Homothetic interval orders Original Research Article

We give a characterization of the non-empty binary relations image on a image-set A such that there exist two morphisms of image-sets image verifying image and image. They are called homothetic interval orders. If image is a homothetic interval order, we also give a representation of image in terms of one morphism of image-sets image and a map image such that image. The pairs image and image are “uniquely” determined by image, which allows us to recover one from each other. We prove that image is a semiorder (resp. a weak order) if and only if image is a constant map (resp. image). If moreover A is endowed with a structure of commutative semigroup, we give a characterization of the homothetic interval orders image represented by a pair image so that u is a morphism of semigroups.