环上的模糊理想幂格及其强截集诱导的格

Fuzzy Ideal Power Lattice and Induced lattice of Fuzzy Ideal Strong Cut Set of a Ring

给出了环上模糊理想幂格的概念,得到相关性质。进而由环上模糊理想强截集诱导出格,讨论了它不是分配格,但为模格。同时,将环上升为主理想环,得到了模糊理想乘积的强截集等于强截集的乘积,且都为环的理想。最后,讨论了Boolean环的模糊子集为模糊理想与其伴随构成交半格的关系。

In this paper,we define a fuzzy ideal power lattice of a ring and obtain relative properties.At the same time,we use strong cut set of fuzzy ideal of a ring to construct lattice,which is a modular lattice but not a distributive lattice.When the ring is stepped up principle ideal ring,we prove that strong cut set of fuzzy ideal＇s product is equal to strong cut set＇s product.Meanwhile,they are ideals of a ring.At last,we prove the relation between fuzzy ideal of Boolean ring and cross-semi lattice formed by accompanying fuzzy subset.