Landslide susceptibility mapping by comparing weight of evidence, fuzzy logic, and frequency ratio methods

ABSTRACT A regional scale basin susceptible to landslide located in Qaemshahr area in northern Iran was chosen for comparing the reliability of weight of evidence (WofE), fuzzy logic, and frequency ratio (FR) methods for landslide susceptibility mapping. The locations of 157 landslides were identified using Google Earth® or extracted from archived data, from which, 22 rockslides were eliminated from the data-set due to their different conditions. The 135 remaining landslides were randomly divided into two groups of modelling (70%) and validation (30%) data-sets. Elevation, slope degree, slope aspect, lithology, land use/cover, normalized difference vegetation index, rainfall, distance to drainage network, roads, and faults were considered as landslide causative factors. The landslide susceptibility maps were prepared using the three mentioned methods. The validation process was measured by the success and prediction rates calculated by area under receiver operating characteristic curve. The ‘OR’, ‘AND’, ‘SUM’, and ‘PRODUCT’ operators of the fuzzy logic method were unacceptable because these operators classify the target area into either very high or very low susceptible zones that are inconsistent with the physical conditions of the study area. The results of fuzzy ‘GAMMA’ operators were relatively reliable while, FR and WofE methods showed results that are more reliable.


Introduction
Natural hazards cause significant casualties and destruction in today's world. The unplanned urbanization especially in developing countries and wide climate changes through global warming increase the risk of natural hazards. Landslide phenomenon is an important worldwide natural hazard and Iran is no exception. The Alborz mountain belt in the north of Iran, due to its climate, geology, and high tectonic activities, is a prone area to landslides that cause the loss of hundreds of millions of dollars annually (Pourghasemi et al. 2013). In this regard, a necessary step for effective land-use management and slope stability is mapping the landslide-prone areas (Akgun 2012). These maps classify the land surface to different zones according to the degree of actual or potential landslide hazard (Rozos et al. 2011). Geomatics by taking advantage of modern tools, such as geographic information system (GIS) and remote sensing (RS) provides a perfect opportunity for using, validation, and comparison of different methods to produce a landslide susceptibility map (LSM). In recent years, several qualitative or quantitative methods have been used to analyze the relationship between landslides and causative factors (Aleotti & Chowdhury 1999;Ayalew & Yamagishi 2005) CONTACT M. Zare zare@susc.ac.ir and the methods are compared by GIS (S€ uzen & Doyuran 2004;Nefeslioglu et al. 2008;Yalcin 2008;Bathrellos et al. 2009;Yilmaz 2009;Pradhan & Lee 2010a;Pourghasemi et al. 2012;Quan & Lee 2012;Zare et al. 2012). The selection of a method depends on the scale of the study area, scientific knowledge, practical experience of the user, economic costs and time constraints of the project, and the instructions of relevant organizations. In a freelance research, probably the scale of LSM, scientific knowledge, and practical experience of the experts are the most important factors for choosing a suitable method.
To produce a small-scale LSM, the qualitative approaches are acceptable for groundwork of an approximate prone area zoning (Yoshimatsu & Abe 2006;Castellanos et al. 2008;Jian & Xiang-guo 2009;B alteanu et al. 2010;Rozos et al. 2011), whereas, the quantitative approaches are more accurate, although are often more expensive and time consuming. For example, Akgun (2012) produced LSMs using logistic regression (LR), frequency ratio (FR), and analytical hierarchy process (AHP) methods. He showed that the prediction rates of these methods were equal to 81.0%, 76.0%, and 71.0%, respectively, and that LR and FR methods (both are quantitative methods) are significantly more accurate than the AHP, although the prediction rates of all three methods are categorized as a fair quality (Abul Hasanat et al. 2010). In the cases that a complete landslide inventory is available, quantitative approaches, such as weight of evidence (WofE), FR, fuzzy logic, and LR are frequently employed in small-scale (large area) mapping (Gorsevski et al. 2006;Lei & Jing-feng 2006;Nandi & Shakoor 2010;Pradhan, Oh et al. 2010;Mohammady et al. 2012). Complicated methods, such as artificial neural network (ANN) require more cost and time for learning and applying. For example, the ANN require a conversion process of