document: Numerical representation of binary relations with a multiplicative error function This paper studies the case of the representation of a binary relation via a numerical function with threshold -LRB- error -RRB- 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
doc_bio_tags: B I O B I O O B I I O O O O O O O O O O O O O O B I O B O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O B I