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Mamdani fuzzy inference systems and artificial neural networks for landslide susceptibility mapping

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Two Artificial Intelligence (AI) methods, Fuzzy Inference System (FIS) and Artificial Neural Network (ANN), are applied to Landslide Susceptibility Mapping (LSM), to compare complementary aspects of the potentials of the two methods and to extract physical relationships from data. An index is proposed in order to rank and filter the FIS rules, selecting a certain number of readable rules for further interpretation of the physical relationships among variables. The area of study is Rolante river basin, southern Brazil. Eleven attributes are generated from a Digital Elevation Model (DEM), and landslide scars from an extreme rainfall event are used. Average accuracy and area under Receiver Operating Characteristic curve (AUC) resulted, respectively, in 81.27% and 0.8886 for FIS, and 89.45% and 0.9409 for ANN. ANN provides a map with more amplitude of outputs and less area classified as high susceptibility. Among the 40 (10%) best-ranked FIS rules, 13 have high susceptibility output, while 27 have low; a cause is that low susceptibility areas are larger on the map. Slope is highly connected to susceptibility. Elevation, when high (plateau) or low (floodplain), inhibits high susceptibility. Six attributes show the same fuzzy set for the 18 best-ranked rules, meaning this fuzzy set is common on the map. Overall findings point out that ANN is best suited for LSM map generation, but, based on them, using FIS is important to help researchers understand more about AI models for LSM and about landslide phenomenon.
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Natural Hazards (2021) 106:2381–2405
1 3
Mamdani fuzzy inference systems andartificial neural
networks forlandslide susceptibility mapping
LuísaVieiraLucchese1 · GuilhermeGarciadeOliveira2 · OlavoCorreaPedrollo1
Received: 25 June 2020 / Accepted: 19 January 2021 / Published online: 8 February 2021
© The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature 2021
Two Artificial Intelligence (AI) methods, Fuzzy Inference System (FIS) and Artificial Neu-
ral Network (ANN), are applied to Landslide Susceptibility Mapping (LSM), to compare
complementary aspects of the potentials of the two methods and to extract physical rela-
tionships from data. An index is proposed in order to rank and filter the FIS rules, selecting
a certain number of readable rules for further interpretation of the physical relationships
among variables. The area of study is Rolante river basin, southern Brazil. Eleven attrib-
utes are generated from a Digital Elevation Model (DEM), and landslide scars from an
extreme rainfall event are used. Average accuracy and area under Receiver Operating Char-
acteristic curve (AUC) resulted, respectively, in 81.27% and 0.8886 for FIS, and 89.45%
and 0.9409 for ANN. ANN provides a map with more amplitude of outputs and less area
classified as high susceptibility. Among the 40 (10%) best-ranked FIS rules, 13 have high
susceptibility output, while 27 have low; a cause is that low susceptibility areas are larger
on the map. Slope is highly connected to susceptibility. Elevation, when high (plateau) or
low (floodplain), inhibits high susceptibility. Six attributes show the same fuzzy set for the
18 best-ranked rules, meaning this fuzzy set is common on the map. Overall findings point
out that ANN is best suited for LSM map generation, but, based on them, using FIS is
important to help researchers understand more about AI models for LSM and about land-
slide phenomenon.
Keywords Rule set· Mass movement· Natural disasters· Map analysis· Map validation·
Fuzzy rule interpretation
* Luísa Vieira Lucchese
1 Instituto de Pesquisas Hidráulicas, Universidade Federal doRio Grande doSul, Av. Bento
Gonçalves, 9500, PortoAlegre, RS91501-970, Brazil
2 Departamento Interdisciplinar, Universidade Federal doRio Grande doSul, Rodovia RS 030,
11700, km 92. Emboaba, Tramandaí, RS95590-000, Brazil
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... Out of the 33 studies analyzed, 19 of them were in the southeast region, in the states of São Paulo (10) [15,[25][26][27][28][29][30][31][32][33], Rio de Janeiro (7) [12,[34][35][36][37][38][39], Minas Gerais (2) [16,40], and Espírito Santo (1) [41]. The remaining 14 were in the south region, in Rio Grande do Sul (8) [14,35,[42][43][44][45][46][47], Santa Catarina (4) [13,[48][49][50], and Paraná (2) [51,52] (Figure 3). Only the article by Bragagnolo et al. [35] had two study areas, one located in Rio Grande do Sul and the other in Rio de Janeiro state. ...
