1 Introduction

Dangerous effects of landslides are in relation to the economic system of many countries (Nefeslioglu et al. 2008). Landslide is one of the most widespread hazardous phenomena (Aleotti and Chowdhury 1999). There are different methods for landslide susceptibility mapping such as probability and bivariate statistical modeling (Bai et al. 2008; Gonzalez et al. 2017; Kouhpeima et al. 2017; Kreuzer et al. 2017; Ercanoglu et al. 2016; Lee et al. 2016; Meten et al. 2015; Hölbling et al. 2015; Mokarram et al. 2015; Kayastha et al. 2013).

Shirani and Arab Ameri (2015) using logistic regression model generated landslide susceptibility zonation map. The results showed that elevation factor was importance data for prediction of landslide susceptibility. Entezari et al. (2015) sued entropy model to zoning of landslide hazard in zar’ab basin, Iran. The findings of this study show that 55% of the total landslide occurred in the medium-risk range, 37% in the high-risk range, and 8% in the low-risk range and the main reason for this was the effect of roads on the increase of landslide in the area. Hejazi (2015) evaluated landslide hazard in Ahar Basin using geographic information system (GIS) and analytic hierarchy process (AHP). Rahimzadeh and Alaiee (2015) used regional model to assessment of hill side instability potential in Zagros. The results showed that the study area consisted of four zoning maps in four levels risk (very high risk, high risk, low risk and very low risk).

Mirnazari et al. (2015) used AHP model and fuzzy logic operators to assessment and zoning of landslide hazard. Result of this paper showed that based on weight of each factor in the AHP model showed that 36% of the catchment area is located in high and very high risk. While the operator of Gama fuzzy indicated 67% of area located in high and very high landslide zoning. model evaluating shows Gama fuzzy 0.7 models is more accurate than AHP model in the study area. Abedini et al. (2015) used statistical method of logistic regression to modelling the hazard of landslides. The results of the study area showed that landslide susceptibility map using SCAI index had high verification in the study area. Using these results can predict future landslides for decreasing their risks and planning for the land use. The review of landslide susceptibility and Fuzzy-AHP can be found in several manuscripts such as: Nowjavan and Hayati (2013), Jouri et al. (2014), Sarvati et al. (2014), Shabani et al. (2014), Dai et al. (2002), Drobne and Lisec (2009), Feizizadeh and Blaschke (2011), Fell (2008), Gorsevski and Jankowski (2008, 2010), Komac (2006), Malczewski (2006), Malczewski et al. (2003), Swets (1988), Van Westen et al. (2000) and Yager (1988).

Therefore the aims of this study is determinate the landslide susceptibility modeling in the north of Khorramabad, west of Kermanshah Province, Iran using fuzzy quantifier and GIS. To study the region, the fuzzy-AHP method was selected to investigate the landslide susceptibility. The rest of this paper is organized as follows; in Sect. 2, the fuzzy modeling is explained. Section 3 holds the case study and the input data properties. Section 3 describes the fuzzy-AHP results. Besides, in the last section that is Sect. 4 conclusions are presented.

2 Methods and Material

2.1 Case Study

The study area was located in north of Khorramabad, west of Kermanshah Province, Iran. It has an area of about 17,133.90 km2, and is located at longitude of 33°11′ to 34°33′N and latitude of 46°40′ to 48°44′E (Fig. 1). The altitude is between 682 and 3487 m in the study area. According to suitable climate and fertile soil, the study area has good potential for agriculture. The principal agricultural crops consist of wheat, beans, barley and rice. Due to the area in Sanandaj Sirjan, impermeable base of the rocks, loose upper sediments, poor vegetation, grazing livestock, high altitude and abundant rainfall, the study area is exposed to landslides (Zareiee 2014; Maleki and Ghorbanpour 2008). Therefore, one of the important factors is the Landslide susceptibility in the study area. In order to forecast the Landslide susceptibility, data on the Aspect, DEM, lithology, slope, land use, river, road, fault, precipitation maps were obtained from the north of Khorramabad, west of Kermanshah Province, Iran.

Fig. 1
figure 1

Geographic position of the study area

Full size image

2.2 Data Source

Slope represents the rate of change of elevation for each digital elevation model (DEM) cell that was prepared from DEM 90 m (2017). The lithology of a rock unit is a description of its physical characteristics visible at outcrop, in hand or core samples or with low magnification microscopy, such as colour, texture, grain size or composition that was prepared from geological map. A fault is a planar fracture or discontinuity in a volume of rock, across which there has been significant displacement as a result of rock-mass movement that generated from geology map. In the study was used precipitation as climatology factors for site select of suitable for landslide susceptibility from Iran Meteorological Organization. Elevation was prepared from DEM (90 m). Stream and aspect maps were extract from DEM in ArcGIS. Land use and road maps were prepared from Ministry of Agriculture Jihad in 2017.

