布尔代数的Ω-模糊商布尔代数  

Ω-Fuzzy Quotient Boolean Algebra of Boolean Algebra

作　　者：刘卫锋[1] 张理涛[1] 李自强[1] LIU Wei-feng;ZHANG Li-tao;LI Zi-qiang(School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450015,China)

机构地区：[1]郑州航空工业管理学院数学学院,河南郑州450046

出　　处：《数学的实践与认识》2020年第8期169-177,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11501525);河南省高等学校重点科研项目(20A110035);河南省高等学校重点科研项目计划基础研究专项(20zx003)。

摘　　要：定义了布尔代数的Ω-模糊理想的概念,证明了布尔代数的Ω-模糊理想的交、同态像和同态逆像等也是布尔代数的Ω-模糊理想.然后,令RΩ表示集合Ω到布尔代数R的所有映射的集合,通过在RΩ上定义三种运算■,■,-,得到布尔代数<RΩ,■,■,-,I0,I1>,并研究与其相关的模糊理想和Ω-模糊理想.最后,研究了布尔代数的Ω-模糊商布尔代数,给出了布尔代数的Ω-模糊商布尔代数的同态定理.The definition ofΩ-fuzzy ideal of Boolean algebra is given,and it is stated that intersection,images and inverse-images under Boolean algebra homomorphism ofΩ-fuzzy ideal of Boolean algebra are respectivelyΩ-fuzzy ideal of Boolean algebra Then,by defining three operations■,■,-in R^Ω,which expressed all mappings from setΩto Boolean algebra R,a Boolean algebra(RΩ,■,■,-,I0,I1)1 s obtained,and fuzzy ideal andΩ-fuzzy ideal about RΩare researched.LastlyΩ-fuzzy quotient Boolean algebra of Boolean algebra is studied,and homomorphism theorem ofΩ-fuzzy quotient Boolean algebra is obtained.

关 键 词：布尔代数 Ω-模糊理想 Ω-模糊商布尔代数 

分 类 号：O159[理学—数学] O153.2[理学—基础数学]