区间线性不等式组的AE区间解  

AE interval solutions to interval linear inequalities

作　　者：夏梦雪 李好好 XIA Meng-xue;LI Hao-hao(Department of Basic,PLA Army Academy of Artillery and Air Defense,Hefei 230000,China;School of Data Sciences,Zhejiang University of Finance and Economics,Hangzhou 310018,China)

机构地区：[1]中国人民解放军陆军炮兵防空兵学院基础部,安徽合肥230000 [2]浙江财经大学数据科学学院,浙江杭州310018

出　　处：《高校应用数学学报（A辑）》2024年第4期485-492,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：浙江省自然科学基金(LY21A010021);校一流学科B类(浙江财经大学数学)资助。

摘　　要：区间线性系统中描述问题的参数带有不确定性,因而在工程及科技实践中更具有实际应用价值和理论研究意义.文中主要探讨区间不等式系统的区间解问题,首次基于逻辑量词提出AE区间解的概念,并刻画了区间线性不等式系统AE区间解的解集特征.主要结果涵盖了区间线性不等式系统中若干类型区间解的既有判别条件为其特例,为统一研究约束域为区间线性不等式组的区间优化问题提供了重要的理论基础.The mathematical models of various uncertain systems in engineering and scientific practice can be described by interval systems and interval optimization models,which are of more practical value and theoretical significance.The article mainly discusses the interval solution problem of interval inequalities.Based on logical quantifiers,a new concept of AE interval solution is defined for thefirst time,and corresponding characterizations are fully proposed.In particular,the characterizations of weak interval solution,strong interval solution,tolerance interval solution and control interval solution of the interval inequalities Ax≤b are established.The main results may provide an theoretical basis for the study of interval optimization problems in a general form.

关 键 词：区间系统 区间线性不等式组 AE区间解 

分 类 号：O151.2[理学—数学]