data, which is a time-consuming process (Yilmaz 2009). However, due to the map scale of the causative factors, complicated methods are not more reliable than the simple approaches in a small-scale study. For example, Park et al. (2013) reported that the LSMs created using the FR, AHP, LR, and ANN methods were not significantly different and they had a similar accuracy and a high correlation. They also reported that the FR method could be applied simply, whereas, the LR method needs data conversion and is of limited value when the data-set is large. In addition, the AHP method generally requires a questionnaire survey to calculate relative weights and requires a separate software program. Lee et al. (2000) stated that 'the ANN model is time consuming and requires high computer capacity for actual applications, because the internal calculation process cannot be easily understood and the calculation is intensive'. Pradhan and Lee (2010b) compared the LSMs produced by the back-propagation ANN, FR, and bivariate LR methods. They reported that the prediction accuracy for these methods were 94.0%, 93.0%, and 90.0%, respectively, showing that the ANN is not much superior to the FR method.
In the case of large-scale (small area) mapping, often the qualitative approaches are unreliable and the using of quantitative approaches, such as statistical and deterministic approaches are in priority, except cases where quantitative approaches are infeasible. For instance, Ruff and Czurda (2008) selected a heuristic approach for their local scale study in the Eastern Alps because the number of events and the density of landslides in their study area did not allow using a quantitative approach.
Although various methods have been compared in many studies, fuzzy Logic, which can be (1) quantitative or qualitative, (2) easy to implement in a GIS software, and (3) high reliable, depending on the approach of obtaining membership values, has been less compared with other methods. Fuzzy logic method has been used solely in the landslides studies (Chung & Fabbri 2001;Ercanoglu & Gokceoglu 2002Lee 2007;Pradhan et al. 2009;Pradhan 2010), and in comparison with a few methods different from the methods used in this study (Kanungo et al. 2006;Tangestani 2009;Pourghasemi et al. 2012), or as the neuro-fuzzy method (Pradhan, Sezer, et al. 2010;Vahidnia et al. 2010;Oh & Pradhan 2011;Tien Bui et al. 2012). In this study, the fuzzy logic approach is considered for comparing with other methods. To be specific, the aims of this study is comparison of the reliability of bivariate statistical-based fuzzy logic with FR and WofE methods, an investigation into the spatial relationship among the causative factors motivating the landslides, and preparing a LSM for Qaemshahr basin. Since, natural hazards assessment maps are a useful tool for land use management, (Bathrellos et al. 2012Miller & Degg 2012Papadopoulou-Vrynioti et al. 2013Rozos et al. 2013;Sara et al. 2014) the final produced maps could be used for land use planning to prevent more losses in future.

Study area
Qaemshahr basin with 990 km 2 is located in Mazandaran province (see figure 1) in northern Iran (latitudes 368 00 0 04 00 to 368 30 0 00 00 N and longitudes 528 30 0 50 00 to 528 55 0 06 00 E). The altitude of the study area ranges from À11 in plain areas to 3709 m above m.s.l on mountainous area. Southern parts of the study area include steep highland slopes that gradually change to flat elevation towards the north.
The basin is located in the north of the central Alborz Mountains. The main structural zone of the study area is the central Alborz geological and structural zone, which includes three classes of Caspian plain in north, northern Mesozoic zone in the central regions, and central PaleozoicÀ Mesozoic range in the south (Gansser & Huber 1962). Lithological units of the study area consist of 28 distinct units with the relevant digitized lithology layer, shown in figure 2. North of the study area, often, includes pluvial and fluvial fans and terraces, alluvial flood plains that composed of conglomerate, silty marl, sandstone, and siltstone. The geological age of these formations is Quaternary. In the mid-latitude of the area, main lithological units are limestone, marl, siltstone, sandstone, dolomite, or a combination of these that are belonging to Triassic to Tertiary periods. Southern regions often consist of shale, sandstone, siltstone, claystone, quartzitic sandstone, and conglomerate belonging to Mesozoic. Total annual rainfall of the study area ranges from 600 to 1000 mm during long-term period. The climatic conditions of the study area are varied from axerique froid in south to mesomediterranean in the north.

