DFI代数的距离函数及其性质
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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.
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.
引文
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[5]朱怡权.FI代数的导出序结构的一些性质[J].模糊系统与数学,2006,20(3):54-58.(ZHU Yiquan.Some Properties of the Induced Ordering in FI Algebras[J].Fuzzy Systems and Mathematics,2006,20(3):54-58.)
[6]朱怡权.基于FI-代数的一个逻辑系统[J].模糊系统与数学,2005,19(2):25-29.(ZHU Yiquan.A Logic System Based on FI-Algebras and Its Completeness[J].Fuzzy Systems and Mathematics,2005,19(2):25-29.)
[7]刘春辉.Fuzzy蕴涵代数的素模糊MP滤子[J].模糊系统与数学,2014,28(6):37-43.(LIU Chunhui.Prime Fuzzy MP-Filters in Fuzzy Implication Algebras[J].Fuzzy Systems and Mathematics,2014,28(6):37-43.)
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[9]代建云,吴洪博.分配的Fuzzy蕴涵代数[J].模糊系统与数学,2008,22(1):26-32.(DAI Jianyun,WU Hongbo.Distributive Fuzzy Implication Algebra[J].Fuzzy Systems and Mathematics,2008,22(1):26-32.)
[10]Turunen E.Mathematics behind Fuzzy Logic[M].Heidelberg:Physica-Verlag,1999:54-56.
[11]吴洪博,谢晶晶.一种度量结构在四种逻辑代数上的共性[J].模糊系统与数学,2014,28(2):104-110.(WU Hongbo,XIE Jingjing.Common Properties of a Logical Structure in Four Logical Algebras[J].Fuzzy Systems and Mathematics,2014,28(2):104-110.)
[12]周建仁,谢晶晶,吴洪博.基于剩余格的一类度量空间及性质[J].吉林大学学报(理学版),2012,50(5):897-901.(ZHOU Jianren,XIE Jingjing,WU Hongbo.A Metric Structure and Its Properties Based on Metric Residual Lattice[J].Journal of Jilin University(Science Edition),2012,50(5):897-901.)
[13]代建云,吴洪博.逻辑代数[0,1]上的度量结构[J].计算机工程与应用,2008,44(2):92-94.(DAI Jianyun,WU Hongbo.Metric Structure on Logical Algebra[0,1][J].Computer Engineering and Applications,2008,44(2):92-94.)
[2]李志伟,孙立民,郑崇友.正则Fuzzy蕴涵代数[J].模糊系统与数学,2002,16(2):22-26.(LI Zhiwei,SUN Limin,ZHENG Chongyou.Regular Fuzzy Implication Algebra[J].Fuzzy Systems and Mathematics,2002,16(2):22-26.)
[3]吴洪博,汪宁.基于正则FI代数的MT理想及其应用[J].电子学报,2013,41(7):1389-1394.(WU Hongbo,WANG Ning.MT Ideals of Regular FI Algebras with Their Applications[J].Acta Electronica Sinica,2013,41(7):1389-1394.)
[4]陈冬青,吴洪博.正则FI-代数与WBR0-代数的关系[J].陕西师范大学学报(自然科学版),2011,39(5):7-10.(CHEN Dongqing,WU Hongbo.The Relation between Regular FI-Algebras and WBR0-Algebras[J].Journal of Shaanxi Normal University(Natural Science Edition),2011,39(5):7-10.)
[5]朱怡权.FI代数的导出序结构的一些性质[J].模糊系统与数学,2006,20(3):54-58.(ZHU Yiquan.Some Properties of the Induced Ordering in FI Algebras[J].Fuzzy Systems and Mathematics,2006,20(3):54-58.)
[6]朱怡权.基于FI-代数的一个逻辑系统[J].模糊系统与数学,2005,19(2):25-29.(ZHU Yiquan.A Logic System Based on FI-Algebras and Its Completeness[J].Fuzzy Systems and Mathematics,2005,19(2):25-29.)
[7]刘春辉.Fuzzy蕴涵代数的素模糊MP滤子[J].模糊系统与数学,2014,28(6):37-43.(LIU Chunhui.Prime Fuzzy MP-Filters in Fuzzy Implication Algebras[J].Fuzzy Systems and Mathematics,2014,28(6):37-43.)
[8]徐扬.格蕴涵代数[J].西南交通大学学报,1993(1):20-27.(XU Yang.Lattice Implication Algebras[J].Journal of Southwest Jiaotong University,1993(1):20-27.)
[9]代建云,吴洪博.分配的Fuzzy蕴涵代数[J].模糊系统与数学,2008,22(1):26-32.(DAI Jianyun,WU Hongbo.Distributive Fuzzy Implication Algebra[J].Fuzzy Systems and Mathematics,2008,22(1):26-32.)
[10]Turunen E.Mathematics behind Fuzzy Logic[M].Heidelberg:Physica-Verlag,1999:54-56.
[11]吴洪博,谢晶晶.一种度量结构在四种逻辑代数上的共性[J].模糊系统与数学,2014,28(2):104-110.(WU Hongbo,XIE Jingjing.Common Properties of a Logical Structure in Four Logical Algebras[J].Fuzzy Systems and Mathematics,2014,28(2):104-110.)
[12]周建仁,谢晶晶,吴洪博.基于剩余格的一类度量空间及性质[J].吉林大学学报(理学版),2012,50(5):897-901.(ZHOU Jianren,XIE Jingjing,WU Hongbo.A Metric Structure and Its Properties Based on Metric Residual Lattice[J].Journal of Jilin University(Science Edition),2012,50(5):897-901.)
[13]代建云,吴洪博.逻辑代数[0,1]上的度量结构[J].计算机工程与应用,2008,44(2):92-94.(DAI Jianyun,WU Hongbo.Metric Structure on Logical Algebra[0,1][J].Computer Engineering and Applications,2008,44(2):92-94.)