This paper presents an approach to the generalization of grayscale morphology to color images. Attaining such a generalization is strongly related to the issues of multivariate ranking and to the Pareto sets of multiobjective optimization. Some ranking schemes for multivariate data are recalled. For color morphology, the most important underlying ranking scheme is reduced ordering (also referre...

We present the first fully syntactic (i.e., non-interpretation-based) AC-compatible recursive path ordering (RPO). It is simple, and hence easy to implement, and its behaviour is intuitive as in the standard RPO. The ordering is AC-total and defined uniformly for both ground and nonground terms, as well as for partial precedences. More important, it is the first one that can deal incrementally ...

Investigated are possibilistic distributions taking as their values sequences from the infinite Cartesian product of identical copies of a fixed finite subset of the unit interval of real numbers. Uniform and lexicographic partial orderings on the space of these sequences are defined and the related complete lattices introduced. Lattice-valued entropy function is defined in the common pattern f...

We give the first systematic study of strong isomorphism reductions, a notion of reduction more appropriate than polynomial time reduction when, for example, comparing the computational complexity of the isomorphim problem for different classes of structures. We show that the partial ordering of its degrees is quite rich. We analyze its relationship to a further type of reduction between classe...

concurrent semantics are also defined. Three classical observations for concurrent semantics — interleaving, partial ordering and mixed ordering — are defined on the graph derivations. Bisimulation is exploited to obtain three equivalences of π-calculus agents corresponding to the observations. As expected, the ordinary observational equivalence for the π-calculus is re-obtained in this context...

In this paper, we present the notion of multimodular triangulation under a new geometrical point of view. We also show the link with multimodular functions by a new proof of the convexity theorem. This is used to de ne a partial ordering compatible with multimodularity called the cone ordering. An application in admission control in queues is then presented.

We consider communication structures for event ordering algorithms in distributed environments where information ows only in one direction. Example applications are multilevel security and hierarchical databases. Although the most general one-directional communication structure is a partial order, partial orders do not enjoy the property of being consistently-ordered, a formalisation of the not...

This manuscript is on the theory and numerical procedures of vector optimization w.r.t. various ordering structures, on recent developments in this area and, most important, on their application to medical engineering. In vector optimization one considers optimization problems with a vectorvalued objective map and thus one has to compare elements in a linear space. If the linear space is the fi...

I survey classification results for countable homogeneous or ‘partially homogeneous’ ordered structures. This includes some account of Schmerl’s classification of the countable homogeneous partial orders, outlining an extension of this to the coloured case, and also treating results on linear orders, and their generalizations, trees and cycle-free partial orders. 2000 Mathematics Subject Classi...

The paper deals with the problem of reasoning about partially ordered events in Kowalski and Sergot's Event Calculus (EC). We home in on EC between its skeptical (SKEC) and credulous (CREC) variants. When only partial knowledge about event ordering is given SKEC and CREC compute the set of maximal validity intervals (MVIs) over which the considered properties are necessarily and possibly true, ...