... The first paper that applied statistical validation methods was published in 2015 [52]. Between 2015 and 2021, 27 articles were published and 15 out of them applied cross tabulation [36,52], success curve [26], AUC [14,16,25,35,40,42], ROC [43,46], or AUC/ROC [15,34,44,45] to validate the susceptibility maps. Two publications mentioned validation curves, but did not provide details about them [13,50]. ...
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Landslide susceptibility studies are a common type of landslide assessment. Landslides are one of the most frequent hazards in Brazil, resulting in significant economic and social losses (e.g., deaths, injuries, and property destruction). This paper presents a literature review of susceptibility mapping studies in Brazil and analyzes the methods and input data commonly used. The publications used in this analysis were extracted from the Web of Science platform. We considered the following aspects: location of study areas, year and where the study was published, methods, thematic variables, source of the landslide inventory, and validation methods. The susceptibility studies are concentrated in Brazil’s south and southeast region, with the number of publications increasing since 2015. The methods commonly used are slope stability and statistical models. Validation was performed based on receiver operating characteristic (ROC) curves and area under the curve (AUC). Even though landslide inventories constitute the most critical input data for susceptibility mapping, the criteria used for the creation of landslide inventories are not evident in most cases. The included studies apply various validation techniques, but evaluations with potential users and information on the practical applicability of the results are largely missing.
... These findings are consistent with the findings of a previous study [105], which discovered that the ANN model produced more accurate and reliable results in the development of the landslide susceptibility model compare with others. Furthermore, the study by [111] found that landslide susceptibility derived by ANN has better accuracy in a study conducted in Rolante River Basin, Southern Brazil. ...
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Landslides are a natural hazard that can endanger human life and cause severe environmental damage. A landslide susceptibility map is essential for planning, managing, and preventing landslides occurrences to minimize losses. A variety of techniques are employed to map landslide susceptibility; however, their capability differs depending on the studies. The aim of the research is to produce a landslide susceptibility map for the Langat River Basin in Selangor, Malaysia, using an Artificial Neural Network (ANN). A landslide inventory map contained a total of 140 landslide locations which were randomly separated into training and testing with ratio 70:30. Nine landslide conditioning factors were selected as model input, including: elevation, slope, aspect, curvature, Topographic Wetness Index (TWI), distance to road, distance to river, lithology, and rainfall. The area under the curve (AUC) and several statistical measures of analyses (sensitivity, specificity, accuracy, positive predictive value, and negative predictive value) were used to validate the landslide predictive model. The ANN predictive model was considered and achieved very good results on validation assessment, with an AUC value of 0.940 for both training and testing datasets. This study found rainfall to be the most crucial factor affecting landslide occurrence in the Langat River Basin, with a 0.248 weight index, followed by distance to road (0.200) and elevation (0.136). The results showed that the most susceptible area is located in the north-east of the Langat River Basin. This map might be useful for development planning and management to prevent landslide occurrences in Langat River Basin.
... Researchers have used quantitative approaches in contemporary periods, viz. artificial neural networks (Lucchese et al. 2021;Jacinth Jennifer and Saravanan 2021), logistic regression analysis (Gu et al. 2021;Crawford et al. 2021;Sujatha and Sridhar 2021), fuzzy logic (Bahrami et al. 2021;Manaouch et al. 2021;Nanehkaran et al. 2021), multivariate regression analysis (Arabameri et al. 2019;Chu et al. 2019;Pham et al. 2021), bivariate regression analysis (Zhou et al. 2021) to delineate LSZ. Machine learning approaches are now widely used to predict natural disasters such as floods, wildfires, earthquakes, and doughtiness, among others (Hong et al. 2018;Ahmadlou et al. 2019). ...
