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.
作者
刘卫锋
张理涛
李自强
LIU Wei-feng;ZHANG Li-tao;LI Zi-qiang(School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450015,China)
出处
《数学的实践与认识》
北大核心
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)。
