Document Type: Research Paper


1 School of Sciences, East China Institute of Technology, Fuzhou, Jiangxi 344000, China

2 Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province 445000, China

3 Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, China


By means of a kind of new idea, we consider  the $(\in,\ivq)$-fuzzy
$h$-ideals of a hemiring.  First, the concepts of $(\in,\ivq)$-fuzzy
left(right) $h$-ideals of a hemiring are provided and some related
properties are investigated. Then, a kind  of quotient hemiring  of
a hemiring by an $(\in,\ivq)$-fuzzy $h$-ideal is presented and
studied. Moreover, the notions of generalized $\varphi$-compatible
$(\in,\ivq)$-fuzzy left(right) $h$-ideals of a hemiring are
introduced and some properties of them are provided. Finally, the
relationships among $(\in,\ivq)$-fuzzy $h$-ideals, quotient
hemirings and homomorphisms are  explored and several homomorphism
theorems are provided.


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