Producing and preparing of the landslide-related factors
The main data layers required for landslide susceptibility, hazard and risk assessment can be subdivided into four groups as (1) landslide inventory map, (2) environmental factors, (3) triggering factors, and (4) elements at risk (van Westen et al. 2006). Based on the well-known principle of 'today and past are keys to the future', the landslide inventory is the most momentous data for landslide susceptibility mapping . Based on the various purposes, scale, and approach of data collection, landslide inventories could be different in spatial resolution and details (Sara et al. 2014). In this regard, the geoscience researchers have a new opportunity to exploit satellite images for detection and mapping of landslides by Google Earth Ò that provides worldwide coverage of high and very high resolution optical satellite images (multi-temporal in most places), and 3D image (figure 3) interpretation (Sato & Harp 2009). In this study, with the help of archived data (Forest, Range & Watershed organization of Iran) and Google Earth Ò , 157 landslides were identified in the study area. Among these, 22 landslides, including the rock falls and rock topples, which occurred in southern uninhabited mountainous areas, were excluded from the study due to the very different influence of the causative factors on their occurrence. The remaining landslides were randomly subdivided to 70% (95 events) for modelling and 30% (40 events) for validation of the output susceptibility maps. Furthermore, the most important available factors, including slope degree, slope aspect, elevation, lithology, land use/cover, normalized difference vegetation index (NDVI), distance to roads, drainage network, faults as the environmental factors, and rainfall as a triggering factor were used. Slope degree, slope aspect, and elevation were extracted from Aster digital elevation model (DEM) with 30 m resolution in spatial analyst tools and the digital layer of drainage network were produced from DEM by hydrology tools in ArcGIS 10 Ò . The lithology, faults, and roads were extracted as shapefile format by the vectorization of geology map of Qaemshahr in 1:100,000 scale. The layers of distance to drainage network, faults and roads were calculated by Euclidean distance tool in spatial analyst tools of ArcGIS 10 Ò . Landsat 8 data were also used for producing the land use/cover and NDVI layers. The land use/cover map was produced by supervised classification of satellite data and was generalized to seven classes.
The rainfall layer was produced by the interpolation of rainfall data from the climatology stations of Mazandaran province in long-term period. Minimum annual average is 600 mm in the south and the north of study area and maximum is 1000 mm for the central regions. All data were converted to raster format with 30 m £ 30 m pixels and each raster was divided into several classes (see figure 4) for calculation of the numbers of landslide and non-landslide pixels.

Methodology
In this study, WofE, FR, and fuzzy logic methods were applied to generate LSMs of the study area in ArcGIS 10 Ò . It is strongly recommended that the LSM production be carried out in a GIS-based system which the LSM readily be applied for land use management and can be updated as more information becomes available (Fell et al. 2008). To assess the reliability of the methods, the 'Area Under Curve' (AUC) of the 'Receiver Operating Characteristics' (ROC) can be calculated as are discussed in the following sections. All LSMs were classified to five landslide susceptibility zones based on the percentage of the area as very low (0%-40%), low (40%-60%), moderate (60%-80%), high (80%-90%), and very high (90%-100%). This type of classification is an appropriate method for easy visual interpretation of several LSMs (Pradhan & Lee 2010b). With the aid of this classification, a density graph was drawn to further interpretation of the produced LSMs as is discussed in the following sections.

