Korean J. Math. Vol. 26 No. 3 (2018) pp.373-385
DOI: https://doi.org/10.11568/kjm.2018.26.3.373

Fuzzy homomorphism theorems on groups

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Published: Sep 30, 2018
Keywords:
Fuzzy mappings, fuzzy homomorphisms, fuzzy normal subgroups, quotient groups induced by fuzzy normal subgroups, fuzzy isomorphism theorems
Mathematics Subject Classification:
03E72, 08A72, 20A99

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Gezahagne Mulat Addis
Department of Mathematics University of Gondar Gondar, Ethiopia

Abstract

In this paper we introduce the notion of a fuzzy kernel of a fuzzy homomorphism on groups and we show that it is a fuzzy normal subgroup of the domain group. Conversely, we also prove that any fuzzy normal subgroup is a fuzzy kernel of some fuzzy epimorphism, namely the canonical fuzzy epimorphism. Finally, we formulate and prove the fuzzy version of the fundamental theorem of homomorphism and those isomorphism theorems.



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