Zhan, Jianming; Hamidi, Mohammad; Borumand Saeid, Arsham Extended fuzzy BCK-subalgebras. (English) Zbl 1357.06018 Iran. J. Fuzzy Syst. 13, No. 4, 125-144 (2016). Summary: 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. MSC: 06F35 BCK-algebras, BCI-algebras Keywords:extended fuzzy BCK-subalgebra; (strongly) fuzzy hyper BCK-ideal; fundamental relation \(\beta^*\) PDFBibTeX XMLCite \textit{J. Zhan} et al., Iran. J. Fuzzy Syst. 13, No. 4, 125--144 (2016; Zbl 1357.06018) Full Text: Link