Fuzzy蕴涵代数的伪赋值OA
Pseudo-valuations on Fuzzy implication algebras
为拓展模糊逻辑代数的相关理论,将伪赋值概念引入Fuzzy蕴涵代数.首先,探究了Fuzzy蕴涵代数伪赋值的相关性质,并讨论了其与滤子之间的对应关系;其次,建立了由伪赋值诱导的Fuzzy蕴涵代数的伪度量空间,并证明了由赋值诱导的伪度量空间是度量空间;最后,讨论了Fuzzy蕴涵代数伪赋值的构造,并根据伪赋值诱导的同余关系研究了Fuzzy蕴涵代数的商结构.
In order to extend the theory of Fuzzy logic algebra,the concept of pseudo-valuations in Fuzzy implication algebras is introduced.Firstly,the properties of pseudo-valuations in Fuzzy implication algebras are explored,and their correspondence with filters is discussed.Secondly,a pseudo-metric space on Fuzzy implication algebras induced by pseudo-valuations is established,and it is further proved that the pseudo-metric space induced by valuations is indeed a metric space.Finally,the construction of pseudo-valuations in Fuzzy implication algebras is discussed,and the quotient structures of Fuzzy implication algebras are studied based on the congruence relations induced by pseudo-valuations.
郭逢贵;周鑫;王旭
伊犁师范大学 数学与统计学院,新疆 伊宁 835000伊犁师范大学 数学与统计学院,新疆 伊宁 835000||伊犁师范大学 应用数学研究所,新疆 伊宁 835000伊犁师范大学 数学与统计学院,新疆 伊宁 835000
数理科学
Fuzzy蕴涵代数伪赋值滤子伪度量空间
Fuzzy implication algebraspseudo-valuationsfilterspseudo-metric space
《浙江大学学报（理学版）》 2026 (3)
334-340,7
伊犁师范大学提升学科综合实力专项(2022XKZY08)新疆维吾尔自治区研究生创新项目(XJ2025G249)伊犁师范大学高级别培育项目(YSPY2022011)国家自然科学基金项目(12471021).
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