BL代数的模糊子代数及其度量  

Fuzzy Subalgebras of BL-algebra and Its Measure

作　　者：朱翔[1,2] 廖祖华 ZHU Xiang;LIAO Zu-hua(Division of General Courses,Wuxi Institute of Technology, Wuxi 214121,China;School of Science,Jiangnan University, Wuxi 214122,China)

机构地区：[1]无锡职业技术学院基础部,江苏无锡214121 [2]江南大学理学院,江苏无锡214122

出　　处：《模糊系统与数学》2019年第1期32-49,共18页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61673193;61170121;11401259);江苏省自然科学基金资助项目(BK20151117);江苏省高等职业院校专业带头人高端研修资助项目(2016GRFX057)

摘　　要：首先给出了BL代数的(模糊)子代数的新概念,并讨论了它的基本性质。其次,为刻画BL代数中的模糊子集是模糊子代数的程度,提出了模糊子BL代数度的概念,研究了其性质并给出了模糊子BL代数度的几种等价刻画。最后还讨论了BL代数的模糊子集簇的交和直积的模糊子BL代数度以及它的模糊子集的同态像与原像的模糊子BL代数度。Firstly, a new concept of the (fuzzy) BL-subalgebra is given, and its basic properties are discussed. Secondly, in order to measure a degree to which a fuzzy subset in a BL-algebra is a fuzzy BL-subalgebra, the concept of the fuzzy BL-subalgebra degree is proposed. The paper puts forward several equivalent characterizations of the fuzzy BL-subalgebra degree by studying its properties.Finally, we study the fuzzy BL-subalgebra degrees of the intersection and fuzzy direct products of fuzzy subsets, and investigate the relationships between the fuzzy subalgebra degrees of the image and preimage of a fuzzy subset under a homomorphism.

关 键 词：BL代数 模糊子代数 同态 直积 度 

分 类 号：O159[理学—数学]