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- Taylor & Francis
- Copyright
- © 2013 Taylor & Francis
- ISSN
- 1947-5713
- eISSN
- 1947-5705
- DOI
- 10.1080/19475705.2013.843206
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Abstract
Geomatics, Natural Hazards and Risk, 2015 Vol. 6, No. 3, 243–271, http://dx.doi.org/10.1080/19475705.2013.843206 A novel hybrid evidential belief function-based fuzzy logic model in spatial prediction of rainfall-induced shallow landslides in the Lang Son city area (Vietnam) DIEU TIEN BUI*yz, BISWAJEET PRADHAN{, INGE REVHAUGy, DUY BA NGUYENz, HA VIET PHAMx and QUY NGOC BUIz yDepartment of Mathematical Sciences and Technology, Norwegian University of Life Sciences, P.O. Box 5003-IMT, N-1432, Aas, Norway zFaculty of Surveying and Mapping, Hanoi University of Mining and Geology, Dong Ngac, Tu Liem, Hanoi, Vietnam xDepartment of Tectonic and Geomorphology, Vietnam Institute of Geosciences and Mineral Resources, Thanh Xuan, Hanoi, Vietnam {Department of Civil Engineering, Faculty of Engineering, University Putra Malaysia, Serdang, Selangor Darul Ehsan 43400, Malaysia (Received 10 July 2013; accepted 7 September 2013) The main objective of this study is to investigate potential application of an inte- grated evidential belief function (EBF)-based fuzzy logic model for spatial predic- tion of rainfall-induced shallow landslides in the Lang Son city area (Vietnam). First, a landslide inventory map was constructed from various sources. Then the landslide inventory map was randomly partitioned as a ratio of 70/30 for training and validation of the models, respectively. Second, six landslide conditioning fac- tors (slope angle, slope aspect, lithology, distance to faults, soil type, land use) were prepared and fuzzy membership values for these factors classes were esti- mated using the EBF. Subsequently, fuzzy operators were used to generate land- slide susceptibility maps. Finally, the susceptibility maps were validated and compared using the validation dataset. The results show that the lowest prediction capability is the fuzzy SUM (76.6%). The prediction capability is almost the same for the fuzzy PRODUCT and fuzzy GAMMA models (79.6%). Compared to the frequency-ratio based fuzzy logic models, the EBF-based fuzzy logic models showed better result in both the success rate and prediction rate. The results from this study may be useful for local planner in areas prone to landslides. The model- ling approach can be applied for other areas. 1. Introduction Landslide susceptibility maps showing the spatial distribution of landslide can be defined as the probability of spatial occurrence of future slope failures (Guzzetti et al. 2005). The term “spatial” is related to the inter-correlation of a set of geo-envi- ronmental factors such as slope, geology, soil type, etc. With the rapid acquisition of remote sensing data (Pirasteh et al. 2009; Merrett & Chen 2012) and the develop- ments of computer and software technology (Wan 2009; Wan et al. 2010; Farrokhnia et al. 2011; Wan et al. 2012), a series of methods and techniques for spatial *Corresponding author. Email: Bui-Tien.Dieu@umb.no 2013 Taylor & Francis 244 D. Tien Bui et al. prediction of landslides have been proposed and they range from simple qualitative techniques to sophisticated mathematical models (Chung & Fabbri 2008; Pradhan et al. 2010a; Mohammady et al. 2012; Pourghasemi et al. 2012b). Good overview of these methods with their disadvantages and advantages can be seen in Guzzetti et al. (1999), Dai et al. (2002), Chacon et al. (2006), and Corominas and Moya (2008). In recent years, new methods such as fuzzy logic (Lee 2007; Wan et al. 2008; Kanungo et al. 2009; Tangestani 2009; Biswajeet & Saied 2010; Srivastava et al. 2010; Pradhan 2011a, 2011b; Blais-Stevens et al. 2012; Kayastha 2012; Pourghasemi et al. 2012a; Tien Bui et al. 2012e; Tien Bui, Ho, et al. 2013; Zare et al. 2013), neuro- fuzzy (Pradhan et al. 2010b; Vahidnia et al. 2010; Oh & Pradhan 2011; Sezer et al. 2011; Tien Bui et al. 2011), and data mining approaches methods (Melchiorre et al. 2008; Nefeslioglu et al. 2008; Yao et al. 2008; Saito et al. 2009; Yilmaz 2009; Prad- han & Lee 2010; Yeon et al. 2010; Marjanovic et al. 2011; Melchiorre et al. 2011; Yilmaz & Kaynar 2011; Ballabio & Sterlacchini 2012; Pradhan 2013; Tien Bui et al. 2012a, 2012c; Wan et al. 2012; Xu et al. 2012) have been widely used in landslide mapping. In general, the prediction capability of the new models possesses better than those obtained from conventional models (Tien Bui, Pradhan, et al. 2013). Compared with other data mining methods, fuzzy logic is straightforward to apply and the weighting of landslide conditioning factors is entirely controlled by the experts (Lee 2007). In addition, fuzzy logic methods do not require the statistical distribution of the data and can be easily implemented within a GIS environment (Pradhan 2011b). Furthermore, fuzzy logic can deal with imprecision and uncertainty by allow- ing spatial objects to be a matter of degree through membership values in fuzzy sets. The imprecision of the data refers to some cases in which value of a factor is given but the precision is not enough whereas the uncertainty refers to the input data that have been wrongly captured (Gorsevski et al. 2005). Therefore, fuzzy logic has been applied in various fields including landslide (Cheng & Agterberg 1999; Carranza & Hale 