A construction of hypergroups from ordered structures and their morphisms

Hyperstructures associated with binary relations

“…It is known that, given a binary relation R on a nonempty set H (i.e., R C_ H x H), several hyperoperations can be defined in many different ways [1, 5,6,7,11,13,15,17]. In the present paper, we deal with the hyperoperation introduced and studied by Corsini [1] in the following way,…”

“…The connections between hyperstructures and binary relations have been analyzed by many researchers, such as Corsini [1][2][3][4], Rosenberg [5], Chvalina [6,7], Konstantinidou [8], Leoreanu [9,10], Serafimidis [11,12], DeSalvo and Lo Faro [13,14], Hort [15], Kehagias [16], and so on.…”

Characterizations of totally ordered sets by their various endomorphisms

“…The motivation for this paper came from the hypergroup theory (cf. [6]), where 2-, 3-, 4-morphisms play an important role [6,7,9]. Here we show that a quite simple relationship between such endomorphisms and isotone selfmappings provides the total ordering of ordered sets in question.…”

“…Conditions ( * ) and ( * * ) from Propositions 1 and 2 are motivated by the so called 2-, 3-, 4-homomorphisms studied in the hypergroup theory [6,7,9]. …”

Foundations of Ordered (Semi)hyperrings

“…Heidari and Davvaz introduced and studied ordered semihypergroup in [15]. Chvalina [6] and Hort [16] used ordered structures for the construction of hypergroups. Chvalina [6] started the concept of ordered semihypergroups as a special class of hypergroups in 1994.…”