布尔代数的模糊点子代数

Fuzzy Dot Subalgebra in Boolean Algebra

模糊点子代数是模糊代数研究的一个重要内容.通过将相关代数理论中的模糊点子代数概念引入到布尔代数之中,给出了布尔代数的模糊点子代数的概念,推广了布尔代数模糊子代数的概念.然后,系统地讨论了布尔代数的模糊点子代数的性质,给出了布尔代数的模糊点子代数的2个简化判断定理,证明了布尔代数的模糊点子代数的交、同态像和同态逆像也是布尔代数的模糊点子代数等相关结论.研究结果推广了布尔代数的模糊子代数及其相关结论,进一步丰富了布尔代数上的模糊理论.

Fuzzy dot subalgebra is an important field in the study of fuzzy algebra. In this paper, the concept of fuzzy dot subalge- bra in the related algebra theory is introduced for Boolean algebra, and the concept of fuzzy dot subalgebra in Boolean algebra, which is a generation of fuzzy subalgebra in Boolean algebra, is proposed. The related properties of fuzzy dot snbalgebra in Boolean algebra are systematically discussed. Two simplified judging theorems of fuzzy dot subalgebra in Boolean algebra are obtained. Furthermore, it is proved that the intersection, images and inverse-images under Boolean algebra homomorphism of fuzzy dot subalgebra in Boolean alge- bra are also fuzzy dot subalgebra in Boolean algebra respectively. These results extend fuzzy subalgebra in Boolean algebra and its relat- ed results, also enriched fuzzy theory in Boolean algebra.