Multialgebraic Systems in Information Granulation

In different fields a conception of granules is applied both as a group of elements defined by internal properties and as something inseparable whole reflecting external properties. Granular computing may be interpreted in terms of abstraction, generalization, clustering, levels of abstraction, levels of detail, and so on. We have proposed to use multialgebraic systems as a mathematical tool for synthesis and analysis of granules and granule structures. The theorem of necessary and sufficient conditions for multialgebraic systems existence has been proved

Topology of WC/Co Interfaces in Cemented Carbides

WC–Co cemented carbides build one of the important classes of metal matrix composites. We show in this paper that the use of machine vision methods makes it possible to obtain sufficiently informative statistical data on the topology of the interfaces between tungsten carbide grains (WC) and a cobalt matrix (Co). For the first time, the outlines of the regions of the cobalt binder were chosen as a tool for describing the structure of cemented carbides. Numerical processing of micrographs of cross sections of three WC–Co alloys, which differ in the average grain size, was carried out. The distribution density of the angles in the contours of cobalt “lakes” is bimodal. The peaks close to 110° (so-called outcoming angles) correspond to the contacts between the cobalt binder and the WC/WC grain boundaries. The peaks close to 240° (or incoming angles) correspond to the WC “capes” contacting the cobalt “lakes” and are determined by the angles between facets of WC crystallites. The distribution density of the linear dimensions of the regions of the cobalt binder, approximated with ellipses, were also obtained. The distribution density exponentially decreases with the lengths of the semi-axes of the ellipsoid, approximating the area of the cobalt binder. The possible connection between the obtained data on the shape of cobalt areas and the crack trajectories in cemented carbides is discussed