2.3 Fuzzy Method

In the study using membership function prepared fuzzy maps for each parameter. A membership function (MF) assigns to each object a grade ranging between 0 and 1 (Zadeh 1965). The value 0 means that x is not a member of the fuzzy set, while the value 1 means that x is a full member of the fuzzy set. A sample of fuzzy set is shown in the following (McBratney and Odeh 1997):

$$A = \left\{ {x,\mu_{A} \left( x \right)} \right\}\quad for\;each\quad x\,\varepsilon \,X$$
(1)

where μA is the MF (membership of x in fuzzy set A) so that:

If x does not belong to A then μA = 0.

If x belongs completely to A then μA= 1.

If x x belongs in a certain degree to A then 0 < μA(x) < 1.

According to Eq. 1 MF was used for slope, elevation, sensitive, land use, aspect, and precipitation (Feizizadeh and Blaschke 2013):

$$\mu_{A} (x) = f(x) = \left\{ {\begin{array}{*{20}l} 0 \hfill & {x \le a} \hfill \\ {{{x - a} \mathord{\left/ {\vphantom {{x - a} {b - a}}} \right. \kern-0pt} {b - a}}} \hfill & {a \prec x \prec b} \hfill \\ 1 \hfill & {x \ge b} \hfill \\ \end{array} } \right\}$$
(2)

where x is the input data and a, b are the limit values.

For distance of river, distance of fault, and distance of road the following MF was used (Feizizadeh and Blaschke 2013):

$$\mu_{A} (x) = f(x) = \left\{ {\begin{array}{*{20}l} 1 \hfill & {x \le a} \hfill \\ {{{b - x} \mathord{\left/ {\vphantom {{b - x} {b - a}}} \right. \kern-0pt} {b - a}}} \hfill & {a \prec x \prec b} \hfill \\ 0 \hfill & {x \ge b} \hfill \\ \end{array} } \right\}$$
(3)

where x is the value of distance of river, distance of fault, and distance of road and a, b are the limit values.

2.4 Analytic Hierarchy Process (AHP)

Analytic hierarchy process as the multicriteria decision analysis (MCDA) procedure is applied to elicit the criteria weights (Saaty and Vargas 1998). AHP is a pairwise comparison method for individual or group decision-makers (Malczewski 1999). In a pairwise each factor is rated against every other factor by assigning a relative dominant value between 1 and 9 to the intersecting cell that show in Table 1.

Table 1 Scales for pairwise comparisons (Saaty and Vargas 1998)
Full size table

3 Results and Discussion

3.1 Preparing Raster Maps

For determining the landslide susceptibility map of the present study, the fuzzy-AHP algorithm was applied on the input data known as the Aspect, DEM, lithology, slope, land use, river, road, fault and precipitation maps. To reach this aim, at first raster maps were prepared for each parameter. By using DEM with spatial resolution of 90 m (Source: http://earthexplorer.usgs.gov), the slope and aspect map in ArcGIS v.10.2 software were prepared that are shown in Fig. 2. In the same figure, many parts of the northeast of the present study area have elevations more than 2500 m. Besides, the slope value is between 0 and 66.8° which is considered as the most slope value among the northeast values and center of the study area (green color). The aspect value is between –1 (flat) and 360 (north) in which aspects of the south and the west are sensitive to landslide (Feizizadeh and Blaschke 2013).

Fig. 2
figure 2

Slope, aspect, and DEM maps for the study area

Full size image

For preparing raster maps of the road distance, fault and river as well as their buffer maps, buffer tools of ArcGIS were used. As shown in Table 2, buffer maps were prepared by using distance from features (Fig. 3). To determine the precipitation map of the present study, the contour line was used that is shown in Fig. 4. The contour line was converted to the raster map in the ArcGIS software. According to Fig. 4, some parts of the south and the southeast of the study area have precipitations more than 500 m. Moreover for determining the landslide susceptibility, DEM, lithology, slope, land use, river, road, fault and precipitation maps were used which is shown in Fig. 5. According to Fig. 5 in the study area, there are six types of land uses (forest, agriculture, rangeland, wood land, bare land, rock and urban). The last method of preparing the landslide susceptibility map of the study area is preparing the sensitive map of water erosion. The sensitive map of five classes was shown in Fig. 6. According to Table 3, if the susceptibility is reduced to erosion, sensitive classes to landslide are increased.

