剩余格上蕴含单调算子的性质  

Properties of Implication-based Monotone Operators on Residuated Lattices

作　　者：刘怡娣[1] 

机构地区：[1]大连理工大学城市学院,辽宁大连116000

出　　处：《信阳师范学院学报（自然科学版）》2014年第1期1-3,共3页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：山东省自然科学基金项目(ZR2011AL003)

摘　　要：针对剩余格上单调算子的性质,首先对比分类了剩余格上蕴含单增算子和蕴含单减算子理想情况下的性质,其次讨论了剩余格上蕴含单增算子和蕴含单减算子的复合算子及其性质,最后分析了蕴含单调算子的拓扑结构,并证明其构成剩余格上的Alexandrov模糊拓扑.The properties of implication-based monotone operators were investigated in residuated lattices .Firstly, a comparable investigation was made for the implication-based isotone and the implication-based antitone operators , and then the differences between them were given .Secondly , the properties of composition of the implication-based isotone and the implication-based antitone operators were discussed .Finally, the topological structures on residuated lattices with implication-monotone operators were analyzed , and it was proved that the sets of the implication-based isotone forms an Alexandrov fuzzy topology .

关 键 词：剩余格 蕴含单调算子 理想条件 模糊拓扑 

分 类 号：O159[理学—数学]