BR_0-分配性及其推广  

BR_0-distributivity and its generalization

作　　者：李玲玲[1] 吴洪博[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：《山东大学学报（理学版）》2012年第2期93-97,共5页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10871121)

摘　　要：在BR0-代数结构中,BR0-分配性a→b∨c=(a→b)∨(a→c)具有十分重要的地位。本文证明了具有BR0-分配性的剩余格同样具备十分良好的性质。首先将BR0-分配性引入到剩余格中,并给出了BR0-分配性的等价形式。其次,在完备剩余格中将BR0-分配性进行了推广,提出了BR0-第一无限分配性和BR0-第二无限分配性。最后,分别在正则完备剩余格,单位区间[0,1]中讨论了两种BR0-无限分配性的关系及性质。BR0-distributivity has an important position in the structure of BR0-algebras which says a→b∨c=（a→b）∨（a→c）.It is proved that residuated lattices with BR0-distributivity also have good properties.BR0-distributivity is introduced in residuated lattices,and its equivalent form is given.Then the BR0-distributivity is generalized in complete residuated lattices,and BR0-first infinite distributivity and BR0-second infinite distributivity are obtained.Finally,the properties and relationship between two kinds of BR0-infinite distributivity are discussed in regular complete residuated lattices and the unite interval ,respectively.

关 键 词：模糊逻辑 剩余格 BR0-代数 BR0-分配性 无限分配性 

分 类 号：O141[理学—数学]