Strongly Generalized Convex Fuzzy-Valued Function and Its Application in Fuzzy Optimization  

模糊数值函数的强广义凸性及其在模糊优化中的应用

作　　者：BAI Yu-juan LIU Kun ZHANG Chen 

机构地区：[1]College of Mathematics and Statistics,Longdong University,Qingyang 745000,China

出　　处：《Chinese Quarterly Journal of Mathematics》2020年第4期370-387,共18页数学季刊（英文版）

基　　金：Supported by Natural Science Foundation of Gansu Province of China (Grant No.18JR3RM238);Research Foundation of Higher Education of Gansu Province of China (Grant No. 2018A-101);Innovation Ability promotion Project of Higher Education of Gansu Province of China (Grant No. 2019A-117)。

摘　　要：Based on the ordering of fuzzy numbers proposed by Goetschel and Voxman,the representations and some properties of strongly preinvex fuzzy-valued function are defined and obtained, several new concepts of strongly monotonicities fuzzy functions are introduced, the relationship among the strongly preinvex, strongly invex and monotonicities under some suitable and appropriate conditions is established and a necessary condition for strongly pseudoinvex functions is given. As an application, the conditions of local optimal solution and global optimal solution in the mathematical programming problem are discussed.

关 键 词：Fuzzy-number-valued functions Strongly generalized convexity Fuzzy optimization 

分 类 号：O159[理学—数学]