Weight of evidence method
This method was originally developed for mineral potential assessment (BonhamÀCarter et al. 1988;Agterberg et al. 1993) and it has also been used in the landslide susceptibility studies (Pradhan, Oh, et al. 2010; Neuh€ auser et al. 2012). The WofE method is a probabilistic approach based on a log  . Landslide contributing-factor layers produced for the study area: (a) elevation, (b) slope aspect, (c) slope degree, (d) NDVI, (e) land use/cover, (f) rainfall, (g) distance to drainage network, (h) distance to roads, and (i) distance to faults. linear form of Bayes' rule written as This method calculates the weight for each landslide predictive factor (B) based on the presence or absence of the landslide (A) within the area, (Bonham-Carter 1994) as (2) where P is the probability and ln is natural log, B is the presence of desired class of landslide causative factor, B is the absence of desired class of landslide causative factor, A is the presence and A is the absence of the landslides. The magnitude of positive weight (Wi C ) is an indicator for the positive correlation between the presence of a desired class of the causative factor and the landslides. On the other hand, the negative weight (Wi À ) indicates the absence of a desired class of the causative factor and shows the level of negative correlation. The difference between the two weights is known as the weight contrast, C ( D Wi C À Wi À ). The magnitude of contrast reflects the overall spatial correlation between the desired class of causative factor and the landslides. The standardized value of C, calculated as the ratio of C to its standard deviation, S(C).The value of C/S(C) serves as a guide to the significance of the spatial correlation and show the relative certainty of posterior probability (Bonham-Carter 1994). The standard deviation of C is calculated as where S 2 Wi C and S 2 Wi À are the variances of the Wi C and Wi À (Agterberg et al. 1990) as Here, a simple form of Wi⁺ and Wiˉequations is expressed for easy implementation in GIS as where LS in % ð Þand nonLS in % ð Þare the percentages of landslide pixels and non-landslide pixels in the desired class, respectively. The ðLS out %Þ and ðnonLS out %Þ are the percentages of landslide pixels and non-landslide pixels out of the desired class.

Fuzzy logic approach
In the classical set theory, the Boolean algebra theorem states that either an object is a member of a set taking a value equal to one, or it is not the member of the set taking a value equal to zero (Tsoukalas & Uhrig 1996). For example, if there are landslides in a pixel then the pixel gains a value equal to one and if there is no landslide in the pixel, the value is equal to zero. Therefore, there are no intermediate values for the pixels with moderate susceptibility. In the fuzzy set theory introduced by Zadeh (1965), a set is explained by assigning the varying degrees of membership values to the elements between zero and one reflecting the certainty degree of the membership (Timothy 1995). The membership values can be based on user-defined, FR, AHP, or any other methods (Saaty 1977;Lee 2007;Pradhan et al. 2009). For LS mapping by fuzzy approach, a pixel of a causal factor can be in the range of no susceptible (membership value D 0) to maximum susceptibility (membership value D 1) and there is no practical constraint on the choice of values in this range. In this study, fuzzy membership values have been assigned based on the normalized ratio of the percentage of occurrence to the percentage of non-occurrence for a given attribute (Bonham-Carter 1994). These FRs are given in table 1.
Given two or more maps with fuzzy membership functions, m A x ð Þ, m B x ð Þ, …, m N x ð Þ, for the same set, a variety of operators can be employed to combine the membership values as follows (An et al. 1991;Chung & Fabbri 2001); When the fuzzy 'OR' and 'AND' operators are used for overlay of the landslide-related factors, only one of the fuzzy membership value from all overlapped pixels in a point makes the resultant value. On the other hand, when the fuzzy algebraic 'SUM' and 'PRODUCT' operators are used, the resultant set is larger or equal to the maximum value and smaller or equal to the minimum value among all fuzzy sets.
In the case of fuzzy 'GAMMA' (equation (13)), if g is equal to one (full compensation) the output results are equal to the results of 'SUM' operator and if g is equal to zero (no compensation), the output results are equal to results of the 'PRODUCT' operator. An appropriate value for g depends on the resultant validation rates of the produced LSMs.

