Extended Fuzzy $BCK$-subalgebras
نویسندگان
1 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
2 Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China
3 Department of Mathematics, Payame Noor University, Tehran, Iran
doi
10.22111/ijfs.2016.2600چکیده
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.
