WBR_0-代数成为Boole代数的条件  

Conditions for WBR_0-algebras to be Boolean Algebras

作　　者：凌雪岷[1] 徐罗山[2] 杨凌云 LING Xue-min;XU Luo-shan;YANG Ling-yun(Department of Common Education, Anhui Xinhua University, Hefei 230011, China;Department of Mathematics, Yangzhou University, Yangzhou 225002, China;Schoolof Mathematics and Statistics,Jiangsu Normal University,Xuzhou 222116 ,China)

机构地区：[1]安徽新华学院通识教育部,安徽合肥230031 [2]扬州大学数学科学学院,江苏扬州225002 [3]江苏师范大学数学与统计学院,江苏徐州221116

出　　处：《模糊系统与数学》2018年第3期16-22,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11671008;61300153);江苏省高校自然科学基金资助项目(15KJD110006);江苏高校品牌专业建设工程项目(PPZY2015B109;PPZY2015A013);安徽省质量工程一般项目(2017jyxm30)

摘　　要：在WBR_0-代数中引入了蕴涵式条件(Imp)和可分解性条件(Dis),证明了在WBR_0-代数中这两个条件等价。引入了(正定)关联WBR_0-代数概念,并证明了满足(Imp)条件的WBR_0-代数与(正定)关联BR0-代数等价。我们也证明了蕴涵式WBR_0-代数与Boole代数等价,由此获得了WBR_0-代数成为Boole代数的四个充要条件。In WBR0-algebras,we introduced the implication type condition（Imp）and dissoluble condition（Dis）.It is proved that in WBR_0-algebras,the two conditions are equivalent.We also introduced the concept of（positive）implicative WBR0-algebras.It is proved that implication type WBR0-algebras are equivalent to（positive）implicative BR0-algebras.We also proved that implication type WBR0-algebras are equivalent to Boolean algebras,obtaining four necessary and sufficient conditions for WBR0-algebras to be Boolean algebras.

关 键 词：BOOLE代数 WBR0-代数 蕴涵式条件 可分解条件 

分 类 号：O189[理学—数学]