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Several natural disasters are taking place on the earth, and landslide is one of them. Darjeeling Himalaya is one of the world's young fold mountainous area, often suffering from landslide hazards. Hence, the study identifies the landslide susceptibility zone in the Ragnu Khola river basin of the Darjeeling Himalayan region by applying the geospatial-based MCDM technique. This research's major goal is to identify whether this GIS-based multi-criteria decision-making (MCDM) technique is validated or not for landslide susceptibility zones (LSZ); if validated, then how much manifest for describing the LSZ in the study area. MCDM evaluation applies to determining weight value to integrate different thematic layers of river morphometry like Drainage Diversity (DD) parameters and Relief Diversity (RD) parameters. Both DD and RD have significant impacts on landslide intensity. Hence, both layers are combined using the analytical hierarchy process (AHP) of the MCDM technique for the final LSZ. The final result has been validated by ROC analysis using landslide occurring point data obtained from the Geological Survey of India (GSI). The outcome of the study shows that1.45% and 17.83% areas of the region fall in 'very high' and ‘high' LSZ, which belongs to near Mull Gaon, Sanchal forest, and Alubri basty. Most of the area (47.70%) is observed in 'moderate' LSZ. Only 1.32% and 31.7% are kept in ‘very low’ and ‘low’ LSZ, respectively, through the study area. The description capability of the technique for LSZ is significant as the area under the curve (AUC) is 72.10%. The validation of the study using the frequency density of the landslides (FDL) also indicates the 'very high' LSZ is associated with the maximum (2.19/km ² ) FDL. The work will be needful to develop the overall socio-economic condition of such kind of tectonically sensitive region by proper effective planning.
... However, a hybrid ANFIS (coupled with imperialist competitive algorithm) with an AUC equal to 0.966 was found to be superior over both regular ANFIS and ANN. Lucchese et al. (2021) employed and compared the ANN with ANFIS for the same purpose in Rolante River Basin, Brazil. Based on the calculated AUCs, 0.8886 for ANFIS and 0.9409 for ANN, the later model could achieve a considerably larger accuracy. ...
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This study deals with landslide susceptibility mapping in the northern part of Lecco Province, Lombardy Region, Italy. In so doing, a valid landslide inventory map and thirteen predisposing factors (including elevation, slope aspect, slope degree, plan curvature, profile curvature, distance to waterway, distance to road, distance to fault, soil type, land use, lithology, stream power index, and topographic wetness index) form the spatial database within geographic information system. The used predictive models comprise a bivariate statistical approach called frequency ratio (FR) and two machine learning tools, namely multilayer perceptron neural network (MLPNN) and adaptive neuro-fuzzy inference system (ANFIS). These models first use landslide and non-landslide records for comprehending the relationship between the landslide occurrence and predisposing factors. Then, landslide susceptibility values are predicted for the whole area. The accuracy of the produced susceptibility maps is measured using area under the curve (AUC) index, according to which, the MLPNN (AUC = 0.916) presented the most accurate map, followed by the ANFIS (AUC = 0.889) and FR (AUC = 0.888). Visual interpretation of the susceptibility maps, FR-based correlation analysis, as well as the importance assessment of predisposing factors, all indicated the significant contribution of the road networks to the crucial susceptibility of landslide. Lastly, an explicit predictive formula is extracted from the implemented MLPNN model for a convenient approximation of landslide susceptibility value.
... To counteract this, a process of defuzzification is employed, which eliminates the fuzziness. Both the fuzzy inference steps that comprise the first two parts of the process are identical: Fuzzyizing the inputs, and then applying the fuzzy operator [31], and this part of the fuzzy is referred to the linguistic system [32], [33]. Mamdanittype has an exponential relationship between the number of rules and premise-part parameters. ...
The purpose of this paper using two algorithms for analyzing EEG signals for Motor Movement / Imagery of the BCI the placement 10-10 international system is used to recorded data which is related with both hand and feet and was adopted with imagination status, equally important and according to the electrical activity of the brain signals it consider as non-stationary, furthermore in this research I propose to use multiscale wavelet transform also I used four level from decomposition of the EEG signals analysis as well as the Debauches of the wavelet families was used another essential point the 2D-DWT method was applied in this study and besides was superior for a features extraction secondly the ANFIS was applied as classification algorithms to classify the input then training and testing however I used five membership with gaussian function with three input finally I conclude the accuracy of the training features was 100% while the performance was 100% for both testing and training.
