The set of additive cost sharing methods when individual demands are integer valued and cost shares are non negative, is characterized by its extreme points and by a network flow representation. The extreme methods allocate costs incrementally along a chain of demand vectors independent of the cost function. The result generalizes Wang’s characterization in that we do not assume the Dummy axiom.

In this paper, we study monotone set functions defined as the composition of an additive measure with a strictly increasing function. This function is unary operator in continuous-valued logic, called tau function, and it generator function-based parametric mapping. We provide necessary sufficient condition for equality two that are induced by different functions. Using its properties, introduc...

SECTION 1 introduces a method for constructing a measure by inner approximation, starting from a set function defined on a lattice of sets. SECTION 2 defines a “tightness” property, which ensures that a set function has an extension to a finitely additive measure on a field determined by the class of approximating sets. SECTION 3 defines a “sigma-smoothness” property, which ensures that a tight...

Let N0 be the set of all non-negative integers and P(N0) be its power set. An integer additive set-indexer (IASI) is defined as an injective function f : V (G) → P(N0) such that the induced function f : E(G)→ P(N0) defined by f(uv) = f(u)+f(v) is also injective, where N0 is the set of all non-negative integers. A graph G which admits an IASI is called an IASI graph. An IASI of a graph G is said...

Interdependency among system parameters may significantly affect the cross-layer design and optimization performance of wireless networks. However, it is very difficult to derive the interdependency among system parameters in a dynamic complex networking system due to the uncertainty of data observation and system modeling. In this research, we propose a new approach for dynamic interdependency...

In this paper, we present different types of continuous set multifunctions with respect to a set norm (such as uniformly autocontinuous or autocontinuous from above), their relationships with non-additive set multifunctions and some properties of atoms and pseudo-atoms for null-null-additive set multifunctions.