Quantale的上粗理想  

Upper Rough Ideals of Quantales

作　　者：周欣[1] 赵彬[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《模糊系统与数学》2013年第5期146-152,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11171196;11301316);中央高校基本科研业务费专项(GK201302003)

摘　　要：利用粗糙集的理论方法,主要对Quantale的上近似进行研究。引入Quantale的上粗子Quantale,上粗理想和上粗拟理想的概念,讨论了它们的若干性质。主要结果是:(1)证明了理想一定是上粗理想,满足上近似集和下近似集相等的上粗理想是理想;(2)证明了Quantale的上粗子Quantale和上粗(左,右)理想在Quantale满同态下的原象仍是上粗子Quantale和上粗(左,右)理想;(3)证明了上粗(左,右)理想是上粗拟理想,同时是半群结构下的理想的上粗拟理想是上粗理想。In this paper, rough quantales. At the same time, rough quasi-ideals of a quantale sets theory is used in discussing the properties of upper approximations of the concepts of upper rough subquantale, upper rough ideals and upper are given, and the properties of these mathematical structures are studied.The main results are： （1） It is proved that ideals must be upper rough ideals, and an upper rough ideal whose upper approximation equals lower approximation must be an ideal~ （2） It is proved that when a quantale homomorphism is surjeetive, the inverse images of upper rough subquantales and upper rough （left, right） ideals are still upper rough subquantales and upper rough （left, right） ideals~ （3） It is proved that upper rough （left, right） ideals must be upper rough quasi-ideals, and an upper rough quasi-ideal which is also an ideal of the structure of semigroup must he an upper rough ideal.

关 键 词：QUANTALE 上粗子Quantale 上粗理想 上粗拟理想 Quantale同态 

分 类 号：O153[理学—数学]