布尔代数的Ⅰ-Ⅴ模糊子代数  

Ⅰ-Ⅴ Fuzzy Subalgebras of Boolean Algebras

作　　者：许宏伟[1] 刘卫锋[1] 

机构地区：[1]郑州航空工业管理学院数理系,郑州450015

出　　处：《重庆师范大学学报（自然科学版）》2014年第4期82-86,共5页Journal of Chongqing Normal University:Natural Science

基　　金：航空科学基金(No.2013ZD55006);河南省教育厅科学技术研究重点项目(No.14A630017)

摘　　要：研究了布尔代数的Ⅰ-Ⅴ(Interval valued)模糊子代数及其相关性质,推广了相关文献中布尔代数的模糊子代数的结果。首先,通过将Ⅰ-Ⅴ模糊集应用于布尔代数,定义了布尔代数的Ⅰ-Ⅴ模糊子代数的概念,得到了布尔代数的Ⅰ-Ⅴ模糊子代数的两个简化判定定理;然后,讨论了布尔代数的Ⅰ-Ⅴ模糊子代数与(模糊)子代数之间的关系,证明了布尔代数上的IV模糊集是Ⅰ-Ⅴ模糊子代数的充要条件是Ⅰ-Ⅴ模糊集的截集是布尔代数的子代数,布尔代数上的Ⅰ-Ⅴ模糊集是Ⅰ-Ⅴ模糊子代数的充要条件是Ⅰ-Ⅴ模糊集的上下隶属函数均为布尔代数的模糊子代数;其次,讨论了布尔代数的Ⅰ-Ⅴ模糊子代数的交、同态等性质,证明了布尔代数的Ⅰ-Ⅴ模糊子代数的交、同态像和同态逆像等也是布尔代数的Ⅰ-Ⅴ模糊子代数;最后,讨论了布尔代数直积上的Ⅰ-Ⅴ模糊子代数。I-V （Interval valued） fuzzy subalgebras of Boolean algebra and its properties were discussed, and some results about fuzzy subalgebras of Boolean algebras in the related references were generalized. Firstly, bV fuzzy sets was applied to Boolean algebras, and I-V fuzzy subalgebras of Boolean algebra was defined and two simplified judging theorems of I-V fuzzy subalgebras were given. Secondly, the relation between interval valued fuzzy subalgebras and （fuzzy） subalgebras of Boolean algebra were discussed, and it was proved that I-V fuzzy sets of Boolean algebras was I-V fuzzy algebras if and only if the cut sets of I-V fuzzy sets was subalgebras of Boolean subalgebras, and I-V fuzzy sets of Boolean algebras was I-V fuzzy algebras if and only if lower and upper membership functions were subalgebras of Boolean subalgebras. Thirdly, the natures about intersection, homomorphisrn of I-V fuzzy subalge, bras of Boolean subalgebras were discussed, and it is stated that intersection, images and inverse-images under Boolean algebra homomorphism of I-V fuzzy subalgebras of Boolean algebra are respectively I-V fuzzy subalgebras of Boolean algebra. Lastly, I-V fuzzy subalgebras of direct product of Boolean algebras were discussed.

关 键 词：布尔代数 模糊子代数 Ⅰ-Ⅴ模糊子代数 子代数 

分 类 号：O174[理学—数学]