2001; Nazari et al. 2012; Peche & Rodriguez 2012) and review of these applications can be seen in Zimmermann (1996) and Demi- cco and George (2003). One of the most important tasks of the application of fuzzy logic in landslide modelling is to determine fuzzy membership values. Since fuzzy set theory does not provide the functions for generating fuzzy membership values of landslide condition- ing factors and theirs classes, therefore various methods have been proposed to address this issue. Champati ray et al. (2007) and Blais-Stevens et al. (2012) used expert knowledge; Lee (2007), Pradhan (2010, 2011a, 2011b), and Pourghasemi et al. (2012a) used the frequency ratio; Ercanoglu and Gokceoglu (2004) and Kanungo et al. (2008, 2009) used the Cosine amplitude; Chung and Fabbri (2008) and Dewitte et al. (2010) used the likelihood ratio function. Similarly, Pradhan et al. (2010b), Sezer et al. (2011), and Tien Bui et al. (2012d) used the neural network method. In general, no agreement has been reached yet on which method is the best to determine the fuzzy membership values in landslide susceptibility assessment. To address this issue, this study proposes a hybrid evidential belief function-based fuzzy logic model in spatial prediction of landslide hazard. The main objective of this study is to investigate potential application of an inte- grated evidential belief function (EBF)-based fuzzy logic model for spatial prediction of rainfall-induced shallow landslides in the Lang Son (LS) city area (Vietnam). The study area is located on the China–Vietnam border in the northeastern mountainous region of Vietnam. In this area, landslides usually occurred during extreme rainfall events, especially in tropical rainstorms. Due to the rapid development of economics A novel hybrid evidential belief function-based fuzzy logic model 245 during the last 20 years, the expansions of the infrastructures and especially deforesta- tion have increased slope disturbance. In addition, the continuation of rapid population has led to the growth of new residential areas and settlement expansions are shifted to the mountainous regions. Therefore, the high hazardous areas showing high potential risk of landslides should be identified and monitored. The difference of this study com- pared to the aforementioned landslide literature is that fuzzy membership values for landslide conditioning factors are obtained by using the belief (Bel) function. Finally, a comparison of the resulting susceptibility maps with those obtained from fuzzy logic model with fuzzy membership derived using the frequency ratio was carried out. 2. Study area and database 2.1. Study area The study area is located around the Lang Son city and the Dong Dang town in the Lang Son province in Vietnam (figure 1). This area belongs to the northeastern part 0 00 0 00 of Vietnam between longitudes 106 41 34 E and 106 48 32 E, and latitudes 0 00 0 00 21 49 43 Nand 21 57 13 N. It covers an area of about 168 km . Elevations range from 194 m a.s.l to 800 m a.s.l with a mean elevation of 328 m. Slope angles range o o o from 0 to 84 . Approximately 66% of the study area has slopes steeper than 15 . Only 23.7% of the study area has slope degrees less than 8 . Quaternary deposits covering 16% of the study area are mainly consisting of granule, grit, breccia, boulder, sand, and clay. Eleven lithologic formations that outcrop in the region are recognized and six of them (Na Khuat, Tam Lung, Khon Lang, Lang Son, Tam Danh, and Mau Son) cover 79.7% of the study area (table 1). The main lithologies are marl, siltstone, tuffaceous conglomerate, gritstone, sandstone, basalt, and clay shale. Land use of the study area is mainly comprises of 35.7% productive forest land, 21.5% paddy land, 20.4% barren land, 7.7% protective forest land, 6.9% settlement areas, 5.7% crop land, and 2.1% water surface. The soil types are mainly ferralic acri- sols (78.5%), dystric gleysols (6.1%), rhodic ferralsols (5.8%), eutric fluvisols (4.8%), plinthic acrisols (1.3%), and dystric fluvisols (1.2%). The study area is situated in the monsoonal region. Average annual rainfall is in the range from 1200 mm to 1600 mm. The rainy season falls within May to Septem- ber. The high amount of rainfall is the main triggering factor for the occurrence of landslides. In the study area, no information about earthquake-induced landslides has been reported. Figure 2 shows two pictures of newly mapped landslide locations in the Lang Son city. According to observations in the last 20 years, the annual average temperature o o ranged from 17 Cto22 C, the highest average monthly temperature is 27.5 Cin July, whereas the lowest is 12.5 C in January. Annual average relative humidity varies from 80% to 85%. The highest and lowest humidity is observed in the month of August and December respectively. 