*2.3. Methods*

In the spatial analyses of the intensity of urban landscapes, understood in this case as land cover, the essential step is the delimitation and classification of land cover types in terms of their urban character. The problem was what types of land cover can be described as urban and what types as rural. Furthermore, how to evaluate them to describe the urban landscape intensity? Furthermore, there are some transitional landscapes, which are difficult to be definitely assigned to urban or rural character. Therefore, the authors decided to use a fuzzy theory. Fuzzy logic is applied in the cases of complex, unclear phenomena and can define and present unspecified, uncertain information [48]. This theory was used by Biłozor et al. [25] for identification of transitional zone between urban and rural area. In this work, a classification of 24 forms of space use was proposed and the value of the degree of belonging of land cover to the urban landscape (M) has been defined for each of them. These values were adopted and adjusted to different types of land cover (Table 2). The value of the M is set between 0 and 1, where 0 indicates rural land cover, and 1 urban land cover.

The value of belonging of land cover to the urban landscape was the basis of the Urban Landscape Intensity Index (ULII). This is represented by the following equation:

$$ULIII = \sum\_{i=1}^{n} fiMi \tag{1}$$

ULII—Urban Landscape Intensity Index, *fi*—share of *i*-th form of land use in the area of the metropolis/municipality/hexagon, *Mi*—the degree of belonging of land cover to the urban landscape, *n*—number of forms of land cover

Analyses of the obtained ULII were conducted at three levels of research: metropolitan area, municipality and hexagon (the area of hexagon was set as 4 km2). After calculation this index, at level 2 (municipalities) and 3 (hexagons), the values of ULII were divided and classified in terms of landscape types using classification proposed by Matuszewska and B ˛edkowski [26]:

