## 1 Introduction  
A landslide is the movement of earthen materials down a slope under the influence of gravity [1] and occurs when earthen material exceeds the shear strength (resistance to shearing) [2]. Landslide events can cause damage to buildings, infrastructure and property and endanger human life [3; 4; 5]. According to [6], landslides are in seventh place when it comes to the destruction of human life and property. It is estimated that the frequency of landslides is increasing. The main reasons for the larger landslide vulnerability are (1) climate change and more extreme weather conditions; (2) the overexploitation of natural resources and deforestation, (3) growing urbanization and unrestrained land use, (4) the increased use of traditionally non-populated mountainous regions for recreational and transportation purposes, pushing the borders further into hazardous terrain [6]. In Poland, the area most susceptible to landslides is the Carpathians. The reason for this is the nature of the relief and the geological structure. The high slopes combined with the flysch conditions render the Carpathians a region strongly prone to landslide occurrence. About 6% of the country is covered by the Carpathians, where 95% of all the landslides in Poland have been registered. In 2010, 50,000-60,000 landslides were recorded in the Carpathians, an average of one landslide per km\({}^{2}\)[7]. Landslide areas cover about 30-40% of the province areas in this region. The activation of numerous landslides in 2000 and 2010 by intense precipitation had disastrous consequences. Many residential buildings and road sections were destroyed [8]. There have been many cases of economic losses, which are estimated in millions of Polish zlotys. Some landslides are activated almost every year, which results in the destruction of residential and commercial buildings, transport infrastructure, transmission routes and agricultural and forest areas [9]. In agricultural areas, soil mixed with the layer located below presents inferior properties for agricultural production. The restoration of soil fertility in such areas is a long-term process [7]. Therefore, to mitigate the negative effects of landslides, it is necessary to effectively estimate landslide susceptibility and hazards [10; 11]. From a mathematical perspective, landslide susceptibility mapping (LSM) presents the probability of landslide occurrence in a specific area based on an analysis of the terrain conditions and environmental conditions calculated from geo-environmental analysis. This describes the degree of proneness of specific terrain to landslides [12]. LSM is necessary for hazard assessment and the effective planning and management of regional sustainable development [13]. It is the subject of various studies worldwide [2; 3; 13; 14; 15; 16; 17]. The factors used for assessing landslide susceptibility are usually called Landslide Controlling Factors (LCFs). These factors are analyzed to create predictive models for landslide susceptibility, and they usually include topographical, geological, hydrological and environmental conditions. Effective LSM provides various land-use planners and decision makers with an opportunity to determine the regions appropriate for urban expansion and allows them to make the best possible use of land while avoiding landslide-prone areas [13; 18]. Researchers all over the world have applied various methods for LSM. These methods can be qualitative or quantitative [14]. Qualitative methods are subjective and determine susceptibility heuristically, while quantitative methods involve the calculation of numerical measures, i.e., the likelihood of the occurrence of landslide phenomena in any susceptibility zone [12]. Among these quantitative approaches, the analytic hierarchy process (AHP) [14], the frequency ratio (FR) [14; 19; 20], the statistical index (SI) [20], the evidential belief function (EBF) [21], Dempster-Shafer (DS) analysis [22], logistic regression (LR) [19], the weights of evidence (WOE) model [20; 21] and fuzzy logic (FL) [23] exist.