2.2. Spatial database Landslide inventory map, which is considered as the simplest form of landslide map- ping (Guzzetti et al. 1999), is the first requirement of susceptibility mapping. Land- slide inventory map is a dataset recording a single or multiple landslide events and can be compiled from aerial photographs analyses or historical information (Malamud et al. 2004). In the study area, the landslide inventory map was 246 D. Tien Bui et al. Figure 1. Location of the study area and landslide inventory map. A novel hybrid evidential belief function-based fuzzy logic model 247 Table 1. Description of the geologic formations in the study area. No. Formation Symbol Area (%) Main characteristic 1 Quaternary Q 16.0 Granule, grit, breccia, boulder, sand, clay, silt 2 Na Khuat T nk 25.6 Marl, siltstone, sandstone, clay shale, limestone 3 Tam Lung J K tl 23.1 Tuffaceous conglomerate, gritstone, sandstone, red- 3 1 violet siltstone, rhyodacite, rhyotrachyte 4 Khon Lang T kl 17.2 Conglomerate, gritstone, sandstone, siltstone, clayish shale, rhyolite, rhyodacite 5 Lang Son T ls 4.7 Sandstone, siltstone, clay shale, clayish limestone, marl 6 Tam Danh Kftd 4.6 Basalt, variolite, tuffs, lenses of claystone and siltstone 7 Mau Son T ms 4.5 Sandstone, quartzitic sandstone, lenses of conglomerate, red siltstone 8 Ha Coi J hc 2.0 Sandstone, conglomerate, siltstone 12 9 Dong Dang P dd 1.4 Bauxite, siltstone, limestone, cherty shale 10 Na Duong E N nd 0.8 Conglomerate, sandstone, siltstone 3 1 11 Diem He T dh 0.1 Clayish limestone 12 Bac Son CPbs 0.1 Massive limestone, oolitic limestone, clayish limestone constructed from various sources: (1) the landslide inventory map of 2006 (Tam et al. 2006); (2) the landslide inventory map of 2009 (Truong et al. 2009); (3) other landslides were identified by the interpretation of aerial photographs with spatial resolution of 1 m. These aerial photographs were acquired by the Aerial Photo- Topography Company (Vietnam) in 2003. Field surveys were conducted at randomly selected landslide sites to verify the landslide locations. Some recent landslides were also included from the multiple field visits. A total of 172 landslides covering 5457 grid cells (5 m 5 m) were identified and registered in the map. They were classified into three types of landslides: the first one that most frequently occurred is rotational slides consisting of 86 landslide locations, the second one is translational slides con- taining 52 translational slides, and the last one is 34 debris flows. Rock fall is very few and is not included in this study. These landslide grid cells were assigned a value of 1, whereas a 0 value was given for the no-landslide grid cells. The identification of landslide conditioning factors is an important task in land- slide susceptibility mapping and influences the quality of the landslide models. Since conditioning factors that control slope stability are numerous, therefore factors are usually selected based on the landslide types, the failure mechanisms, the map scale of analysis, and the characteristics of a particular study area (Glade & Crozier 2005). In general, factors related to topography, geology, soil types, hydrology, geomor- phology, and land use are considered to be the most commonly used parameters in landslide analyses (Van Westen et al. 2008). In the study area, a total of six landslide conditioning factors are considered for the landslide modelling. They are slope, aspect, lithology, distance to faults, soil type, and land use (table 2). First, the digital elevation model (DEM) for this study area was generated from the National Topographic Maps at scales 1:5,000 for the Lang Son city and 1:10,000 for the surrounding areas. The spatial resolution of the DEM is 5 5 m. Slope angle and slope aspect maps were extracted from the DEM. Based on the landslide literature and the landslide inventory map, six slope categories were constructed for the slope map (figure 3(a)). In the case of the aspect map, nine layer classes were constructed (figure 3(b)). 248 D. Tien Bui et al. Figure 2. Photographs of some recently landslides in the Lang Son area (Photos taken on October 2012 by Ha Viet Pham). Lithology that influences the physical behaviour of rocks and engineering soil (Varnes 1984) has been widely used for the assessment of landslides. In this study, the lithology and distance to faults were extracted from four tiles of the Geological and Mineral Resources Map of Vietnam at 1:50,000 scale (Quoc et al. 1992; Truong et al. 2009). This is because no geological map with larger scale is available for the study area. And then the lithological map (figure 3(c)) with seven groups was A novel hybrid evidential belief function-based fuzzy logic model 249 Table 2. Fuzzification parameters for landslide conditioning factors using frequency ratio and belief function. Fuzzification parameters Number of Landslide Data layers Class Frequency ratio Bel value pixels in class pixels Slope angle 0–8 39,813,500 0 0.100 0.000 (degree) 8–15 17,114,025 39 0.122 0.012 15–25 35,543,725 796 0.315 0.120 25–35 47,169,725 1549 0.415 0.175 35–45 25,972,525 1204 0.544 0.247 > 45 2,455,275 205 0.900 0.446 Slope aspect Flat 7,881,175 0 0.100 0.000 North 18,304,150 33 0.122 0.010 Northeast 21,121,050 159 0.192 0.041 East 20,045,575 262 0.261 0.071 Southeast 19,713,650 959 0.698 0.264 South 20,360,850 1326 0.900 0.353 Southwest 22,370,700 847 0.565 0.205 West 20,089,900 198 0.221 0.053 Northwest 18,181,725 9 0.106 0.003 Lithology Conglomerate 30,238,950 1086 0.900 0.285 Basalt 7,775,900 54 0.255 0.055 Quaternary 26,912,475 204 0.269 0.060 Siltstone 45,368,200 1081 0.631 0.189 Limestone 248,450 0 0.100 0.000 Sandstone 18,722,500 597 0.810 0.253 Tuff 38,802,300 771 0.543 0.158 Land use Annual crop land 4,499,225 64 0.395 0.102 Populated area 10,566,150 155 0.404 0.105 Protective forest 12,473,925 322 0.635 0.185 land Productive forest 61,029,725 1325 0.550 0.155 land Paddy land 39,295,850 584 0.408 0.106 Barren land 33,753,675 1304 0.900 0.276 