The purpose of this article is to investigate the class of intra-regular $LA$-semihyperrings. Then, characterizations of intra-regular $LA$-semihyperrings by the properties of many types of their hyperideals are obtained. Moreover, we present a construction of $LA$-semihyperrings from ordered $LA$-semirings.

The concept of Fermatean fuzzy sets was introduced by Senapati and Yager in 2019 as a generalization of fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets. In this article, we apply the notions of Fermatean fuzzy left (resp., right) hyperideals and Fermatean fuzzy (resp., generalized) bi-hyperideals in semihypergroups to characterize intra-regular semihypergroups, such as $S$ is an intra-regular semihypergroup if and only if $\mathcal{L}\cap \mathcal{R}\subseteq \mathcal{L}\circ \mathcal{R}$, for every Fermatean fuzzy left hyperideal $\mathcal{L}$ and Fermatean fuzzy right hyperideal $\mathcal{R}$ of a semihypergroup $S$. Moreover, we introduce the concept of Fermatean fuzzy interior hyperideals of semihypergroups and use these properties to describe the class of intra-regular semihypergroups. Next, we demonstrate that Fermatean fuzzy interior hyperideals coincide with Fermatean fuzzy hyperideals in intra-regular semihypergroups. However, in general, Fermatean fuzzy interior hyperideals do not necessarily have to be Fermatean fuzzy hyperideals in semihypergroups. Finally, we discuss some characterizations of semihypergroups when they are both regular and intra-regular by means of different types of Fermatean fuzzy hyperideals in semihypergroups.