The development of generalisation (simplification) methods for the geometry of features in digital cartography in most cases involves the improvement of existing algorithms without their validation with respect to the similarity of feature geometry before and after the process. It also consists of the assessment of results from the algorithms, i.e., characteristics that are indispensable for automatic generalisation. The preparation of a fully automatic generalisation for spatial data requires certain standards, as well as unique and verifiable algorithms for particular groups of features. This enables cartographers to draw features from these databases to be used directly on the maps. As a result, collected data and their generalised unique counterparts at various scales should constitute standardised sets, as well as their updating procedures. This paper proposes a solution which consists in contractive self-mapping (contractor for scale s = 1) that fulfils the assumptions of the Banach fixed-point theorem. The method of generalisation of feature geometry that uses the contractive self-mapping approach is well justified due to the fact that a single update of source data can be applied to all scales simultaneously. Feature data at every scale s < 1 are generalised through contractive mapping, which leads to a unique solution. Further generalisation of the feature is carried out on larger scale spatial data (not necessarily source data), which reduces the time and cost of the new elaboration. The main part of this article is the theoretical presentation of objectifying the complex process of the generalisation of the geometry of a feature. The use of the inherent characteristics of metric spaces, narrowing mappings, Lipschitz and Cauchy conditions, Salishchev measures, and Banach theorems ensure the uniqueness of the generalisation process. Their application to generalisation makes this process objective, as it ensures that there is a single solution for portraying the generalised features at each scale. The present study is dedicated to researchers concerned with the theory of cartography.
In this paper, the systems of real estate mass appraisal in some selected European countries will be discussed, in comparison with those of individual countries on other continents, in terms of similarities and differences in law, institutional scope and subjects responsible for its execution. With selected countries serving as an example, the practical aspects of operating the real estate owners' taxation system will be discussed as well the data acquiring process, considered price-making factors, proceeding methodology and circumstances taken into account in real estate cadastral valuation, giving consideration to national specificity.
The key goal of the market analysis carried out for property valuation purposes is to select pricing attributes of real properties and to assign so-called weights to them, which would illustrate their influence on the prices in a given market (Regulation 2004). Correlation analysis is a very useful tool in this respect. However, the fact that it is limited to the use of classical Pearson’s linear correlation coefficients is too much of a simplification due to the frequently occurring heterogeneity of the real estate market. The research paper proposes to use the possibilities offered by the broadly understood correlation analysis which, among linear correlations, takes into account not only Pearson’s correlation but also rank correlations. At the same time, analyses of various non-linear correlations are being carried out where linear relationships are not reliable enough. The aim of this research is the simultaneous verification of the existence of various types of correlative relationships, taking into account the nature of random variables that the analyses relate to, and the nature of relationships between them. This approach makes it possible to adjust the weighting of market attributes, the values of which are improved in a few subsequent steps, in order to eventually approach the optimal result as close as possible.
The market of non-residential premises is the subject of analyses less frequently than the housing market. There are two main reasons which probably contribute thereto. First of all, commercial premises are relatively less frequently objects of trade than dwelling units; secondly, they are more diverse due to their various uses. The category includes garages, office premises, commercial premises, as well as warehouses. Such differences in their uses result in significantly different characteristics, such as surface area. The article attempts to analyse a selected non-residential segment of the commercial property market in Krakow based on a large set of data (280 objects), referring to the transactions concluded in the last five years. The size of the data enabled the use of multidimensional modelling of the selected market in different size variants. This made it possible to draw reliable conclusions which undermine the widespread belief regarding very limited possibilities of using the method of market statistical analysis in the comparative approach, especially in this segment of the real estate market, as well as in others, where transactions are concluded less frequently than on the housing market.
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