Perennial crop land 3,974,925 39 0.303 0.070 Water surface land 2,498,475 0 0.100 0.000 Grass land 36,825 0 0.100 0.000 Soil type Ferralic acrisols 133,741,975 3285 0.817 0.298 Dystric gleysols 10,298,575 90 0.355 0.106 Plinthic acrisols 2,195,825 4 0.153 0.022 Water area 1,788,350 0 0.100 0.000 Dystric fluvisols 2,082,500 0 0.100 0.000 Eutric fluvisols 8,029,575 220 0.900 0.332 Rhodic ferralsols 9,744,950 194 0.681 0.242 Rocky mountain 247,025 0 0.100 0.000 Distance to 0–100 28,343,050 837 0.474 0.225 faults (m) 100–200 25,966,100 1292 0.900 0.379 200–300 22,463,775 402 0.229 0.136 300–400 17,874,600 399 0.323 0.170 > 400 73,481,250 863 0.100 0.089 250 D. Tien Bui et al. Figure 3. Landslide conditioning factors: (a) Slope angle; (b) slope aspect; (c) lithology; (d) distance to faults; (e) land use (ACL: Annual Crop Land; BL: Barren Land; GL: Grass Land; Pl: Paddy Land; PCL: Perennial Crop Land; PA: Populated Area; PDL: Productive Forest Land; PTL: Protective Forest Land; WSL: Water Surface Land); (f) soil type (DF: Dystric Fluvisols; DG: Dystric Gleysols; EF: Eutric Fluvisols; FA: Ferralic Acrisols; PA: Plinthic Acrisols; RF: Rhodic Ferralsols; RM: Rocky Mountain; WA: Water area). constructed: conglomerate, basalt, quaternary, siltstone, limestone, sandstone, and tuff. The distance-to-faults map (figure 3(d)) was compiled by buffering the fault lines. Five fault buffer categories were constructed: 0–100, 100–200, 200–300, 300– 400, and >400 m. A novel hybrid evidential belief function-based fuzzy logic model 251 Figure 3. (Continued). The soil type map for the study area was extracted from the National Pedology Maps at scale of 1:100,000. A total of eight layers were constructed (figure 3(e)). The land use data for the study area was extracted from the Land Use Status Map of the Lang Son province at a scale of 1:50,000. This land use status map is a result of the Status Land Use Project of the National Land Use Survey in Vietnam in 2010. For analysis, the land use map was constructed with nine classes (figure 3(f)). These classes were generalized the 21 original types in the land use status map. 252 D. Tien Bui et al. Figure 3. (Continued). 3. Landslide susceptibility mapping using a hybrid evidential belief function (EBF)- based fuzzy logic 3.1. Overview of the methodology The overall methodology flow chart of this study is shown in figure 4. Fuzzy logic has a well-known theory to deal with uncertainty in the field of geosciences where spatial A novel hybrid evidential belief function-based fuzzy logic model 253 Figure 3. (Continued). data are often lacking (Bonham-Carter 1994). A fuzzy set can be expressed as a set of elements in which their boundaries are ambiguous or vague, and an element can be participated in several fuzzy sets with different membership values (Ross 2010). In classical set theory, the membership of a set is defined as only a value of 0 and 1. In fuzzy set theory, the membership of a set can take any value in the range from 0 to 1 using a membership function and is called as degree of membership. The element with value of 1 indicates that it has a full membership, whereas value is 0 the element 254 D. Tien Bui et al. Figure 3. (Continued). does not belong to the set. Values in the range of 0–1 reflect the degree of closeness that a spatial object to the defined class. For landslides, if the fuzzy membership value is close to 1, it is more likely to be the landslides class of the set. Many different procedures have been proposed to implement the fuzzy principles. In landslide study, three main steps can be used to implement a fuzzy model as: (1) identification of landslide conditioning factors and their layer classes; (2) determina- tion of fuzzy membership function values for these classes; (3) integration of the layer A novel hybrid evidential belief function-based fuzzy logic model 255 Figure 3. (Continued). classes. Once the landslide conditioning factors and their classes have been identified, the fuzzification process will be carried out to assign fuzzy membership values to these layer classes. The fuzzy membership values must reflect the relative importance of each layer class of a single conditioning map (Bonham-Carter 1994). Finally, the defuzzification process will be carried out to integrate of the layer classes to produce landslide susceptibility maps using the fuzzy operators. 256 D. Tien Bui et al. Figure 4. The overall methodology flow chart. Assume that F is a parameter class jth of landslide conditioning factors ij F ði ¼ 1; ... ; nÞ. The parameter class jth in a fuzzy set is formed of ordered pairs ðF ;mðF ÞÞ. With mðF Þ is called the fuzzy membership function that expresses a ij ij ij degree of “compatibility” of F in F . Based on correlation of landslide occurrences ij i and conditioning factors, fuzzy membership values will be determined for parameter classes. To calculate landslide susceptibility index, a variety of operators such as fuzzy AND, fuzzy OR, fuzzy SUM, fuzzy PRODUCT, and fuzzy GAMMA can be used to combine the membership values (Zimmermann 1991; Bonham-Carter 1994; Lee 2007; Pradhan 2011a). According to Bonham-Carter (Bonham-Carter 1994), fuzzy AND is a logical intersection that combines fuzzy membership values of landslide conditioning factors using the fuzzy minimum operator as the following equation: m ¼ MIN½mðF Þ: ð1Þ ij AND Fuzzy OR will combine fuzzy membership values of landslide conditioning factors by using the fuzzy maximum operator, and is defined as: m ¼ MAX½mðF Þ: ð2Þ OR ij Fuzzy PRODUCT is a modified intersection that combines landslide conditioning factors by multiplying their membership function values, the formula is defined as: m ¼ mðF Þ: ð3Þ ij PRODUCT i¼1 A novel hybrid evidential belief function-based fuzzy logic model 257 Fuzzy SUM is a modified of fuzzy union and is defined as: m ¼ 1 ½1 mðF Þ: ð4Þ ij SUM i¼1 Fuzzy GAMMA is defined as: λ 1λ m ¼ðFuzzySUMÞ :ðFuzzyPRODUCTÞ : ð5Þ GAMMA In the fuzzy GAMMA operation, values of lambda (λ) can be selected in the range of [0, 1]. The choice of lambda for the fuzzy GAMMA ensures a compromise between the increasing tendencies of fuzzy SUM and the decreasing effect of the fuzzy PRODUCT. 