The magnetic properties of electrical steel such as magnetization behavior and specific magnetic losses are related to the microstructure and texture of the steel. The interest in the case of FeSi-alloys is to realize a low intensity on the 111 fiber, which is a different goal than that of conventional steels, where a high intensity on the 111 fiber and small grain size is desired. In this paper, we present and discuss some results of our recent studies on FeSi-alloys without phase transformation. The resulting grain structure and the relevant magnetic texture components for nonoriented electrical steels before and after cold rolling as well as after annealing were analyzed.Index Terms-Crystallographic texture, magnetic anisotropy, silicon steel.

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Abstract. In the concept of fuzzy regions we introduced before, a region was considered to be a fuzzy set of points, each having its own membership grade. While this allows the modelling of regions in which points only partly belong to the region, it has the downside that all the points are considered independently, which is too loose a restriction for some situations. The model is not able to support the fact that some points may be linked together. In this contribution, we propose an extension to the model, so that points can be made related to one another. It will permit the user to, for instance, specify points or even (sub)regions within the fuzzy region that are linked together: they all belong to the region to the same extent at the same time. By letting the user specify such subregions, the accuracy of the model can be increased: the model can match the real situation better; while at the same time decreasing the fuzziness: if points are known to be related, there is no need to consider them independently. As an example, the use of such a fuzzy region to represent a lake with a variable water level can be considered: as the water level rises, a set of points will become flooded; it is interesting to represent this set of points as a subset of the region, as these points are somewhat related (the same can be done for different water levels). The impact of this extension to the model on both surface area calculation an distance measurement are considered, and new appropriate definitions are introduced.

Traditional databases can manage only crisp information, a limitation that also holds for geographic information systems and spatial databases. In this paper, we present a technique based on triangulated irregular networks (or TINs for short) and fuzzy set theory to model imprecise or uncertain regions. A fuzzy region is represented by a Extended TIN, which allows for an associated value for each point of the region in the presented approach to be considered; this associated value will be a membership grade. As is common in fuzzy set theory, membership grades can indicate a degree of "belonging to the set"; in our approach these are the degree to which every crisp location belongs to the fuzzy region (membership grades in fuzzy set theory can have other interpretations7 as well, but these are not needed for the modelling of fuzzy regions). While modelling a fuzzy region as described provides a more accurate model of a real world situation, it does require many operators from the geographic realm to be extended and also new operators (mainly from the fuzzy realm) to be added at the object level. In this paper, from the GIS realm, the calculation of the surface area and the minimum bounding rectangle for fuzzy regions are considered; from the fuzzy realm the calculation of the α-cut is considered. Other operations (i.e. convex hull of a fuzzy region, distance between two fuzzy regions, …) are still under development.

The map overlay problem occurs when mismatched gridded data need to be combined, the problem consists of determining which portion of grid cells in one grid relates to the partly overlapping cells of the target grid. This problem contains inherent uncertainty, but it is an important and necessary first step in analysing and combining data; any improvement in achieving a more accurate relation between the grids will positively impact the subsequent analysis and conclusions. Here, a novel approach using techniques from fuzzy control and artificial intelligence is presented to provide a new methodology. The method uses a fuzzy inference system to decide how data represented in one grid can be distributed over another grid using any additionally available knowledge, thus mimicking the higher reasoning that we as humans would use to consider the problem.

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