Landslide is a devastating natural disaster, causing loss of life and property. It is likely to occur more frequently due to increasing urbanization, deforestation, and climate change. Landslide susceptibility mapping is vital to safeguard life and property. This article surveys machine learning (ML) models used for landslide susceptibility mapping to understand the current trend by analyzing published articles based on the ML models, landslide causative factors (LCFs), study location, datasets, evaluation methods, and model performance. Existing literature considered in this comprehensive survey is systematically selected using the ROSES protocol. The trend indicates a growing interest in the field. The choice of LCFs depends on data availability and case study location; China is the most studied location, and area under the receiver operating characteristic curve (AUC) is considered the best evaluation metric. Many ML models have achieved an AUC value > 0.90, indicating high reliability of the susceptibility map generated. This paper also discusses the recently developed hybrid, ensemble, and deep learning (DL) models in landslide susceptibility mapping. Generally, hybrid, ensemble, and DL models outperform conventional ML models. Based on the survey, a few recommendations and future works which may help the new researchers in the field are also presented.
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Landslides can be a major challenge in mountainous areas that are influenced by climate and landscape changes. In this study, we propose a hybrid machine learning model based on a rotation forest (RoF) meta classifier and a random forest (RF) decision tree classifier called RoFRF for landslide prediction in a mountainous area near Kamyaran city, Kurdistan Province, Iran. We used 118 landslide locations and 25 conditioning factors from which their predictive usefulness was measured using the chi-square technique in a 10-fold cross-validation analysis. We used the sensitivity, specificity, accuracy, F1-measure, Kappa, and area under the receiver operating characteristic curve (AUC) to validate the performance of the proposed model compared to the Artificial Neural Network (ANN), Logistic Model Tree (LMT), Best First Tree (BFT), and RF models. The validation results demonstrated that the landslide susceptibility map produced by the hybrid model had the highest goodness-of-fit (AUC = 0.953) and higher prediction accuracy (AUC = 0.919) compared to the benchmark models. The hybrid RoFRF model proposed in this study can be used as a robust predictive model for landslide susceptibility mapping in the mountainous regions around the world.
The traditional landslide risk research mostly focuses on the spatial distribution of landslide occurrence probability, but the research on the time distribution of landslide occurrence probability is not in-depth, and there is no effective professional management advice for specific risk areas, so it has great limitations. This paper takes the landslide-prone area along the Qingjiang River in Jianshi County, Hubei Province as the research area, takes the slope as the unit, and uses the information value method to complete the landslide geological disaster risk assessment in the study area. Through the characteristics of landslide risk in time and space, the dynamic management measures of landslide risk in different periods of the study area are formulated. The map of landslide prevention and control planning measures in different periods in the study area can be obtained, which provides a basis for realizing the balance between safety and economy of landslide prevention and control planning. This has obvious guiding significance for landslide prevention and control planning in other regions.
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The Three Gorges Reservoir region in China is the Yangtze River Economic Zone’s natural treasure trove. Its natural environment has an important role in development. The unique and fragile ecosystem in the Yangtze River’s Three Gorges Reservoir region is prone to natural disasters, including soil erosion, landslides, debris flows, landslides, and earthquakes. Therefore, to better alleviate these threats, an accurate and comprehensive assessment of the susceptibility of this area is required. In this study, based on the collection of relevant data and existing research results, we applied machine learning models, including logistic regression (LR), the random forest model (RF), and the support vector machine (SVM) model, to analyze landslide susceptibility in the Yangtze River’s Three Gorges Reservoir region to analyze landslide events in the whole study region. The models identified five categories (i.e., topographic, geological, ecological, meteorological, and human engineering activities), with nine independent variables, influencing landslide susceptibility. The accuracy of landslide susceptibility derived from different models and raster cells was then verified by the accuracy, recall, F1-score, ROC curve, and AUC of each model. The results illustrate that the accuracy of different machine learning algorithms is ranked as SVM > RF > LR. The LR model has the lowest generalization ability. The SVM model performs well in all regions of the study area, with an AUC value of 0.9708 for the entire Three Gorges Reservoir area, indicating that the SVM model possesses a strong spatial generalization ability as well as the highest robustness and can be adapted as a real-time model for assessing regional landslide susceptibility.
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One of the biggest risks that need to be considered before any construction operation such as road construction or construction is to determine the exact location of subsidence and predict the places with the potential to cause these complications.There are various methods for identifying and predicting the occurrence of these phenomena. In this article, hierarchical analysis methods (AHP and FAHP) and programming in MATLAB environment with the help of Evalfis function to study and map these hazards in the southwest of Iran has acted as a case study.Studies of lithological layers, slope, distance from fault and distance from waterway in both methods express very good and significant results in predicting this type of hazards.According to these results, the most hazards occur in places that have evaporitic lithology and have the shortest distance from waterways and faults with a slope between 20 to 70 degrees.The output of these studies is to provide a map of subsidence (sinkhole) hazards for the first time by integrating the stated methods with operational accuracy above 90% and introducing a very useful software in MATLAB program for experts.
