NEW TYPES OF FUZZY n-ARY SUBHYPERGROUPS OF AN n-ARY HYPERGROUP

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.