布尔代数的Ω-模糊子代数  

Ω-fuzzy subalgebra of Boolean algebra

作　　者：刘卫锋[1] 

机构地区：[1]郑州航空工业管理学院数理系,河南郑州450015

出　　处：《湖北大学学报（自然科学版）》2013年第2期144-148,共5页Journal of Hubei University：Natural Science

基　　金：河南省教育厅科学技术研究重点项目(12B110027);郑州航空工业管理学院青年科研基金(2011113003)资助

摘　　要：研究布尔代数的Ω-模糊子代数及其性质.定义布尔代数的Ω-模糊子代数,给出布尔代数的Ω-模糊子代数的两个简化判定定理,并证明布尔代数的Ω-模糊子代数的交、同态像和同态逆像等也是布尔代数的Ω-模糊子代数.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3种运算,■,-,得到布尔代数〈RΩ,,■,-,I0,I1〉,并研究与其相关的模糊子代数和Ω-模糊子代数.Ω-fuzzy subalgebra of Boolean algebra and its properties were discussed in this paper. Ω-fuzzy subalgebra of Boolean algebra was defined and two judging theorems of Ω-fuzzy subalgebra of Boolean algebra were given, and it was stated that intersection-images and inverse-images under Boolean algebra homomorphism of Ω-fuzzy subalgebra of Boolean algebra were respectively Ω-fuzzy subalgebra of Boolean algebra. Then, by defining three operations , ,- over Rn where RΩ expressed all mappings from set Ω to Boolean algebra R, a Boolean algebra （RΩ, , ,-, I0, I1 ） was obtained, and fuzzy subalgebra and Ω-fuzzy subalgebra about Rawere researched.

关 键 词：布尔代数 Ω-模糊子代数 模糊子代数 运算 

分 类 号：O159[理学—数学]