## 1 Introduction  
Sinkholes, a commonly used term to express collapse dolines, are natural phenomena with sizes and depths ranging from centimeters to meters, occurring in karstic regions containing carbonate and evaporitic rocks that cover approximately 20% of the Earth's surface [1]. Sinkhole formations occur under the control of many topographic, geological-tetonic, environmental-anthropogenic, hydrogeological, and climatic (meteorological) factors. These determining factors can be exemplified as the surface and groundwater level that enable dissolution with soluble carbonate and evaporitic karst rocks, the flow direction and hydro-chemical propertiesof water, precipitation, evaporation, stratification that facilitates the movement of water in rocks, porosity and permeability, and cracks and fractures [1,2]. Sinkholes, where anthropogenic effects may trigger their formation, pose a serious risk to residential areas and human life, as well as agricultural areas, energy investment areas, energy production areas, transmission lines, pipelines, and transportation networks. The spatial distribution of conditioning factors that cause the initiation and development of subsidence processes on the surface has an important role in understanding the formation mechanism, determining the areas suitable for sinkhole formation, assessing the relevant spatial hazard and preventing potential damage, as well as in better managing land use activities in areas prone to sinkhole formation. Susceptibility maps show the relative probability of sinkhole formation at any location in the future, while hazard maps show the probability of sinkhole formation in each hazardous area [3,4]. Therefore, in order to accurately predict the location of possible sinkholes, it is necessary to determine the conditioning factors that may cause sinkhole formation and to collect data on these factors. Sinkhole susceptibility studies aim to evaluate the relationship between existing sinkhole formations and conditioning factors, determine the effects of these factors in sinkhole formation, and map the spatial distribution of potentially susceptible areas [5]. However, due to the influence of many distinct factors, it is challenging to model sinkhole formations in temporal and spatial dimensions [6, 7, 8]. For this reason, the modeling of sinkhole susceptibility maps is a complex process, as in other types of natural phenomena, and performing these operations with classical methods can be a very time-consuming and puzzling task for the decision-makers. Geographic Information System (GIS), an advantageous tool in collecting and analyzing spatial data, has been used effectively in solving these and many similar spatial problems for many years. Especially in recent years, various methods have been developed to produce sinkhole susceptibility maps. Models developed for SSM can be broadly classified into qualitative, semi-quantitative, and quantitative methods. Qualitative methods are based on expert judgment and field observations; however, due to their inherent subjectivity, they can produce varying results when applied by different researchers [9,10]. Although these methods are particularly useful in data-scarce regions, they become limited in terms of consistency and repeatability. Semi-quantitative methods integrate both qualitative and quantitative approaches. One of the most frequently used methods in this category is the Analytic Hierarchy Process (AHP). AHP is considered a semi-quantitative method because it quantifies the weighting of factors based on expert judgment [11, 12, 13, 14]. Additionally, other multi-criteria decision-making methods, such as the Best-Worst Model (BWM), can also be classified within this category [15]. Quantitative methods encompass deterministic, statistical, and ML models. Deterministic models attempt to analyze sinkhole formation based on hydrogeological and geotechnical data within the framework of physical and mechanical principles.