3.2. Preparation of training and validation landslide data The selection of an appropriate mapping unit is considered as an important task in landslide susceptibility assessment. Selection of a mapping unit for the analysis will affect the uncertainties in the input data and the degree of fit of the model to the input data (Guzzetti et al. 1999). Although several mapping units have been pro- posed such as (i) slope units, (ii) terrain units, (iii) topographic units, (vi) unique con- dition units, (v) administrative units, and (vi) geo-hydrological units (Van Den Eeckhaut et al. 2009), however the mapping unit of grid cells may be the most widely used phenomena in landslide studies. In this study, the landslide inventory and six conditioning factor maps were con- verted to a grid cell format with spatial resolution of 5 m. In the landslide inventory map, landslide pixels were assigned to a value of “1”, whereas a “0” was assigned for grid cells outside a landslide i.e. non-landslide pixels. In order to assess the prediction capability of a landslide susceptibility model, a landslide inventory should be partitioned into two subsets; one is used for calibrating the landslide models and the other is used for model validation (Chung & Fabbri 2003). The partition of landslide inventories by temporal distribution is considered to be the best method (Chung & Fabbri 2008). However, such kind of temporal land- slide inventory map is not available for the study area since the dates for the past landslide are unknown. Therefore, the landslide inventory map was randomly split in a 70/30 ratio for building and validation of the model, respectively. The training dataset contains 117 landslide locations (3793 landslide grid cells) were used for building models, where the validation dataset has 55 landslide locations (1664 land- slide grid cells). 3.3. EBF-based fuzzy membership function In this study, the evidential belief functions (EBF) (Carranza et al. 2005) was used to calculate fuzzy membership values for each layer class of the six landslide condition- ing factors using the landslide grid cells in the training dataset. The Bel function is one of four basic functions of evidential belief functions (EBF). Four basic functions of EBF (Carranza et al. 2008) are Bel (degree of belief), Dis (degree of disbelief), 258 D. Tien Bui et al. Unc (degree of uncertainty), and Pls (degree of plausibility); however, only the Bel function was considered to use for calculating the fuzzy membership values. Suppose that the study area LS consists of N(LS) total number of grid cells and the training dataset T has N(T) total number of landslide grid cells. F is called the jth ij layer class of the landslide conditioning factors F and NðF Þ is the total number of i ij grid cells in the class F . By overlaying the landslide grid cells in the training dataset ij on each of the six landslide conditioning maps, the number of grid cells in F overlap- ij ping with the landslide grid cells NðT \ F Þ was determined. And fuzzy membership ij values were calculated using the following equation: ij mðF Þ¼ ; ð6Þ ij ij j¼1 where NðT \ F Þ=NðTÞ ij W ¼ : ð7Þ ij ½NðF Þ NðT \ F Þ=½NðLSÞ NðTÞ ij ij In equation (7), the numerator is the proportion of landslide pixels that occur in fac- tor class, whereas the denominator is the proportion of non-landslide pixels in factor class. For the purpose of comparison, fuzzy membership values using frequency ratio were also included. The following equation was used to obtain these values: NðT \ F Þ=NðTÞ ij FR ¼ : ð8Þ ij NðF Þ=NðLSÞ ij Frequency ratio was then normalized into the range [0,1] to derive fuzzy membership values using the Max–Min normalization procedure (Tien Bui et al. 2012e). Table 2 shows the fuzzy membership values for the six landslide conditioning fac- tors in this study. It can be seen that the fuzzy membership values reflect the relative importance of each layer class in a single conditioning factor to landslides. In the slope map, slope angles > 45 have the highest Bel value indicating the highest prob- 0 0 0 0 ability of landslides. It is followed by slope ranges of 35 45 and then 25 35 and 0 0 15 25 : In the remaining slope ranges, Bel values are low, indicating low probabil- ity of landslide occurrence. For aspect map, the south, southeast, and southwest fac- ing slopes have high Bel values, indicating high probability of landslide occurrence. They are followed by the East, West, and Northeast categories. The remaining aspect categories have low Bel values, indicating low probability of landslides. In the lithol- ogy map, high Bel values are seen for the conglomerate, sandstone, siltstone, and tuff groups indicating a high probability of landslide occurrence. The remaining groups have low Bel values. For the land use factor, the barren land has the highest Bel value indicating the highest probability of landslides. It is followed by protective forest land, productive forest land, paddy land, populated area, and annual crop land. In the soil type factor, the highest Bel value is for the ferralic acrisols, eutric fluvisols, and rhodic ferralsols, indicating high probability of landslide. The low Bel values are observed for the A novel hybrid evidential belief function-based fuzzy logic model 259 remaining soil type groups. For distance to faults factor, high Bel values are for dis- tance to faults less than 200 m, indicating a high probability of landslides. 