We study the watersheds in edge-weighted graphs. Contrarily to previous works, we define the watersheds following the intuitive idea of drops of water flowing on a topographic surface. We establish the consistency (with respect to characterizations of the catchment basins and dividing lines) of these watersheds, prove their optimality (in terms of minimum spanning forests) and derive a linear-t...

In this paper, a novel method for ranking of fuzzy numbers are proposed. In this method, decision maker is defined based on the center of mass at some cuts of a pair of fuzzy numbers in discreet version and center of mass on all of cuts of a pair of fuzzy numbers in continuous version. Our method can rank more than two fuzzy numbers simultaneously. Also, some properties of methods are described...

With stochastic integer programming as the motivating application, we investigate techniques to use integrality constraints to obtain improved cuts within a Benders decomposition algorithm. We compare the effect of using cuts in two ways: (i) cut-and-project, where integrality constraints are used to derive cuts in the extended variable space, and Benders cuts are then used to project the resul...