FUZZY QUOTIENT STRUCTURES OF BCK-ALGEBRAS INDUCED BY FUZZY BCK-FILTERS

Title & Authors
FUZZY QUOTIENT STRUCTURES OF BCK-ALGEBRAS INDUCED BY FUZZY BCK-FILTERS
Jun, Young-Bae;

Abstract
In this paper, we establish a generalization of fundamental homomorphism theorem in BCK-algebras by using fuzzy BCK-filters. We prove that if $\small{{\mu}}$. (resp. v) is a fuzzy BCK-filter of abounded BCK-algebra X (resp. Y), then $\small{\frac{X{\times}Y}{{\mu}{\times}v}{\approxeq}X/{\mu}{\times}Y/v;\;and\;if\;{\mu}}$ and F is a BCK-filter in a bounded BCK-algebra X such that $\small{F/{\mu}}$ is a BCK-filter of $\small{X/{\mu}}$, then $\small{\frac{X/{\mu}}{F/{\mu}}{\approxeq}X/F}$.
Keywords
(fuzzy) BCK-filter;fuzzy quotient BCK-algebra;
Language
English
Cited by
1.
Quotient BCK/BCI-algebras induced by soft sets, Afrika Matematika, 2016, 27, 7-8, 1339
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