关于模糊值凸函数的共轭问题的研究

The research on conjugate problem of fuzzy-valued convex function

在Goetschel-Voxman所引进的序关系下,首先给出了模糊值凸函数的共轭函数的概念,并证明了模糊值凸函数的共轭函数是模糊值凸函数等相关性质;其次给出了模糊值凸函数的二次共轭函数的概念,并证明了相关性质;最后讨论了模糊值凸函数的共轭与下卷积之间的关系,证明了两个模糊值凸函数的共轭函数与其下卷积的共轭函数之间的等式关系.

In this paper, based on the ordering introduced by Goetschel-Voxman, we firstly give the conception of the conjugate function for fuzzy-valued convex function and prove some related properties, e. g. the conjugate function of fuzzy-valued convex function is also fuzzy-valued convex function. Secondly, we define the secondary conjugate function of the fuzzy-valued convex function and prove relevant properties. Finally we discuss the relationship between the conjugate and infimal convolution of the fuzzy-valued convex function and proved the equated relationship between the conjugate function of two fuzzy-valued convex functions and the conjugate function of infimal convolution.