极大代数上区间线性不等式组的可解性  

Solvabilities of Interval Linear Inequalities over Max-min Algebra

作　　者：李好好 王璐璐 贾胜男 Li Haohao;Wang Lulu;Jia Shengnan(School of Data Sciences,Zhejiang University of Finance and Economics,Hangzhou 310018,China;School of Sciences,Hangzhou Dianzi University,Hangzhou 310018,China)

机构地区：[1]浙江财经大学数据科学学院,杭州310018;[2]杭州电子科技大学理学院,杭州310018

出　　处：《数学理论与应用》2024年第2期51-64,共14页Mathematical Theory and Applications

基　　金：supported by the Natural Science Foundation of Zhejiang Province(No.LY21A010021)。

摘　　要：极值代数上区间系统的特征研究是一个具有重要意义的研究方向.本文讨论极大代数上区间不等式系统的各种类型的可解性:弱可解性、强可解性、容许与强容许可解性、控制与强控制可解性,给出对应的可解性特征.更进一步,我们分析以上各种解的存在性与相应的可解性,证明二者在某些情形下的等价性.此外,我们还在各种可解性下求其对应的最大解.The characteristics of interval systems under the framework of extremum algebra is a meaningful research direction.In this paper we study the characterizations of various kinds of solvabilities of interval linear inequalities in the max-min algebra,including the weak solvability,strong solvability,tolerance solvability,strongly tolerance solvability,control solvability and strongly control solvability.Furthermore,we analyze the existence of solutions and the solvabilities,and show these two concepts are equivalent in certain situations.In addition,we find the maximum solutions corresponding to different kinds of solvabilities.

关 键 词：区间线性系统 极大代数 最大解 

分 类 号：O178[理学—数学]