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Landslide susceptibility maps can be developed with artificial neural networks (ANNs). In order to train our ANNs, a digital elevation model (DEM) and a scar map of one previous event were used. Eleven attributes are generated, possibly containing redundant information. Our base model is formed by, essentially, one input (the DEM), eleven attributes, 30 neurons, and one output (susceptibility). Principal components (PCs) group information in the first projected variables, the last ones can be expendable. In the present paper, four groups of models were trained: one with eleven attributes generated from the DEM; one with 8 out of 11 attributes, in which 3 were eliminated by their high correlation with others; other, with the data projected over its PCs; and another, using 8 out of 11 PCs. The used number of neurons in hidden layer is 30, calibrated based on a complexity analysis that is an in-house developed method. The ANN models trained with the original data generated better statistical results than their counterparts trained with the PC transformed input. Keeping the original 11 attributes calculated provided the best metrics among all models, showing that eliminating attributes also eliminates information used by the model. Using 11 PC transformed attributes hindered trained. However, for the model with eight PCs, training was much faster than its counterpart with little accuracy loss. The metrics and maps achieved were considered acceptable, conveying the power of our model based on ANNs, which uses essentially one input (the DEM) for mapping areas susceptible to mass movements.
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Landslide susceptibility mapping is vital for landslide risk management and urban planning. In this study, we used three statistical models [frequency ratio, certainty factor and index of entropy (IOE)] and a machine learning model [random forest (RF)] for landslide susceptibility mapping in Wanzhou County, China. First, a landslide inventory map was prepared using earlier geotechnical investigation reports, aerial images, and field surveys. Then, the redundant factors were excluded from the initial fourteen landslide causal factors via factor correlation analysis. To determine the most effective causal factors, landslide susceptibility evaluations were performed based on four cases with different combinations of factors (“cases”). In the analysis, 465 (70%) landslide locations were randomly selected for model training, and 200 (30%) landslide locations were selected for verification. The results showed that case 3 produced the best performance for the statistical models and that case 2 produced the best performance for the RF model. Finally, the receiver operating characteristic (ROC) curve was used to verify the accuracy of each model’s results for its respective optimal case. The ROC curve analysis showed that the machine learning model performed better than the other three models, and among the three statistical models, the IOE model with weight coefficients was superior.
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Landslides are typically triggered by earthquakes or rainfall occasionally a rainfall event followed by an earthquake or vice versa. Yet, most of the works presented in the past decade have been largely focused at the single event-susceptibility model. Such type of modeling is found insufficient in places where the triggering mechanism involves both factors such as one found in the Chuetsu region, Japan. Generally, a single event model provides only limited enlightenment of landslide spatial distribution and thus understate the potential combination-effect interrelation of earthquakes-and rainfall-triggered landslides. This study explores the both-effect of landslides triggered by Chuetsu-Niigata earthquake followed by a heavy rainfall event through examining multiple traditional statistical models and data mining for understanding the coupling effects. This paper aims to compare the abilities of the statistical probabilistic likelihood-frequency ratio (PLFR) model, information value (InV) method, certainty factors (CF), artificial neural network (ANN) and ensemble support vector machine (SVM) for the landslide susceptibility mapping (LSM) using high-resolution-light detection and ranging digital elevation model (LiDAR DEM). Firstly, the landslide inventory map including 8459 landslide polygons was compiled from multiple aerial photographs and satellite imageries. These datasets were then randomly split into two parts: 70% landslide polygons (5921) for training model and the remaining polygons for validation (2538). Next, seven causative factors were classified into three categories namely topographic factors, hydrological factors and geological factors. We then identified the associations between landslide occurrence and causative factors to produce LSM. Finally, the accuracies of five models were validated by the area under curves (AUC) method. The AUC values of five models vary from 0.77 to 0.87. Regarding the capability of performance, the proposed SVM is promising for constructing the regional landslide-Remote Sens. 2019, 11, 638 2 of 30 prone potential areas using both types of landslides. Additionally, the result of our LSM can be applied for similar areas which have been experiencing both rainfall-earthquake landslides.