Frequency ratio method
The FR is a bivariate statistical method that is simple to implement with accurate results (Lee & Pradhan 2007;Yilmaz 2009;Pradhan & Lee 2010a, 2010bPradhan, Lee, et al. 2010;Choi et al. 2012;Mohammady et al. 2012;Park et al. 2013). The FR is the ratio of landslides in a desired class as a percentage of all landslides (%L d ) to the area of the class as a percentage of the entire map (%C d ): where FR d is the FR weight of the desired class. The landslide susceptibility index (LSI) for each pixel, is the summation of total overlapped pixels as The LSI can easily be calculated for all pixels by raster calculator tool of ArcGIS 10 Ò . Fuzzy membership

Validation of landslide susceptibility models
Validation of the produced LSM reveals the reliability of the modelling processes and permits to compare the results of different models and the choice of their parameter variables (Beguer ıa 2006). The 'success rate' and 'prediction rate' methods are used in the validation process of landslide susceptibility analysis (Dietrich et al. 1995;Chung and Fabbri 2003;Neuh€ auser et al. 2012). The success rate helps to determine how well the resultant maps have classified the areas of existing landslides (Chung & Fabbri 1999). However, this may be inappropriate for evaluation of the models predictability, because, the success rate uses the landslide data-set utilized in the modelling stage Pourghasemi et al. 2012). The prediction rate using the validation data-set (30% of the whole set D 40 events) can explain how well the models and causal factors predict future landslides (Chung & Fabbri 2003;Pradhan & Lee 2010a). In this study, the ROC method was selected for validation, which is discussed in the next section. In addition, to further validation of the produced LSMs, a density graph, which is explained in Section 4.4.2, was prepared.

ROC method
ROC is a popular method that can show the success and prediction curves of the output LSMs of different methods. ROC curve is a graph of 'sensitivity' versus 'specificity', which is calculated for several thresholds. Where, sensitivity is the ratio of unstable pixels above a desired threshold that correctly predicted by the model over the total observed unstable pixels and specificity is the ratio of stable pixels below the desired threshold that correctly predicted by the model over the total observed stable pixels. The AUC of ROC curve can be used as a statistical measurement of the success and prediction rates of models (Chung & Fabbri 2003;Lee et al. 2003;Pradhan & Lee 2010c). The AUC is calculated (Beguer ıa 2006) as the total area of polygons between the thresholds as

Density graph
In this study, landslide density graphs of the produced LSMs were plotted for WofE, fuzzy gamma, and FR methods. This graph is a proper approach to show how the landslides are distributed in different susceptible zones of an output LSM. For plotting a landslide density graph, the density of landslides (the ratio of pixels with occurred landslides over the ratio of non-occurred landslide pixels) per each classified susceptible zone will be plotted on a diagram. In accordance with the theoretical base, the landslide density value should increase from the very low to the very high susceptible zones (Pradhan & Lee 2010a) with an increasing rate.

Spatial relationship between causative factors and landslides
The causative factors were classified into several classes and weights were assigned to them for FR, fuzzy logic, and WofE methods as are presented in columns 7, 8, and 15 in table 1. These results show that the relative susceptibility of each class is approximately similar for all three methods. This means that if a class has a higher/lower susceptibility this is true for all three methods. The highest susceptible classes of elevation are 100À500, 1000À2000 and 3000< m above m.s.l. It seems there is no specific correlation between the landslide occurrence and elevation. Unlike elevation, there is a strong correlation between the slope degree and the landslide occurrence so that the weights are increased with a greater degree of the slope apart from the slope above fifty degrees. In the case of slope aspect factor, the most susceptible classes are SW and SE directions.
The most susceptible classes of the lithology factor in the order of importance includes (1) marl, calcareous sandstone and siltstone, silty marl, sandy limestone, mudstone, (2) greyÀgreenÀyellow limestone, marly limestone, calcareous marl and marl, and (3) young alluvial fans and terraces.
Regarding the land use/cover factor, the most susceptible class is a mixture of agricultural and forestry areas with the highest FR several times greater than other classes.
With regard to the rainfall, two classes with the precipitation higher than 900 mm are the most susceptible. Regarding the NDVI, the susceptibility increases gradually with the raising NDVI value, thus the class with NDVI value greater than 0.4 is the most susceptible area to landslide occurrence.
In the case of distance to the linear factors, by moving away from drainage networks and roads, the susceptibility is reduced, especially for drainage network. However, for distance to faults factor, there is no a clear reduction of susceptibility of the classes and the classes of 0À200, 200À400, and 600À1000 m have an approximately similar susceptibility.

