格的模糊半素理想及其度量  

Fuzzy Semiprime Ideals of Lattices and Its Measure

作　　者：黄飞[1] 廖祖华[2] HUANG Fei;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》2020年第5期38-52,共15页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61170121,11401259,61673193);江苏省自然科学基金资助项目(BK2015117)。

摘　　要：首先给出了格的模糊半素理想的新概念,并讨论了它的基本性质。其次,为刻画格的模糊子集是模糊半素理想的程度,提出了模糊半素理想度的概念,给出了模糊半素理想度的几种等价刻画。最后还讨论了格的模糊半素理想度的性质。Firstly,a new concept of the fuzzy semiprime ideal on lattices is given,and its basic properties are discussed.Secondly,the new concept of the measure of fuzzy semiprime ideals is given,and use measures of fuzzy semiprime ideals to discuss that the fuzzy subset is the degree of fuzzy semiprime ideals.Meanwhile,this paper puts forward several equivalent characterizations of the fuzzy semiprime ideal degree by studying its properties.Finally,we study the fuzzy semiprime ideal degrees of the intersection and fuzzy direct products of fuzzy subsets,and investigate the relationships between the fuzzy semiprime ideal degrees of the image and preimage of a fuzzy subset under a homomorphism.

关 键 词：格 半素理想 模糊半素理想 度 

分 类 号：O159[理学—数学]