title: Numerical representation of binary relations with a multiplicative error function
abstract: This paper studies the case of the representation of a binary relation via a numerical function with threshold (error) depending on both compared alternatives. The error is considered to be multiplicative, its value being either directly or inversely proportional to the values of the numerical function. For the first case, it is proved that a binary relation is a semiorder. Moreover, any semiorder can be represented in this form. In the second case, the corresponding binary relation is an interval order
keyphrases: numerical representation binary relations multiplicative error function error numerical function threshold semiorder interval order