Jianming Zhan - Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei ۴۴۵۰۰۰, China
Mohammad Hamidi - Department of Mathematics, Payame Noor University, Tehran, Iran
Arsham Borumand Saeid - Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

This  paper extends the notion of fuzzy BCK-subalgebras to fuzzy hyper BCK-subalgebras and defines an extended fuzzy BCK-subalgebras. This study  considers  a type of fuzzy hyper  BCK-ideals  in this  hyperstructure  and  describes   the  relationship  between hyper  BCK-ideals and  fuzzy hyper  BCK-ideals.  In fact, it tries to introduce   a  strongly  regular  relation  on hyper BCK-algebras. Moreover,  by using  the   fuzzy hyper  BCK-ideals, it defines a congruence  relation  on (weak commutative) hyper BCK-algebras  that under some conditions is strongly regular and  the quotient of any hyper BCK-algebra via this relation  is a (hyper  BCK-algebra) BCK-algebra.

Extended fuzzy BCK-subalgebra, (Strongly) Fuzzy hyper BCK-ideal, Fundamental relation beta^*