Document Type : Research Paper


1 College of Mathematics and Information Sciences, East China Insti- tute of Technology, Fuzhou, Jiangxi 344000, China

2 Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province 445000, China

3 Department of Mathematics, Yazd University, Yazd, Iran


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 $alpha,betain{in_{gamma},
 q_{delta},in_{gamma}wedge q_{delta}, ivq}$,  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


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