模糊值m-凸函数的性质及其共轭问题的研究  

On characterization and conjugate problem involving fuzzy-valued m-convex functions

作　　者：廖甲根 杜廷松[1,2] 

机构地区：[1]三峡大学理学院数学系,湖北宜昌443002 [2]武汉科技大学冶金工业过程系统科学湖北省重点实验室,湖北武汉430081

出　　处：《纯粹数学与应用数学》2016年第1期84-92,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(61374028);湖北省自然科学基金(2013CFA131);三峡大学培优基金(2015PY072)

摘　　要：基于m-凸函数提出了一类称为模糊值m-凸函数的新概念.首先,研究了模糊值m-凸函数的若干基本性质;其次,给出了模糊值m-凸函数的共轭函数的概念,并给出了模糊值m-凸函数在一定的条件下的共轭函数是模糊值m-凸函数等相关性质;最后,讨论了两个模糊值m-凸函数的共轭函数与其下卷积的共轭函数之间的相互关系.In this paper, we introduced a new class of generalized fuzzy-valued convex functions which called fuzzy-valued m-convex functions by modulating the m-convex functions. First, we studied some basic properties of the fuzzy-valued m-convex functions. Then we presented the conception of the conjugate function for fuzzyvalued m-convex functions and proved some related properties which the conjugate function of fuzzy-valued m-convex functions is also fuzzy-valued m-convex function under certain conditions. Finally we discuss the relationship between the conjugate functions and inf-convolution of two fuzzy-valued m-convex functions.

关 键 词：模糊值m-凸函数 共轭函数 下卷积 

分 类 号：O159.2[理学—数学]