokyo Institute of Technology,1974.
[4]LIGINLAL O,OW T T. Moduling attitude to risk in human decision process:an application of fuzzy measures[J]. Fuzzy sets and systems,2006,157:3 040-3 054.
[5]LI J,SONG J J. Lebesgue theorems in non-additive measure theory[J]. Fuzzy sets and systems,2005,149:543-548.
[6]LI J,MESIAR R,PAP E. Atoms of weakly null-additive monotone measures and integrals[J]. Information sciences,2014,257:183-192.
[7]WATANABE T. On sufficient conditions for the Egoroff theorem of an ordered topological vector space-valued non-additive measure[J]. Fuzzy sets and systems,2011,162:79-83.
[8]WATANABE T,KAWASAKI T,TANAKA T. On a sufficient condition of Lusin’s theorem for non-additive measures that take values in an ordered topological vector space[J]. Fuzzy sets and systems,2012,194:66-75.
[9]GAGOLEWSKI M,MESIAR R. Monotone measures and universal integrals in a uniform framework for the scientific impact assessment problem[J]. Information sciences,2014,263:166-174.
[10]WANG Z. The autocontinuity of set function and the fuzzy integral[J]. J Math Anal Appl,1984,99:195-218.
[11]WANG Z. Asymptotic structural characteristics of fuzzy measures and their applications[J]. Fuzzy sets and systems,1985,16:277-290.
[12]WANG Z,KLIR G J. Fuzzy measure theory[M]. New York:Plenum Press,1992.
[13]LI J. Order continuity of monotone set function and convergence of measurable functions sequence[J]. Applied mathematics and computation,2003,135:211-218.
[14]LI J. On Egoroff’s theorems on fuzzy measure space[J]. Fuzzy sets and systems,2003,135:367-375.
[15]LI J,OUYANG Y,YASUDA M.Pseudo-convergence of measurable functions on Sugeno fuzzy measure space[C]//Proceeding of the 17th Joint Conference on Information Science,North Carolina,2003:56-59.
[16]SONG J J,LI J. Regularity of null-additive fuzzy measure on metric spaces[J]. International journal of general systems,2003,32(3):271-279.
[17]李桂玲,李军. 单调集函数的连续性与可测函数序列的收敛[J]. 模糊系统与数学,2005,19(3):111-115.
[18]GUO C,ZHANG D. On set-valued fuzzy measures[J]. Information sciences,2004,160:13-25.
[19]SOFIAN B F N. Another Gould type integral with respect to a multisubmeasure[J]. Annals of the alexandru ioan cuza university-mathematics,2011,57:13-30.
[20]GAVRILUT A C. Remarks on monotone interval-valued set multifunctions[J]. Information sciences,2014,259:225-230.
[21]高娜,李艳红,王贵君. 集值模糊测度的自连续性[J]. 四川师范大学学报(自然科学版),2008,31(4):386-389.
[22]汪彬,王贵君. 新序意义下集值模糊测度的伪自连续性[J]. 模糊系统与数学,2010,24(2):88-92.
[23]赵新虎,王贵君. 新序结构下函数列的伪依集值模糊测度收敛[J]. 模糊系统与数学,2011,25(2):2-6.
[24]GAVRILU A. Properties of regularity for multisubmeasures[J]. Annals of the alexandru ioan cuza university-mathematics,2004,50:373-392.
[25]PRECUPANU A,GAVRILUT A. A set-valued Egoroff type theorem[J]. Fuzzy sets and systems,2011,175:87-95.
[26]PRECUPANU A,GAVRILUT A. Set-valued Lusin type theorem for null-null-additive set multifunctions[J]. Fuzzy sets and systems,2012,204:106-116.
[27]开学文,吴健荣,李姣姣. 集值单调测度空间上的Lesbegue与Egoroff定理[J]. 西南师范大学学报(自然科学版),2015,40(8):10-15.

备注/Memo

备注/Memo:
收稿日期:2016-11-18.
基金项目:国家自然科学基金(11371013).
通讯联系人:吴健荣,教授,研究方向:非线性分析. E-mail:jrwu@mail.usts.edu.cn
更新日期/Last Update: 2017-09-30