DFI代数的距离函数及其性质  

Distance Function of DFI-Algebras and Its Properties

作　　者：刘慧敏[1] 吴洪博[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710119

出　　处：《吉林大学学报（理学版）》2016年第2期207-214,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11171196);中国高校基本科研业务费专项基金(批准号:GK201501001)

摘　　要：考虑分配的Fuzzy蕴涵代数(DFI代数).首先将距离函数的概念引入到DFI代数中,得到了DFI代数中距离函数的一些基本性质,并给出了在某些特殊的DFI代数(如全序DFI代数)上距离函数的特殊性质;其次,在DFI代数中引入一个新运算,得到了DFI代数距离函数的等价定义和性质;最后,根据所引进的距离函数建立相应的距离空间,并给出了一些性质.In order to further study DFI-algebra,firstly,the definition of a distance function in DFI-algebra was given. Its properties were discussed,and some special properties of the distance function of some kinds of special DFI-algebras,for example,linear DFI-algebras were given. Secondly,a new operation was introduced in DFI-algebra,and the equivalent definition of the distance function of DFI-algebras and some farther properties were given; finally,the corresponding metric space based on the distance function was introduced.

关 键 词：FI代数 正则FI代数 DFI代数 距离函数 

分 类 号：O141.1[理学—数学]