复模糊集值复模糊测度空间上的可测函数及其性质  

Measurable Function on Complex Fuzzy Set-valued Complex Fuzzy Measure Space and Its Properties

作　　者：马生全[1,2] 赵虎[1] 李生刚[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安陕西710062 [2]海南师范大学信息科学技术学院,海口海南571158

出　　处：《模糊系统与数学》2014年第6期73-79,共7页Fuzzy Systems and Mathematics

基　　金：国家国际科技合作专项基金资助项目(2012DFA11270);国家自然科学基金资助项目(11071151)

摘　　要：以改进的实可测函数的概念,借用新定义的模糊实数值可测函数概念,进一步将模糊测度与模糊可测函数概念扩展到更广泛的复模糊集上,给出复模糊集值复模糊可测函数概念,研究复模糊集值复模糊测度空间上的可测函数的性质,讨论了复模糊集值复模糊可测函数在此定义下一些基本性质的遗传性,得到了复模糊集值复模糊可测函数的一些重要性质,这些性质实际上拓广了经典可测函数的相应结论。为进一步讨论复模糊集值复模糊积分的研究奠定基础。In this paper, the concept of improved measurable function is used. In terms of a new fuzzy real valued measurable function, we will further extend fuzzy measure and fuzzy measurable function tocomplex fuzzy set, and we will give the notion of measurable function on complex fuzzy set-valued complex fuzzy measure space, then we will study the properties of measurable function on complex fuzzy set-valued complex fuzzy measure space and discuss it＇s genetic properties. Thus, we can obtain some important properties of such fuzzy measurable function, these results generalize classical conclusions and provide the theoretical basis to further discuss complex fuzzy set-valued complex fuzzy integral.

关 键 词：复模糊集 模糊测度 模糊可测函数 复模糊可测函数 

分 类 号：O159[理学—数学]