3.4. Data integration into the landslide susceptibility maps In order to generate the final susceptibility maps, six landslide conditioning factors were integrated using the fuzzy-logic overlay methods. This is called the defuzzifica- tion process that maps fuzzy sets into a landslide susceptibility index (LSI) values. In this study, three fuzzy operators were used: fuzzy PRODUCT, fuzzy SUM, and fuzzy GAMMA. The fuzzy PRODUCT operator multiples fuzzy membership values of the landslide conditioning maps to produce the LSI values. The fuzzy SUM opera- tor is the complementary to the fuzzy PRODUCT, whereas the fuzzy GAMMA operator is a combination of the fuzzy PRODUCT and the fuzzy SUM. Six lambda values (0.1, 0.3, 0.5, 0.7, 0.9, and 0.95) were used for the fuzzy GAMMA operator to generate the LSI. Using the fuzzy membership values and the three fuzzy operators, the LSI values were calculated to produce the landslide susceptibility maps. The statistics of the LSI values for the susceptibility models are shown in table 3. It could be observed that the LSI values were in the ranges of [0, 0.978] and [0, 0.919] the fuzzy logic models using the frequency ratio and the Bel function, respectively. The obtained LSI values were then reclassified into five landslide susceptible clas- ses ranging from very low to very high. Many methods have been proposed for the reclassification of landslide susceptibility index values such as the quantiles, natural breaks, equal intervals, and standard deviations methods (Ayalew & Yamagishi 2005). In this study, the equal-area classification method proposed by Pradhan and Lee (2010) and Pradhan (2011b) was used. The final susceptibility maps were classi- fied into five classes such as: high (5%), moderate (15%), low (20%), very low (20%), and no landslide susceptibility areas (40%). A total of 16 landslide susceptibility maps were produced using five fuzzy operators, eight maps for each case of using the Bel function and the frequency-ratio values. For the purpose of visualization, only three landslide susceptibility maps that derived from the fuzzy SUM, the fuzzy PRODUCT, and fuzzy GAMMA (λ ¼ 0:5) using the Bel function are shown (figure 5). 4. Validation and comparison of landslide susceptibility models 4.1. Validation and comparison Validation is considered to be the most important step in landslide susceptibility modelling and without validation, the landslide models will have no scientific signifi- cance (Chung & Fabbri 2003). In this study, goodness-of-fit and the prediction skill of the susceptibility models were evaluated using success-rate and prediction-rate methods (Chung & Fabbri 2003; Van Westen et al. 2003). By overlaying the landslide susceptibility maps with the landslide locations in the training datasets, cumulative percentages of the landslide pixels corresponding to landslide susceptibility area (starting from the highest to the lowest of LSI values) were calculated. The success-rate curves were then obtained by plotting on the x-axis (cumulative percentage of susceptibility map) and on the y-axis (the cumulative per- centage of landslide pixels) (figures 6 and 7). In general, the closer the curve is to the 260 D. Tien Bui et al. Table 3. Statistics of the LSI values. LSI (used the frequency-ratio LSI (used the EBF-based Landslide based fuzzy logic) fuzzy logic) susceptibility No. Min Max StD Min Max StD model 1 Fuzzy AND 0.100 0.817 0.208 0.000 0.276 0.086 2 Fuzzy OR 0.229 0.900 0.193 0.089 0.446 0.094 3 Fuzzy SUM 0.508 0.978 0.038 0.139 0.919 0.115 4 Fuzzy PRODUCT 0.000 0.482 0.023 0.000 0.001 0.000 5 Fuzzy GAMMA (λ ¼ 0.1) 0.000 0.519 0.028 0.000 0.003 0.000 6 Fuzzy GAMMA (λ ¼ 0.3) 0.000 0.600 0.043 0.000 0.010 0.001 7 Fuzzy GAMMA (λ ¼ 0.5) 0.001 0.695 0.068 0.000 0.036 0.004 8 Fuzzy GAMMA (λ ¼ 0.7) 0.014 0.804 0.103 0.000 0.131 0.018 9 Fuzzy GAMMA (λ ¼ 0.9) 0.160 0.930 0.107 0.000 0.480 0.072 10 Fuzzy GAMMA (λ ¼ 0.95) 0.160 0.930 0.107 0.000 0.664 0.091 upper-left corner, the better in term of goodness-of-fit is the model. For quantitative comparison, the areas under the prediction-rate curves (AUC) were calculated. The AUC value ranges from 0.5 to 1.0. If the AUC equal to 0.5 the goodness-of-fit of the landslide model to the training data is considered to be the chance, whereas the AUC equal to 0.5 indicating the perfect in degree of fit of the landslide model to the train- ing data. The result (figures 6 and 7) shows that the goodness-of-fit are satisfied for all the models. Using the Bel membership function, the fuzzy SUM has the lowest degree of fit (AUC ¼ 0.829), the goodness-of-fits are almost equal for the remaining fuzzy logic models (AUC ¼ 