Methods used to produce LSM
The classified layers of factors as a raster format were used for producing a LSM for different methods in ArcGIS 10 Ò . In the case of the fuzzy logic method, most of the operators used in overlay process were unacceptable. The 'PRODUCT' and 'AND' operators produced the LSMs with the values ranging from 0 to 0.447 and 0 to 0.566 so 98% and 87% of their area were exactly equal to zero (not susceptible). In addition, in the case of the 'GAMMA' operator for g equal to 0.6, more than 73% of the produced LSM's area was equal to zero. In contrast, when both 'SUM' and 'OR' operators were used, more than 72% of the pixels of the output LSMs obtained a value equal to one, which reflects the maximum susceptibility. Therefore, due to their unreliable results, the mentioned operators were excluded from the LSM production. Table 2 lists the validation results (success and prediction rates) of the output LSMs of the fuzzy gamma (g value of 0.7, 0.8, 0.9, 0.95, and 0.975), FR, and WofE methods obtained by the ROC method. The related ROC curves are shown in figure 5. In the case of fuzzy gamma, the success and prediction rates increase for higher gamma to the extent that g D 0.975 shows the best result. The success and prediction rates of the FR and WofE methods are in the range of 0.80À0.90 (table 2) indicating good performance of the models. For the fuzzy gamma, the results are in the range of 0.70À0.80, which suggest a fair quality of the model. Note that in the difference of success and prediction rates of the FR and WofE methods that is about 1% while this is more than 4% for fuzzy gamma (see table 2). The output LSMs of the FR, fuzzy gamma when g is 0.975, and WofE methods were classified to five susceptible zones shown in figure 6. Examining figure 6 shows that the produced LSMs of FR and WofE are different in the spatial distribution of susceptible zones, although these methods are similar in the success and prediction rates.
The landslide density graphs, which presented in figure 7, show an increasing rate of landslide density from very low to very high susceptible zones for all three methods. However, this increasing rate for the FR method is higher than the other methods so the landslide density of very high susceptible zone for this method is the highest. The landslide percentage per each susceptible zones is given in table 3 indicate that in the very high susceptible zone of LSMs, the percentage of landslides for FR method is clearly higher than the other methods especially in comparison with the fuzzy gamma operator.  6. Discussion

