City Boundaries—Utilizing Fuzzy Set Theory for the Identification and Localization of the Urban–Rural Transition Zone

This article examines the potential of fuzzy set theory for analysing gradual changes in land use patterns within peri-urban areas. The primary objective of the study was to propose a methodology based on fuzzy set theory for the precise delineation of city boundaries and the identification and spatial localisation of the urban–rural transition zone. The analysis focused on elucidating the defining parameters of this area and the scope of land use changes within the urban–rural transition zone. The analysis employed data from four discrete time points. The data were collected in 2005, 2010, 2017, and 2022. The characteristics of the urban–rural transition zone were evaluated through an examination of historical data and the current land use patterns in regions experiencing direct urbanization pressure. The study demonstrated that, although spatial barriers remain, the city’s development has continued at a consistent pace. Between 2005 and 2010, the area of land classified as urban exhibited a 10% increase, with a further 7% increase observed in the subsequent period, spanning 2010 to 2017. In the most recent period under examination, the urban land area increased by 9%, a figure that is consistent with the rates observed in previous years. These results indicate the stability of urbanization processes in the analysed city, while also revealing significant changes in the limits of urban development and in the intensity of land use. The research project concentrated on the city of Olsztyn and the neighbouring suburban areas, which are subject to direct influence from the city’s expansion. The area under study encompasses 202.4 km2 within an eight-km radius of the city centre. The authors of the study emphasized the necessity for systematic monitoring of changes in the transition zone between urban and rural areas. This is to ensure effective control of spatial development and ongoing adjustment of planning tools to effectively prevent uncontrolled expansion. The methodology used enabled the precise delimitation of urban development and the transition zone. This allowed for an in-depth analysis of changes in land use intensity.