Hasankhani, A., Saadat, H. (2004). SOME QUOTIENTS ON A BCK-ALGEBRA GENERATED BY A
FUZZY SET. Iranian Journal of Fuzzy Systems, 1(2), 33-43. doi: 10.22111/ijfs.2004.503

Abbas Hasankhani; Hamid Saadat. "SOME QUOTIENTS ON A BCK-ALGEBRA GENERATED BY A
FUZZY SET". Iranian Journal of Fuzzy Systems, 1, 2, 2004, 33-43. doi: 10.22111/ijfs.2004.503

Hasankhani, A., Saadat, H. (2004). 'SOME QUOTIENTS ON A BCK-ALGEBRA GENERATED BY A
FUZZY SET', Iranian Journal of Fuzzy Systems, 1(2), pp. 33-43. doi: 10.22111/ijfs.2004.503

Hasankhani, A., Saadat, H. SOME QUOTIENTS ON A BCK-ALGEBRA GENERATED BY A
FUZZY SET. Iranian Journal of Fuzzy Systems, 2004; 1(2): 33-43. doi: 10.22111/ijfs.2004.503

SOME QUOTIENTS ON A BCK-ALGEBRA GENERATED BY A
FUZZY SET

^{1}Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

^{2}Islamic Azad University Science and Research Campus, Kerman, Iran

Abstract

First we show that the cosets of a fuzzy ideal μ in a BCK-algebra X form another BCK-algebra X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show that X/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra is compatible, then P is a fuzzy quotient BCK-algebra. Finally we define the notion of a coset of a fuzzy ideal and an element of a BCK-algebra and prove related theorems.

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