摘要
在Goetschel-Voxman所引进的序关系下,首先给出了生成函数的概念,证明了由一类凸集生成的函数是模糊值凸函数;其次利用上图的性质,建立了模糊值凸函数的下卷积、右乘等概念,并给出了相应的定理;最后讨论了模糊值函数的凸化问题,并给出了其刻画定理。
In this paper, we first present the conception of generated function under the total order introduced by Goetschel-Voxman and prove that the function generated by a kind of convex sets is fuzzy-valued function. Secondly, we use the properties of epigraph construct the definitions of infimal convolution, right scalar multiplication and give corresponding theorems. At last, we discuss the convex optimization problem of fuzzy-valued function and give the depict theorems.
出处
《模糊系统与数学》
CSCD
北大核心
2012年第5期167-171,共5页
Fuzzy Systems and Mathematics
基金
内蒙古自治区自然科学基金资助项目(2010MS0119)
关键词
模糊值凸函数
生成函数
下卷积
右乘数
凸包
Fuzzy-valued Function
Generated Function
Infimal Convolution
Right Scalar Multiplication
Convex Hull
