Author/Authors :
Yunqiang Yin، Yunqiang Yin نويسنده Yunqiang Yin, Yunqiang Yin , Jianming Zhan، Jianming Zhan نويسنده Jianming Zhan, Jianming Zhan , Bijan Davvaz، Bijan Davvaz نويسنده Bijan Davvaz, Bijan Davvaz
Abstract :
In this paper, the new notions of ``belongingness ($\in_{\gamma}$)"
and ``quasi-coincidence ($q_\delta$)" of a fuzzy point with a fuzzy
set are introduced. By means of this new idea, the concept of
$(\alpha,\beta)$-fuzzy $n$-ary subhypergroup of an $n$-ary
hypergroup is given, where $\alpha,\beta\in\{\in_{\gamma},
q_{\delta},\in_{\gamma}\wedge q_{\delta}, \ivq\}$, and
it is shown that, in 16 kinds of $(\alpha,\beta)$-fuzzy $n$-ary
subhypergroups, the significant ones are the
$(\in_{\gamma},\in_{\gamma})$-fuzzy $n$-ary subhypergroups,
$(\in_{\gamma},\ivq)$-fuzzy $n$-ary subhypergroups and the
$(\in_{\gamma}\wedge q_{\delta},\in_{\gamma})$-fuzzy $n$-ary
subhypergroups.