0.869). For the case of the fuzzy logic models using the frequency-ratio membership function, the fuzzy SUM has the lowest degree of fit (AUC ¼ 0.786). The remaining models have almost the same degree of fit value (AUC ¼ 0.846). The prediction-rate method was used to assess the predictive capability of each model. The prediction-rate curves and area under the prediction-rate curves (AUC) were plotted and calculated in the same way as the case of the success-rate method. By overlaying each of all the landslide susceptibility maps on the landslide locations of validation dataset (landslides have not used in the process of model building), the prediction-rate curves and their AUC were calculated. The result is shown in table 4. The result shows that the prediction capability of all the fuzzy logic models used the Bel membership function is higher than those obtained from the fuzzy logic mod- els used the frequency-ratio membership function. Fuzzy SUM has the lowest predic- tion capability whereas the prediction capability is almost the same for fuzzy PRODUCT and fuzzy GAMMA. For the case of fuzzy GAMMA, the selection of different lambda values does not affect significantly the prediction capability of the final landslide models. 4.2. Relative contribution of conditioning factors The determination of the relative contribution of different conditioning factors for landslide occurrence is considered as a main task in landslide susceptibility model- ling. The relative contribution of each conditioning factor to the susceptibility A novel hybrid evidential belief function-based fuzzy logic model 261 Figure 5. Landslide susceptibility maps of the Lang Son city area using the fuzzy logic model with the Bel membership function: (a) Fuzzy SUM; (b) fuzzy PRODUCT; (c) fuzzy GAMMA (0.50). models can be estimated by excluding the factor out of the models and subsequently success-rate curves and area under the curves (AUC) were plotted and estimated (Kawabata & Bandibas 2009; Tien Bui et al. 2012b). In this study, the relative contributions of the six conditioning factors for the fuzzy logic models (the fuzzy SUM, fuzzy PRODUCT, the fuzzy GAMMA (λ ¼ 0:5)) using the Bel and the frequency-ratio membership functions were calculated. The 262 D. Tien Bui et al. Figure 5. (Continued). result is shown in table 5 and 6. It can be seen that the highest success-rate value was obtained for a case of using all of the six landslide conditioning factors. The aspect factor has the highest contribution to the susceptibility model and the lithology and land use factors have equal contribution for all of three cases. There is no difference in the order of contribution of the six conditioning factors for the cases of the fuzzy PRODUCT and the fuzzy GAMMA (λ ¼ 0:5). On the contrary, the highest differ- ence in relative contribution of a conditioning factor between the three models is the A novel hybrid evidential belief function-based fuzzy logic model 263 Figure 5. (Continued). slope. The slope factor has the second importance in the fuzzy SUM but it has the lowest contribution for the fuzzy PRODUCT and fuzzy GAMMA (λ ¼ 0:5). 5. Discussions and conclusion This study represents the result of application of the evidential belief function-based fuzzy logic method for spatial prediction of rainfall-induced shallow landslides in the 264 D. Tien Bui et al. Figure 6. Success-rate curves and area under the curves (AUC) for the fuzzy logic models using the Bel membership function. Figure 7. Success-rate curves and area under the curves (AUC) for the fuzzy logic models using the frequency-ratio membership function. A novel hybrid evidential belief function-based fuzzy logic model 265 Table 4. Prediction capability of the fuzzy logic models. Prediction capability (%) Fuzzy membership values Fuzzy membership values obtained from the obtained from the No. Fuzzy models Bel function frequency ratio 1 Fuzzy SUM 76.60 73.07 2 Fuzzy PRODUCT 79.68 76.84 3 Fuzzy GAMMA (0.10) 79.67 76.84 4 Fuzzy GAMMA (0.30) 79.67 76.84 5 Fuzzy GAMMA (0.50) 79.67 76.84 6 Fuzzy GAMMA (0.70) 79.67 76.84 7 Fuzzy GAMMA (0.90) 79.53 76.84 8 Fuzzy GAMMA (0.95) 79.22 76.84 Table 5. Success rate for the fuzzy logic models using the Bel membership function. Success rate (%) No. Conditioning factors Fuzzy SUM Fuzzy PRODUCT Fuzzy GAMMA (0.50) 1 Minus slope 80.02 75.47 75.41 2 Minus aspect 76.31 54.13 54.11 3 Minus lithology 83.01 62.36 62.29 4 Minus distance to faults 82.29 60.38 60.33 5 Minus soil type 82.71 62.45 62.38 6 Minus land use 83.01 62.36 62.29 7 All 82.90 87.00 86.90 Lang Son city area of Vietnam. The resultant maps only represent spatial location of the landslides that might occur in the future. In this area, landslides are considered to be a major natural hazard in the mountainous regions and often occur during heavy rainfall, and especially in the tropical rainstorm. The landslide inventory was compiled mainly from the two projects, the interpretation of aerial photographs, and multiple field surveys. Since dates of landslide occurrence are unknown, the temporal Table 6. Success rate for the fuzzy logic models using the frequency-ratio membership function. Success rate (%) No. Conditioning factors Fuzzy SUM Fuzzy PRODUCT Fuzzy GAMMA (0.50) 1 Minus slope 76.86 81.01 81.00 2 Minus aspect 72.79 77.74 77.69 3 Minus lithology 78.85 84.43 84.39 4 Minus distance to faults 77.98 84.55 84.52 5 Minus soil type 78.40 84.30 84.24 6 Minus