Quantitative Analysis of Peri-Urbanization: Developing a Peri-Urban Index for Medium-Sized Cities Using the Analytic Hierarchy Process—A Case Study of Yozgat, Turkey

The rapid development of urbanization necessitates effective analytical methods to address its complexities. Peri-urbanization, the expansion of settlement boundaries and urban spread, is a critical aspect of this phenomenon. This study introduces a quantitative method to analyze peri-urbanization, providing a peri-urban index (PUI) for medium-sized cities based on peri-urban dynamics. Utilizing the analytical hierarchy process (AHP), the weight values of influencing dynamics are calculated, establishing a peri-urban scale (PUS) ranging from one to five based on rural and urban characteristics. Applied to a medium-sized case study city, the method assesses the peri-urbanization from 2007 to 2022. Four main dynamics—socio-demographics, economic-employment, land use-accessibility, and building-texture patterns—and fourteen sub-dynamics were identified and weighted using AHP. The city’s PUI values over different years reveal a 41.6% increase, indicating significant peri-urbanization. This quantitative approach, which innovatively integrates multiple numerical analysis methods, not only highlights the peri-urbanization trends of the city but also provides a comparative analysis framework for other cities. The method’s ability to track changes over time and compare different urban areas supports the development of sustainable urbanization strategies, ensuring balanced growth and resource allocation. This method offers urban planners, policymakers, and architects a powerful tool to manage and guide future urban expansion effectively through interdisciplinary collaboration.