模糊映射不动点的存在性与稳定性  

The Existence and Stability for Fixed Points of Fuzzy Mappings

作　　者：周丽 贾文生 ZHOU LI;JIA WENSHENG(College of Mathematics and statistics,Guizhou University,Guiyang 550025)

机构地区：[1]贵州大学数学与统计学院,贵阳550025

出　　处：《应用数学学报》2023年第1期101-113,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金([12061020],[71961003]);贵州省自然科学基金(20201Y284,20205016,2021088,20215064);贵州省优秀青年科技基金(2021)5064;贵州大学基金[201811]资助项目。

摘　　要：本文给出了模糊映射不动点的一个存在性定理,并应用有限理性研究的统一模式,研究了一类特殊的模糊不动点问题的稳定性,即在有限理性框架下证明了当模糊映射和可行集发生扰动时,在Baire分类意义下大多数模糊不动点问题都是稳定的.更进一步,在一定条件下给出了有限理性下模糊不动点问题的逼近定理,为关于模糊不动点问题的求解算法提供了理论支持.In this paper,the existence result for fixed points of fuzzy mappings is investigated,and the stability result for a special class of fuzzy fixed points problems is studied by utilizing a technique of bounded rationality.That is,under the framework of bounded rationality,we prove that most of the fuzzy fixed points problems are stable on the meaning of Baire category with the perturbation of fuzzy mappings and feasible sets.Moreover,an approximation theorem for fuzzy fixed points problems is proved under appropriate conditions,which provides a theoretical support for the solving algorithm on the fuzzy fixed point problems.

关 键 词：模糊不动点 有限理性 结构稳定性 鲁棒性 逼近定理 

分 类 号：O225[理学—运筹学与控制论]