We analyze different separability conditions that characterize the numerical representability
of semiorders through a real-valued function and a strictly positive threshold. Any necessary …

In the framework of the analysis of orderings whose associated indifference relation is not
necessarily transitive, we study the structure of a semiorder, and its representability through …

In the framework of the analysis of orderings whose associated indifference relation is not
transitive, we study the structure of a semiorder, paying attention to the problem of its …

We furnish a characterization of the representability of an interval order through a pair of
continuous real-valued functions which in addition represent two total preorders associated …

We analyze the structure of a semiorder, paying attention to its representability through a
real-valued function and a positive constant threshold (the so-called Scott–Suppes …

Suppose we have a number representation of a semiorder< A, P> such that aPb iff f (a)+ δ
(a)< f (b), for all a, b∈ A, where δ is a nonnegative function describing the variable jnd. Such …

Conditions on a semiorder,< X,≻>(where X is a subset of Euclidean space), are presented
under which the semiorder can be represented by a continuous, real-valued function, u …

This paper presents several necessary and sufficient conditions for real interval
representability of biorders, interval orders, and semiorders. Let A and X be nonempty sets …

A Z-product is a modified lexicographic product of three total preorders such that the middle
factor is the chain of integers equipped with a shift operator. A Z-line is a Z-product having …

This paper discusses two types of real interval representations for interval orders and
semiorders≺ on a set X of arbitrary cardinality. In each type, each x in X is mapped into a …