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

Document Type: Research Paper

Authors

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.

Keywords


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