Fuzzy蕴涵代数  

FUZZY IMPLICATION ALGEBRAS

作　　者：吴望名[1] 

机构地区：[1]上海师范大学数学系

出　　处：《模糊系统与数学》1990年第1期56-64,共9页Fuzzy Systems and Mathematics

摘　　要：本文讨论一个新的代数系统Fuzzy蕴涵代数,简称FI代数。FI代数是[0,1]值逻辑的蕴涵连接词的代数抽象,我们讨论了两类重要的FI代数—正则FI代数和HFI代数,并指出正则HFI代数与Boole代数的内在联系。The purpose of this paper is to study a new algebra of type (2,0) which is called a fuzzy implication algebra.By a fuzzy implication algebra (FIA, for short)we mean an algebra (X,→,0) satisfying the following postulates:(I1) x→(y→z)=y→(x→z);(I2) (z→y)→((y→z)→(x→z))=1;(I3) (x→x)=1;(I4) If x→y=y→x=1 then x=y;(I5) 0→x=1;where 1=0→0.We investigate two classes of FIA, One is the regular FIA and the other is Heyting FIA. We shall point out thatt there exists an essential connection between regular Heyting FIA and Boolean algebras.

关 键 词：FI代数 滤子 同态 模糊蕴涵代数 布尔代数 

分 类 号：O159[理学—数学] O141.3[理学—基础数学]