格蕴涵代数的(∈,∈∨q)-模糊蕴涵理想  

(∈,∈∨q)-Fuzzy Implicative Ideal of Lattice Implication Algebras

作　　者：彭家寅[1] PENG Jiayin(School of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641100,China)

机构地区：[1]内江师范学院数学与信息科学学院,四川内江641100

出　　处：《内江师范学院学报》2020年第10期30-34,共5页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(11071178,11671284)。

摘　　要：利用模糊点与模糊集的属于和重于概念,引入格蕴涵代数的(∈,∈∨q)-模糊蕴涵理想的概念,研究它的相关性质.给出了(∈,∈∨q)-模糊蕴涵理想的几个等价刻画,指出了(∈,∈∨q)-模糊蕴涵理想与(∈,∈∨q)-模糊理想的关系,证明了(∈,∈∨q)-模糊蕴涵理想的交、积、投影、同态原象或同构象仍为(∈,∈∨q)-模糊蕴涵理想.By using the concept of belonging to and quasi-coincidence of a fuzzy point with a fuzzy set,the notion of(∈,∈∨q)-fuzzy implicative ideals in lattice implication algebras is introduced,and their related properties are studied.Several equivalent characterizations of(∈,∈∨q)-fuzzy implicative ideal are given,and the relationships between(∈,∈∨q)-fuzzy implicative ideal and(∈,∈∨q)-fuzzy ideal are discussed.Finally,it is proved that the intersection,product,projection,homomorphic preimage and isomorphic mage of(∈,∈∨q)-fuzzy implicative ideals are still(∈,∈∨q)-fuzzy implicative ideals.

关 键 词：格蕴涵代数 蕴涵理想 (∈ ∈∨q)-模糊理想 (∈ ∈∨q)-模糊蕴涵理想 

分 类 号：O159[理学—数学]