模糊分析中的泛函空间  

The functional space in fuzzy analysis

作　　者：吴从炘[1] 任雪昆[1] 吴冲[2] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001 [2]哈尔滨工业大学管理学院,哈尔滨150001

出　　处：《中国科学：数学》2015年第9期1473-1486,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:10271035;71271070和11401137)资助项目

摘　　要：本文从四个方面简要综述了模糊分析中泛函空间的若干研究工作,包括:(1)在拓扑线性空间和某些模糊赋范线性空间框架下模糊泛函分析的发展;(2)模糊数空间的各种度量及对具有线性结构的相应具体泛函空间的嵌入;(3)模糊连续函数空间与针对不同模糊连续性的多层正则模糊神经网络的逼近;(4)基于单调测度论的可测函数空间和Sugemo可积函数空间.文中也提出今后开展研究的几点建议.吴从炘在1952–1955年期间是东北人民大学数学系的一名本科生,徐利治先生给予了吴长期指导与诸多支持.In this paper, we briefly summarize some work on the area of functional spaces in fuzzy analysis and devoted to four directions. The first direction is the development of the fuzzy functional analysis on the setting of topological linear space and several kinds of fuzzy normed linear spaces. Next direction is fuzzy number spaces with different metrics and the embeddings to concrete functional spaces with a linear structure. The third direction is fuzzy continuous function spaces and the approximation by multilayer regular fuzzy neural networks for various fuzzy continuities. The last direction is the space of measurable functions and the space of （Sugeno）- integrable functions based on the theory of monotonic measures. In this paper, we also present several suggestions on future research. Wu Congxin was an undergraduate student of the Mathematics Department of Northeastern People＇s University during 1952-1955, and Professor Hsu guided and supported him so much for long time.

关 键 词：模糊分析 泛函空间 模糊数 非可加测度 

分 类 号：O177[理学—数学]