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.
出处
《模糊系统与数学》
CSCD
1990年第1期56-64,共9页
Fuzzy Systems and Mathematics