Spatial relationship between causative factors and landslides
Although the elevation factor does not directly affect the landslide occurrence, in relation to other factors, such as tectonics, erosion À weathering processes, and precipitation, it contributes to landslide occurrence and influences the whole system, thus, the elevation factor could not be excluded (Rozos et al. 2008). However, Pourghasemi et al. (2012), Zare et al. (2012), and Park et al. (2013) have stated that the susceptibility is reduced for the higher altitude. This condition may be due to the presence of rocky cliffs in higher altitudes which are resistant to weathering processes (Mohammady et al. 2012). Nevertheless, in our study the susceptibility for the elevation class of 3000<, which its area is only 2.24% of the total area, is high due to the occurrence of three landslides on it. However, since the statistical population of the events and the area of this class is small, evaluation of its susceptibility is difficult.
Generally, the increasing of susceptibility with increasing the slope degree is due to the rising of shear stress. In this study, the class with 50< slope degree was unsusceptible to landslide perhaps due to (1) exclusion of 22 rock falls and rock topples which mostly occurred in steep slope, (2) less accumulation of weathered materials which fall gradually, and (3) outcropping of bedrock which is resistant to weathering processes.  In the case of slope aspect factor, the higher susceptibility of SW and SE classes can be justified by the river flow direction that is toward the north of the study area. A meandering river can respectively cause outside lateral erosion and inside deposition on the floodplain. In the study area, the lateral erosion occurred on the side of SW and SE aspects and deposition has occurred in NE and NW aspects.
In regards to lithology, Varnes (1984) stated that lithology includes composition, fabric, texture, or any other attribute that influences the physical and chemical behaviour of rocks and engineering soils which are important in determining the shear strength, permeability, susceptibility to chemical and physical weathering, and other characteristics of the soil and rock materials, which in turn, affect the slope stability. In our study, although all three classes of lithology, which mentioned (in Section 5.1) as the highest susceptible classes, have a susceptible lithology, some other classes with the similar lithology are not very susceptible. This maybe is concurrence with the smaller impact of the other factors.
For land use/cover, the most susceptible class is a mixture of agricultural and forestry areas due to the deforestation close to the rivers for farming.
As expected in the case of rainfall, those classes with high precipitation were more susceptible. Water is one of the most important causative factors in landslide occurrence. The increasing of some variables, such as pore water pressure, swelling of some clay minerals, and increasing the weight of unstable earth mass, which can cause a landslide, depend on the infiltrated water. In addition, water is a lubricant factor on a sliding surface that facilitates landslide occurrence (Varnes 1984).
For the NDVI factor, a gradual increase of the FR of landslides occurred with the increasing of NDVI values. The NDVI can be used as a good indicator of landslide occurrence because the NDVI value is higher in some regions prone to landslide, such as the area with high precipitation, closer distance to the rivers, and a fertile soil, which are suitable conditions for plant growth.
Not surprisingly, in the case of the distance to linear factors the classes with the nearest distance to the roads and drainage network show the most susceptibility to landslide occurrence due to the natural slope disruption by roads construction and slope toe erosion by rivers. However, for the distance to fault factor, the unclear relationship between the increasing distance and landslide occurrence is perhaps due more to the influences of other factors on landslide occurrence.
A fact in examining the spatial relationship between causative factors and landslides is the interaction effects of the factors. The most important effective factors show the most logical correlation with landslides, whereas, the correlation of least important factors with landslides is obscured under the influences of other factors.

Methods used to produce LSM
The similar relative susceptibility of the classes, which mentioned in Section 5.1, could be explained owing to the fact that, although the methods are different, they have bivariate statistical bases. Considering the bivariate statistical base of the methods, the differences of the relative susceptibility can be a good indicator of user error degree in the weighting process, which in this study is minimal.
In the case of fuzzy logic method, the inefficiency of the operators, including 'PRODUCT', 'AND', 'SUM', 'OR', and 'GAMMA' when g value is 0.6 could be explained by the nature of them. Considering their equations, the 'PRODUCT' and 'AND' operators produce an unsusceptible area of 98% and 87% of output LSMs, respectively, because these operators give a minimum membership value from all overlapped pixels falling in a pixel of output LSM. Also in the 'GAMMA' operator (g D 0.6), more than 73% of the LSM area is unsusceptible due to a more effective role of 'PROD-UCT' operator in its equation. In the contrary, the 'SUM' and 'OR' operators give a maximum membership value from all overlapped pixels which fall in an output pixel, thus, a large area of the output LSMs show the maximum susceptibility to landslide occurrence. The unacceptable results of 'PRODUCT' and 'SUM' operators for LSM production was also reported by Tangestani (2009). The increasing trend of success and prediction rates of gamma operators along with the increasing of g value is due to the balanced effect of 'PRODUCT' and 'SUM' operators on its equation.
Although, the accuracy of fuzzy gamma (when g D 0.975), FR, and WofE methods are acceptable, the higher difference of success and prediction rates of the fuzzy gamma in comparison with FR and WofE shows that this method is a weaker predictor of the future landslide occurrence. Since all conditions of this study (study area, number of landslides, causative factors etc.) were the same for all three methods, the relative inferiority of fuzzy gamma could be mainly attributed to (1) the inherent inefficiency of fuzzy method, (2) the base of obtaining membership values which was FRs, and (3) the normalization process of these ratios.
Due to the rejection of first reason, good results of the fuzzy gamma method are reported in other studies (Tangestani 2009;Pradhan 2010;Pourghasemi et al. 2012). The second reason is rejected as well, because, the FRs (calculated in column 7 in table 1), which directly used in the FR modelling with the highest success and prediction rates (see figure 7 and table 3), were normalized as a membership value for the fuzzy modelling.
Regarding the third reason, it can be noted that normalization process causes equality in the maximum and minimum fuzzy membership values of all contributing factors. For example, the maximum weights among several classes of distance to drainage network and NDVI factors are 7.77 and 1.20 for the WofE method (column 15 in table 1) and are 3.07 and 1.81 for FR method (column 7 in table 1), respectively, but both are equal to one in the fuzzy membership values (column 8 in table 1). As a result, the normalization of the FRs caused uniformity in the effect of factors with different influences on landslide occurrence, which increases the theoretical error in the overlapping process of the causative factors.
An important finding of this study is that, although the validation rates of methods be equal, their output LSMs may be different in the spatial distribution of susceptible zones. For example, the output LSMs of FR and WofE methods have a visible spatial differences although their validation rates are almost equal (less than 1% difference). The same consequences can be seen in the other similar studies (Mohammady et al. 2012;Park et al. 2013). In the study of Mohammady et al. (2012), although the success and prediction rates of FR and DempsterÀShafer methods have a less than 2% difference, but their output LSMs, which were classified to five similar zones with an equal area, are very different. Moreover, in the study of Park et al. (2013) while the validation rates of FR and LR methods were exactly equal, their output LSIs (with a same visualization technique) are different. It can be seen that different methods possibly do not produce the same LSMs, even with a same classification method and with an equal validation rate.

