布尔代数模糊理想的度量  

Fuzzy Ideals of Boolean Algebra and Their Measure

作　　者：杨先伟[1] 廖祖华[2] YANG Xian-wei;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》2021年第4期49-58,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61170121);江苏省自然科学基金资助项目(BK20151117);江苏省高等学校自然科学基金资助项目(19KJD100006);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,通过蕴涵运算给出布尔代数的模糊理想度的概念,用来刻画一个布尔代数的模糊子集是布尔代数的模糊理想的程度。其次,研究布尔代数的模糊理想度的等价刻画。最后,讨论了布尔代数的模糊子集簇的交和直积的模糊理想度,以及模糊子集的同态像与原像的模糊理想度。Firstly, a new concept ofthe Fuzzy ideals of Boolean algebra degree is given by means of the implication operator, which could measure the degree that a fuzzy subset of Boolean algebra is a fuzzy ideals of Boolean algebra. Secondly, the equivalent characterizations ofthe fuzzy ideals of Boolean algebra degree are studied. Finally, we discuss the fuzzy ideals of Boolean algebra degrees of the intersection and direct products offuzzy subsets, and investigate the ideal degrees of the image and preimage ofa fuzzy subset under a homomorphism.

关 键 词：布尔代数 模糊理想 同态 直积 度 

分 类 号：O159[理学—数学]