Approximations of \(\left(∈,∈∨{q}_{k}\right)\)-Fuzzy Hyperideals in Ordered LA-Semihypergroups

Abstract

This paper concerns the relationship between rough sets, $\left(\in ,\in \vee q_k\right)$ -fuzzy sets, and the LA-semihypergroups. We proved that the lower approximation ( $l$ -approx) and the upper approximation ( $u$ -approx) of different hyperideals of LA-semihypergroups become again hyperideal and also provided some examples. We also provided a result which shows that, if $\vartheta$ is not a hyperideal of an LA-semihypergroup $P$ , then its lower approximation is also not a hyperideal.