模糊群的公理体系  

Axiom System for Fuzzy Groups

作　　者：邱东[1] 舒兰[1] 

机构地区：[1]电子科技大学应用数学学院,四川成都610054

出　　处：《模糊系统与数学》2008年第5期51-56,共6页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(10671030);电子科技大学青年学术带头人培养计划项目(Y02018023601033)

摘　　要：给出了模糊群的几个等价刻画,建立模糊群的公理体系并得到了五个最小完备系。此外还讨论以消去律为条件的模糊群的刻画,给出了有限模糊群和周期模糊群的最小完备系,同时也得到了一个一般模糊群的等价刻画,根据其三个推论可清楚地区分周期模糊群、无扭模糊群和混合模糊群。In this paper,we have given several equivalent characterizations of the concept of fuzzy subgroup,established the axiom system for fuzzy subgroup,and gotten five minimum complete axiom systems.Furthermore,we also have discussed on fuzzy group based on cancellation law,gotten the minimal complete system for fuzzy finite group and fuzzy periodic group,and obtained an equivalent characterization of general fuzzy group,according to which corollaries fuzzy periodic group,fuzzy torsion-free group and fuzzy mixed group can be clearly distinguished.

关 键 词：模糊群 公理体系 消去律 最小完备系 

分 类 号：O159[理学—数学]