Int-soft structures applied to ordered semihypergroups

Molodtsov introduced the theory of soft sets, which canbe seen as a new mathematical approach to vagueness. The main goal of thispaper is to introduce and study some classes of ordered semihypergroups andto investigate some interesting characterizations theorems of these classesin terms of int-soft hyperideals. In this respect, we characterize weaklyregular ordered semihypergroups for example (see Theorems 25, 26 and 28)intra-regular and left weakly-regular ordered semihypergroups (see Theorems30 and 32) and semisimple ordered semihypergroups (see Theorems 37 and 39)in terms of int-soft hyperideals. In this regard, we study semisimpleordered semihypergroups and characterize it in terms of int-softhyperideals. We also characterize intra-regular and weakly-regular orderedsemihypergroups in terms of int-soft hyperideals