we generalize concepts of left hyperfilters, right hyperfilters and an ordered semihypergroup by introducing left-m-hyperfilters, right-n-hyperfilters (m,n)-hyperfilters semihypergroup. Then, some properties these generalized have been studied. Finally, left-m-hyperfilters (resp. right-n-hyperfilters, (m,n)-hyperfilters) (m, 0)-regular (0,n)-regular, (m,n)-regular) semihypergroups characterize in terms...

In this paper, we introduce the concept of a locally associative LA-semihypergroup by generalizing the idea of a locally associative LA-semigroup given in Mushtaq–Yusuf, 1979, and study an (m,n)regular class of a locally associative LA-semihypergroup. We give some examples to connect an LA-semihypergroup with commutative hypergroups and commutative semihypergroups. We also characterize a locall...

We consider the fundamental relation on a semihypergroup to interpret the lower and upper approximations as subsets of the fundamental semigroup / and we give some results in this connection. Also, we introduce the notion of a bi-hyperideal to study the relationship between approximations and bi-hyperideals.