Q-代数中的粗糙理想  

Rough Ideal in Q-algebras

作　　者：梁少辉[1] 魏博涛 周婉婷 王美丽[1] LIANG Shao-hui;WEI Bo-tao;ZHOU Wan-ting;WANG Mei-li(Collage of Sciences,Xi'an University of Science and Technology,Xi'an 710054,China)

机构地区：[1]西安科技大学理学院,陕西西安710054

出　　处：《模糊系统与数学》2024年第2期62-68,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金(12001420);陕西省教育厅自然科学专项(17JK0510).

摘　　要：首先,给出了Q-代数中粗糙集的概念,讨论了Q-代数中粗糙集的一系列重要性质,将粗糙集理论引入Q-代数中。其次,提出了Q-代数中的粗糙理想的定义,探讨了Q-代数中理想与粗糙理想的相互关系。最后,引入了Q-代数中弱同余的概念,得到了弱同余的一些刻画,证明了Q-代数中的所有上粗糙理想之集是dcpo,Q-代数中所有下粗糙理想之集是代数格。In this paper,we first introduce the concept of rough set in Q-algebra,discuss a series of important properties of rough set in Q-algebra,and introduce rough set theory into Q-algebra.Secondly,the definition of rough ideal in Q-algebra is proposed,and the relationship between ideal and rough ideal in Q-algebra is discussed.Finally,the concept of weak congruence in Q-algebras is introduced,and some characterizations of weak congruence are obtained.It is proved that the set of all upper rough ideals in Q-algebras is dcpo,and the set of all lower rough ideals in Q-algebras is algebraic lattice.

关 键 词：QUANTALE Q-代数 粗糙集 粗糙理想 代数格 

分 类 号：O153[理学—数学]