Changes in land use, which accompany the development of towns, generate a transitional zone on the border between areas of urban and rural use, which—due to its complex (unspecified, fuzzy) land use—cannot be identified either as a rural or an urban area. In order to prevent the unplanned development, it should go according to plan, in line with the spatial order principles, making a coherent whole, taking into account all functional, socio-economic, cultural, as well as aesthetic factors and requirements. This paper describes studies and analyses of the fuzzy set theory applicability in studies of land use in areas around towns. The main aim of the study was to present the methodology, which employs fuzzy logic to identify and locate a transitional zone between rural and urban areas. This study dealt with the transitional zone at the junction of the urban and rural area and its parameters, which affect the type of land use. The attributes of the transitional zone were defined based on an analysis of current land use methods in areas under direct urbanisation pressure. The study was conducted in the city of Olsztyn (Poland) and on its outskirts, directly exposed to the impact of the developing city, with an area of 202.4 km2, within an 8-km radius of the city centre. The study determined the impact of individual forms of land use on the development of urban or rural use. The degree of each type of use—urban or rural—allowed for developing a fuzzy town and country model, identifying the urban investment border and its spatial dispersion, as well as identifying and locating the transitional zone between urban and rural areas. Moreover, land cover models based on the Corine land cover (CLC) data as well as high-resolution layers (HRL) impervious and canopy data were developed. The borders of urban investment determined on the basis of the fuzzy set theory assumptions, CLC, and HRL data were also identified and verified.
The dynamic development of spatial structures entails looking for new methods of spatial analysis. The aim of this article is to develop a new theory of space modeling of network structures according to six value aggregation paths: minimum and maximum value difference, minimum and maximum value decrease, and minimum and maximum value increase. The authors show how values presenting (describing) various phenomena or states in urban space can be designed as network structures. The dynamic development of spatial structures entails looking for new methods of spatial analysis. This study analyzes these networks in terms of their nature: random or scale-free. The results show that the paths of minimum and maximum value differences reveal one stage of the aggregation of those values. They generate many small network structures with a random nature. Next four value aggregation paths lead to the emergence of several levels of value aggregation and to the creation of scale-free hierarchical network structures. The models developed according to described theory present the quality of urban areas in various versions. The theory of six paths of value combination includes new measuring tools and methods which can impact quality of life and minimize costs of bad designs or space destructions. They are the proper tools for the sustainable development of urban areas.
The study demonstrated that the rate of spatial development is correlated with its fractal dimension. The presented results indicate that the fractal dimension can be a useful tool for describing different phases of urban development. Therefore, the formulated research hypothesis states that the fractal dimension of cities’ external boundaries is correlated with the rate of spatial development in urban areas. The above implies that the higher the rate of spatial development, the smoother the external boundaries of urban investment. Rapidly developing cities contribute to considerable changes in land management, in particular in municipalities surrounding the urban core. Urban development processes often induce negative changes in land management and contribute to chaotic and unplanned development. To address these problems, new methods are being developed for modeling and predicting the rate of changes in transitional zones between urban and rural areas. These processes are particularly pronounced in urban space, whose expansion proceeds at an uneven pace. The aim of this study was to propose a method for describing urbanization processes that are based on the dependence between the urban growth rate, the fractal dimension, and basic geometric parameters, such as city area and the length of city boundaries. Based on the calculated changes in the values of these parameters, a classification system was proposed to identify distinctive phases of urban development. The study revealed that land cover databases are highly useful for such analyses. The study was conducted on 58 medium-size European cities with a population of up to 300,000, including France, Germany, Italy, Poland, and Croatia. The study demonstrated that the fractal dimension and the basic geometric parameters of urban boundaries are significantly correlated with the rate of the spatial development of cities. The proposed indicators can be used to describe the spatial development of urban areas and the rate of urban growth. The development of the analyzed cities was modeled with the use of CORINE Land Cover (CLC) data for 2000–2006–2012–2018, acquired under the EU Copernicus program.
Analyses of the correlations between social and economic phenomena are rarely limited to simple evaluations of the relationships that exist between two features. Information about the structure and behaviour of complex phenomena and processes in the natural environment and social systems is usually incomplete and uncertain. Grey relational analysis (GRA) poses an alternative to statistical methods (e.g., correlation analysis, variance analysis, regression analysis and direct comparisons) to evaluate complex phenomena. In GRA, the number of assumptions relating to the size and distribution of samples is far smaller than in statistical methods. The required number of observations in the GRA is n ≥ 4. Therefore, the grey system theory (GST) provides useful tools for analysing limited and imperfect data. GST can be used to predict a system’s future behaviour and to evaluate the relationships between observation vectors. The study aimed to determine the strength of the relationships between the analysed features with the use of GST and to analyse the model’s behaviour for a different number of variables. The main assumptions and definitions relating to GST were presented. The residential preferences of a selected social group were analysed. The proposed approach supports the development of effective decision-making procedures in urban planning.
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