A graph G = (V, E) is said to be represented by a family F of nonempty sets if there is a bijection f:V--*F such that uv ~ E if and only iff(u)Nf(v)q=~. It is proved that if G is a countable graph then G can be represented by open intervals on the real line if and only if G can be represented by closed intervals on the real line, however, this is no longer true when G is an uncountable graph. S...

This paper discusses an Interval Quadratic Programming (IQP) problem, where the constraints coefficients and the right-hand sides are represented by interval data. First, the focus is on a common method for solving Interval Linear Programming problem. Then the idea is extended to the IQP problem. Based on this method each IQP problem is reduced to two classical Quadratic Programming (QP) proble...

Two definitions of division by an interval containing zero are compared: a functional one and a relational one. We show that the relational definition also provides interval inverses for other functions that do not have point inverses, such as max and the absolute-value function. Applying the same approach to the ≤ relation introduces the “companion functions” of relations. By regarding the ari...

Starting at time 0, unit-length intervals arrive and are placed on the positive real line by a unit-intensity Poisson process in two dimensions; the left endpoints of intervals appear at the rate of 1 per unit time per unit distance. An arrival is accepted if and only if, for some given x, the interval is contained in 0 x and overlaps no interval already accepted. This stochastic, on-line inter...

This paper presents a new kind of interpolation theorems about Neighbourhood Logic (NL, [ZH96]) and Interval Temporal Logic (ITL, [Mos85, Dut95]). Unlike Craig interpolation, which holds for these logics too, the new theorems treat the existence of interpolants which specify properties of selected intervals in the models of NL and ITL.

In the framework of interval uncertainty, a well-known classical problem in numerical analysis is considered, namely, to find “the best” interval solution for interval system of linear algebraic equations. This problem is known to be NP-hard and can be solved via multiple linear programming. In present paper, a simple approach is proposed for some particular models of interval uncertainty. This...

Generally, vagueness is modelled by a fuzzy approach and randomness by a stochastic approach. But in some cases, a decision maker may prefer using interval numbers as coefficients of an inexact relationship. In this paper, we define a linear programming problem involving interval numbers as an extension of the classical linear programming problem to an inexact environment. By using a new simple...