land use 78.85 84.43 84.39 7 All 78.60 84.57 84.55 266 D. Tien Bui et al. distribution of landslide was impossible, therefore the data were randomly parti- tioned for model building and validation process. The randomly partitioned method may cause an overestimated of estimated prediction power of future landslides (Chung & Fabbri 2008) if spatial separation between training and validation land- slide is small (Brenning 2005; Tien Bui et al. 2012c). This distribution of training and validation dataset remains as a future research question. The selection of landslide conditioning factors for landslide susceptibility model- ling is an important task and it will affect the quality of the resulting models. In this case, four criteria were used to select conditioning factors: (i) the map scale of analy- sis, (ii) the landslide type, (iii) the failure mechanisms, and (iv) the characteristics of the study area (Glade & Crozier 2005). Although no agreement on the universal guideline has been reached for the selection of conditioning factors (Tien Bui et al. 2012c), however, conditioning factors that relate to topography, geology, soil types, hydrology, geomorphology, and land use are most commonly used (Van Westen et al. 2008). Therefore, six landslide conditioning factors (slope, aspect, lithology, distance to faults, land use, and soil type) were selected in this study. Various methods and techniques for the landslide study have been proposed; how- ever, fuzzy logic, together with multiple regression analysis, and artificial intelligence are considered as the most popular used methods during the last 10 years (Akgun 2012). It is important to note that if the procedures are simple with high accuracy, the better the landslide models. Therefore, fuzzy logic method is a good choice due to its simple, cost-effective, and easy to apply with high prediction capability (Tien Bui et al. 2012e). Furthermore, fuzzy logic has been successfully used in landslide modelling in the literature (Ercanoglu & Gokceoglu 2004; Biswajeet & Saied 2010; Pradhan 2011b; Pourghasemi et al. 2012a). The application of fuzzy logic in landslide studies is critical due to the determina- tion of fuzzy membership values. When comparing results from this study with the other fuzzy logic approaches from literature showed that knowledge-based approaches (Champati ray et al. 2007; Blais-Stevens et al. 2012) determined fuzzy membership values simply based on subjective judgement (Bonham-Carter 1994), and therefore the quality of the landslide models is strongly dependent on those experts and is very subjective. In the case of data-driven approaches, fuzzy member- ship values were obtained by normalizing the frequency-ratio values for each condi- tioning factor (Lee 2007; Pradhan 2010; Pradhan 2011b). There is no doubt that the relative importance between the conditioning factors is lost. In other case of data- driven approaches where fuzzy membership values were obtained using Cosine amplitude (Ercanoglu & Gokceoglu 2004; Shujun et al. 2006; Kanungo et al. 2008; Kanungo et al. 2009), the application is not suitable for areas if the ratio of the num- ber of landslide pixels to the number of pixels in the factor class is too small (Tien Bui et al. 2012e). In this study, a new method for the determination of fuzzy member- ship values is introduced and successfully implemented. This method used the Bel membership function (Carranza & Hale 2002) that has been rarely used in fuzzy logic. The results in this study show that the fuzzy logic models using the Bel member- ship function performed better than the fuzzy logic models that used the frequency ratio in terms of both success and prediction rates. In the case of the success rate, the smallest difference (2.4%) is seen for the fuzzy SUM whereas the largest difference (4.3%) is for the fuzzy PRODUCT and fuzzy GAMMA. In the case of the prediction rate, the fuzzy GAMMA (λ ¼ 0.95) has the smallest difference (2.38%) and the fuzzy A novel hybrid evidential belief function-based fuzzy logic model 267 SUM has the highest difference (3.53%). The result of this study shows that the EBF can be used for the determination of fuzzy logic membership values. Using the EBF, the normalization process for each conditioning factor is not needed compared to the frequency-ratio method. Therefore, the relative importance between the condi- tioning factors is remained. However, using the EBF, in the class where landslides were not occurred, the Bel value is set to zero (no belief), but this case sometime is considered only uncertainty (the exceptional case is zero values for slope classes). To address this issue, more case studies should be conducted. The results from this study may be useful for local planner in areas prone to landslides. Acknowledgements The authors gratefully acknowledge Mr Vu Manh Hao (the Centre for Geological Appraisal and Technology, Ministry of Natural Resources and Environment of Vietnam) for providing the geological data. The authors would like to thank Mr Ho Tien Chung (Vietnam Institute of Geosciences and Mineral Resources) for valuable comments on the lithologic classification. This research was supported by the Geomatics Section, Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Norway. References Akgun A. 2012. 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"Geomatics, Natural Hazards and Risk" – Taylor & Francis
Published: Apr 3, 2015