摘要
模糊逻辑代数分析是模糊逻辑研究领域的热点问题之一。运用代数学和格论的方法及原理,深入研究了Fuzzy蕴涵代数及其理想问题。首先,利用伪补算子给出了Fuzzy蕴涵代数的若干新性质。其次,在Fuzzy蕴涵代数中引入理想和生成理想的概念并考察其性质特征和等价刻画。最后,讨论了由给定Fuzzy蕴涵代数全体理想构成的集合的格论特征,证明了该集合关于集合包含序构成分配的连续(代数)格,特别地构成完备Heyting代数,进而构成Frame的重要结论。
Algebraic analysis of fuzzy logic is one of the hot issues in the field of fuzzy logic research.In this paper,Fuzzy implication algebras and its ideals problem are further studied by using the method and principle of algebra and lattice theory.Firstly,some new properties of Fuzzy implication algebras are revealed by using pseudo-complement operators.Secondly,the concepts of ideal and generating ideal are introduced in Fuzzy implication algebras,and their properties and equivalent characterizations are investigated.Finally,the lattice theory characteristics of the set consisting of all ideals in a given Fuzzy implication algebra are discussed,it is proved that the set forms a distributive continuous(algebraic)lattice with respect to the set-inclusion order,in particular,it forms a complete Heyting algebra,and then forms a Frame.
作者
刘春辉
LIU Chunhui(Education Science College,Chifeng University,Chifeng 024000,Inner Mongolia Autonomous Regions,China)
出处
《浙江大学学报（理学版）》
CAS
CSCD
北大核心
2023年第4期391-401,408,共12页
Journal of Zhejiang University（Science Edition）
基金
内蒙古自治区高等学校科学研究项目(NJZY21138,NJZY22146)
内蒙古自治区社会科学基金项目(2022DY31)
内蒙古残疾人联合会研究项目(2023KTYJ19)
赤峰学院2022年教育教学研究重点项目(JYJXZ202204)。
关键词
模糊逻辑
FUZZY蕴涵代数
理想
生成理想
分配格
连续格
fuzzy logic
Fuzzy implication algebra
ideal
generating ideal
distributive lattice
continuous lattice
