Fuzzy implicative ideals of BCK-algebras

被引：43

作者：

Meng, J

Jun, YB

Kim, HS

机构：

[1] GYEONGSANG NATL UNIV,DEPT MATH EDUC,CHINJU 660701,SOUTH KOREA

[2] CHUNGBUK NATL UNIV,DEPT MATH EDUC,CHONJU 360763,SOUTH KOREA

来源：

FUZZY SETS AND SYSTEMS | 1997年 / 89卷 / 02期

关键词：

fuzzy; (implicative; positive implicative; commutative); ideal; BCK-algebra;

D O I：

10.1016/S0165-0114(96)00096-6

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The notion of fuzzy implicative ideals of BCK-algebras is introduced. The following results are obtained: for a BCK-algebra X, any fuzzy ideal mu of X must be a fuzzy subalgebra of X; suppose that mu and nu are fuzzy ideals of X with mu less than or equal to nu and mu(0) = nu(0); if mu is a fuzzy implicative ideal of X then so is nu; a fuzzy ideal mu of X is fuzzy implicative if and only if mu is both fuzzy positive implicative and fuzzy commutative; a BCK-algebra X is implicative (resp. positive implicative, commutative) if and only if every fuzzy ideal of X is fuzzy implicative (resp. fuzzy positive implicative, fuzzy commutative). Also, several characterizations of fuzzy implicative ideals are given. (C) 1997 Elsevier Science B.V.

引用

页码：243 / 248

页数：6

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