Summary and conclusion
Landslide is an important natural hazard, and therefore, recognition of both landslide-prone areas and landside susceptibility mapping is the interest of responsible organizations and researchers. Various methods and many causative factors can be used for LSM production depending on the scale and scope of the study. Selection of a method for mapping is an important decision. Comparison of the results of different methods in the same conditions is helpful for assessment of the relative reliability of them, although the reliability of methods is often dissimilar in different conditions.
In this study, bivariate statistical-based fuzzy logic, WofE, and FR methods were compared at a regional scale, on the Qaemshahr basin, in the north of Iran considering 10 causative factors. With the extraction of landslide inventory data by means of Google Earth Ò , it is found that this software is an excellent tool to improve landslides archived data. With the aid of GIS, the spatial relationship between occurred landslides and causative factors, including elevation, slope degree, slope aspect, lithology, land use/cover, NDVI, rainfall, distance to drainage network, roads, and faults were calculated. The results showed that slope degree, lithology, rainfall, and distance to drainage network are the most important factors among all.
Between the utilized methods in this study, 'AND', 'OR', 'SUM', and 'PRODUCT' operators of the fuzzy logic does not produce an acceptable LSM due to the placement of large number of the pixels either in very low or in very high susceptible zones. On the other hand, the fuzzy 'GAMMA' operator especially for g D 0.975 has acceptable output LSMs, although, it is less reliable in comparison with the FR and WofE methods due to the effect of the normalization process for obtaining fuzzy membership values. The FR method shows the best results and the WofE method with a minor difference is in the second order, though its application is more difficult. Considering the results of this study, it seems that the simple methods like FR and WofE are adequate for producing a small scale LSM when a suitable landslide inventory can be prepared.
Despite the slight difference in the validation rates of FR and WofE methods, the observed spatial difference of zones between the outputs LSMs is a serious problem in implementing management projects. However, these LSMs produced in this way, are useful in land use management. The choice of what LSM or a combination of LSMs is suitable depends on the study area conditions. Nevertheless, in this study LSMs produced in a regional scale (small-scale map), and further studies are needed in the LSM production for the slope stability and land use management projects in the larger-scales. Also, more studies for comparing the reliability of other methods in small-scale might be helpful.