Table 2 Distance of fault, stream, and road for determination of landslide susceptibility
Full size table
Fig. 3
figure 3

Fault, stream, and road maps in the study area

Full size image
Fig. 4
figure 4

Precipitation map of the study area

Full size image
Fig. 5
figure 5

Land use map for the study area

Full size image
Fig. 6
figure 6

Sensitivity map of the study area

Full size image
Table 3 Description of sensitive classes of lithology to erosion
Full size table

3.2 Fuzzy Method

In the ArcGIS software, linear membership function (MF) is used in order to determine the fuzzy map of each parameter. The maximum and minimum values of the membership functions are determined in Table 4, for example the MF value for a DEM which is higher than 3000 is 1, the value of smaller than 1200 m is MF = 0 and MF is measured between 0 and 1 for the DEM values between 1200 and 3000 m. In the same example, the quantity of DEM for other parameters is defined by using minimum and maximum values of MF. Based on Table 5, membership functions were defined for each parameter between 0 and 1. The fuzzy maps prepared for the landslide susceptibility parameters are shown in Fig. 7, where MF is closer to 0 with decreasing the landslide susceptibility whereas MF is closer to 1 with increasing the landslide susceptibility. According to Fig. 7 all the parameters (aspect, distance of road, distance of stream, distance of fault, slope, DEM (g) land use, precipitation, and lithology) were closer to 1 in northeast of the study area. According to Fig. 9, the north and the northeast of the study area had a value close to 1 that showed the high landslide susceptibility.

Table 4 Maximum and minimum values of criteria (Feizizadeh and Blaschke 2013)
Full size table
Table 5 Pairwise comparison matrix, factor weights and consistency ratio of the data layers used
Full size table
Fig. 7
figure 7

Fuzzy map of studied area for each landslide susceptibility parameter: a aspect, b distance of road, c distance of stream, d distance of fault, e slope, f DEM, g land use, h precipitation, i lithology (sensitive)

Full size image

3.3 AHP Method

In the present research, authors utilized the AHP method to incorporate different types of input data and the pairwise comparison method for comparing two criteria (Feizizadeh and Blaschke 2013). According to Table 5, the lithology and DEM have the highest and lowest weight, respectively.

3.4 Fuzzy and AHP Methods

According to the fuzzy maps in Fig. 7 and weight of each parameter in Table 5, the final fuzzy map for landslide susceptibility was determined that was shown in Fig. 8. Based on Fig. 8 landslide susceptibility map was between 0 and 1 that value more than 0.75 had high landslide susceptibility, values between 0.5 and 0.75 had medium landslide susceptibility, value between 0.25 and 0.5 had low landslide susceptibility and value between 0 and 0.25 had very low landslide susceptibility. Then, the fuzzy map reclassified in four classes consisted of very low (0.73%), low (77.62%), medium (10.67%) and high (10.98%) (Figs. 9, 10 and Table 2).

Fig. 8
figure 8

The fuzzy-AHP combination map for landslide susceptibility classes

Full size image
Fig. 9
figure 9

Map of the fuzzy classification

Full size image
Fig. 10
figure 10

The area (%) for each class of the landslide susceptibility

Full size image

Based on Fig. 10, for created of precision and accuracy of fuzzy and AHP method were used 150 sample points randomly. For 150 sample points nine parameters including, DEM, DEM, lithology, slope, land use, river, road, fault, and precipitation maps were evaluated. Also, the class of landslide susceptibility was forecasted by fuzzy-AHP model for each point. Then for determination of precision and accuracy of fuzzy-AHP method were compared the class of landslide susceptibility by fuzzy-AHP model with nine parameters values which showed in Table 3. Overall, based on Table 6, the model of Fuzzy-AHP was a benefit tool for prediction of landslide susceptibility status in each point of the case study. The results show that method was a useful tool for prediction of landslide susceptibility status in each case study (Feizizadeh and Blaschke 2013). Chacón et al. (2006), Chamaptiray ray et al. (2006) and Srivastava et al. (2010) using fuzzy to determined landslide susceptibility map that results show that fuzzy AHP is a useful method for prediction of hazardous phenomena such as landslide.

Table 6 The properties of sample points of the case study
Full size table

4 Conclusions

Landslide susceptibility mapping has been made possible due to the accessibility and variety of remote sensing and GIS data. Almost all of the landslides are referred to as significant geomorphic processes. This paper evaluated the spatial distribution of the landslide susceptibility with different risk levels by using the fuzzy-AHP method. According to AHP model, the most important factors in landslide susceptibility were lithology and precipitation the least important parameters were DEM and aspect in the study area. The class of landslide susceptibility was predicted by fuzzy-AHP model for each point which showed that 10.98% of the lands had high landslide susceptibility, 10.67% medium landslide susceptibility, 77.62% low landslide susceptibility and 0.73% very landslide susceptibility. Overall, more than half of the study area had medium landslide susceptibility. According the result, it can be concluded that fuzzy-AHP method was suitable for investigation of landslide susceptibility mapping.