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A landslide susceptibility map (LSM) is an imperative element in the planning of sustainable development practices and geo-environmental conservations in mountainous terrains. In recent times, approaches that couple soft computing techniques and Geographic Information System (GIS) has emerged as better-suited models that can diminish the flaws and limitations of heuristic, probabilistic and distribution approaches in landslide susceptibility mapping. This paper presents an improved fuzzy expert system (FES) model, a fusion of Mamdani fuzzy inference system (Mamdani-FIS) and frequency ratio method for GIS-based landslide susceptibility mapping. The improved FES model has been applied for mesoscale (1:15,000) landslide susceptibility mapping of Mussoorie Township, Uttarakhand, India, along with conventional fuzzy set procedure (FSP) and an existing FES model, MamLand. The LSMs generated through different procedures have been validated and compared by means of spatial distribution of susceptibility zones and statistical analysis with the help of landslide inventory. The validation and comparative analysis have indicated the significantly better performance of the improved FES model over FSP and MamLand.
Landslide susceptibility assessment using Artificial Neural Networks (ANNs) requires occurrence (landslide) and nonoccurrence (not prone to landslide) samples for ANN training. We present empirical evidence that a priori intervention on the nonoccurrence samples can produce models that are improper for generalization. Thirteen nonoccurrence cases based on GIS data from Rolante River basin (828.26 km²) in Brazil are studied, divided in three groups. The first group was based on six combinations of buffers with different minimum and maximum distances from the mapped scars (BO). The second group (RO) acquired nonoccurrence only from a rectangle in the lowlands, known for not being susceptible to landslides. For BR, six alternatives respectively to BO were presented, with the inclusion of nonoccurrence samples acquired from the same rectangle used for RO. Accuracy (acc) and the Area Under Receiving Operating Characteristic Curve (AUC) were calculated. RO resulted in perfect discrimination between susceptible and not susceptible to landslides (acc = 1 e AUC = 1). This occurred because the model simply provided susceptible classification to points in which attributes are different from those in the rectangle, harming the classification of nonoccurrence sampling points outside the rectangle. RO map shows large areas classified as susceptible which are known to be non-susceptible. In BR, sampling points from the rectangle, which are easy to classify, were added to the verification sample of BR. Average acc for BO 00 m (minimum buffer distance to scars of 0 m): 89.45%, average acc for BR 00 m: 92.33%, average AUC for BO 00 m: 0.9409, average AUC for BR 00 m: 0.9616. Maps of groups BO and BR were alike. This indicates that metrics can be artificially risen if biased samples are added, although the final map is not visibly affected. To avoid this effect, the employment of easily classifiable samples, generated based on expert knowledge, should be made carefully.
The hydrological sciences typically present grey or fuzzy information, making them quite messy and a choice challenge for fuzzy logic application. Providing readers with the first book to cover fuzzy logic modeling as it relates to water science, the author takes an approach that incorporates verbal expert views and other parameters that allow him to eschew the use of mathematics. The book's first seven chapters expose the fuzzy logic principles, processes and design for a fruitful inference system with many hydrological examples. The last two chapters present the use of those principles in larger scale hydrological scales within the hydrological cycle.
The aim of this study is to evaluate the susceptibility of landslides at Klang valley area, Malaysia, using a Geographic Information System (GIS) and remote sensing. Landslide locations were identified in the study area from interpretation of aerial photographs and from field surveys. Topographical and geological data and satellite images were collected, processed, and constructed into a spatial database using GIS and image processing. A data derived model (frequency ratio) and a knowledge-derived model (fuzzy operator) were combined for landslide susceptibility analysis. The nine factors that influence landslide occurrence were extracted from the database and the frequency ratio coefficient for each factor was computed. Using the factors and the identified landslide, the fuzzy membership values were calculated. Then fuzzy algebraic operators were applied to the fuzzy membership values for landslide susceptibility mapping. Finally, the produced map was verified by comparing with existing landslide locations for calculating prediction accuracy. Among the fuzzy operators, in the case in which the gamma operator (? = 0.8) showed the best accuracy (91%) while the case in which the fuzzy algebraic product was applied showed the worst accuracy (79%).