ArticlePublisher preview available

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

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract and Figures

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.
This content is subject to copyright. Terms and conditions apply.
Vol.:(0123456789)
Natural Hazards (2021) 106:2381–2405
https://doi.org/10.1007/s11069-021-04547-6
1 3
ORIGINAL PAPER
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
Abstract
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
luisa.lucchese@ufrgs.br
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.
... Fuzzy neural networks are essentially conventional neural networks that are given fuzzy input signals and fuzzy weights, and their learning algorithms are usually neural network learning algorithms or generalization algorithms. The inference rules of Mamdani-type fuzzy neural networks conform to the normal human thinking habits and, therefore, can represent human knowledge more accurately (Yucel et al., 2017;Zhang et al., 2018a;Lucchese et al., 2021;Mohammed and Hussain, 2021). However, their computations are generally complex and are not conducive to mathematical analysis. ...
Article
Full-text available
In order to break through the existing battery technology of electric vehicles, this paper proposes to use heat pump air conditioning instead of the original PTC heating system potential. First, the advantages and disadvantages of different heat pump models for new energy vehicles are analyzed and compared. Second, a fuzzy inference system is constructed based on the machine learning model to observe the temperature of the passenger compartment using the temperature sensor inside the tram and to determine the need for the air conditioning system to be turned on in the heating/cooling mode by comparing it with the set temperature. Finally, the results show that the machine learning algorithm is able to monitor and adaptively adjust the interior temperature to further enhance the adaptability of the system with low volatility and high accuracy. The proposed research study can lay the foundation for further optimizing the design of heat pump air conditioners for electric vehicles.
... At 25 m resolution, Ruijin City is divided into 8,633,837 rasters. The 370 landslides that have occurred are divided into 507,852 raster cells with 25m resolution (assigned 1), and the same number of non-landslide rasters as the landslide raster (assigned 0) are randomly selected as the model output variable [62]. In the landslide and non-landslide grids, the model training set and test set [63] are randomly divided by 7:3. ...
Article
Full-text available
Two significant uncertainties that are crucial for landslide susceptibility prediction modeling are attribute interval numbers (AIN) division of continuous landslide impact factors in frequency ratio analysis and various susceptibility prediction models. Five continuous landslide impact factor interval attribute classifications (4, 8, 12, 16, 20) and three data-driven models (deep belief networks (DBN), random forest (RF), and neural network (back propagation (BP)) were used for a total of fifteen different scenarios of landslide susceptibility prediction studies in order to investigate the effects of these two factors on modeling and perform a landslide susceptibility index uncertainty analysis (including precision evaluation and statistical law). The findings indicate that: (1) The results demonstrate that for the same model, as the interval attribute value rises from 4 to 8 and finally to 20, the forecast accuracy of landslide susceptibility initially increases gradually, then progressively grows until stable. (2) The DBN model, followed by the RF and BP models, provides the highest prediction accuracy for the same interval attribute value. (3) AIN = 20 and DBN models have the highest prediction accuracy under 15 combined conditions, while AIN = 4 and BP models have the lowest. The accuracy and efficiency of landslide susceptibility modeling are higher when the AIN = 8 and DBN models are combined. (4) The landslide susceptibility index uncertainty predicted by the deeper learning model and the bigger interval attribute value is comparatively low, which is more in line with the real landslide probability distribution features. The conditions that the environmental component attribute interval is divided into eight parts and DBN models are used allow for the efficient and accurate construction of the landslide susceptibility prediction model.
... The precision or dependability of the landslide susceptibility maps is particularly signifi- performance should be assessed [15,76]. The area under the ROC curve (AUCROC) is plotted based on the sensitivity (true positive rate) and specificity (false negative rate) [77]. ...
Preprint
Full-text available
Landslides around the main roads in the mountains not only cause fatal events but also cause ecosystem damage, including land degradation. This study aims to map the susceptibility of the landslides around the Saqqez-Marivan main rod of Kurdistan province, Iran, using ensemble Fuzzy logic with Analytic Network Process (Fuzzy Logic-ANP; FLANP), and with TOPSIS (Fuzzy Logic-TOPSIS; FLTOPSIS). A total of 100 landslides were first recognized by field surveys and then they were randomly divided into a 70% dataset (70 locations) and a 30% dataset (30 locations), respectively, for training and validating the methods. Eleven landslide conditioning factors, including slope, aspect, elevation, lithology, land use, distance to fault, distance to a river, distance to road, soil type, curvature, and precipitation were used. The performance of the methods was checked by the areas under the receiver operating curve (AUCROC). Results concluded that the prediction accuracy based on validating datasets were, respectively, 0.882 and 0.918 for FLANP and FLTOPSIS methods. Our findings demonstrated that although both models were known as promising techniques, the FLTOPSIS method had a better capacity for predicting the susceptibility of landslides in the studied area. Therefore, the susceptibility map developed by the FLTOPSIS method can be used for the proper management of areas with high landslide potential and also for managers and planners during the implementation of land allocation and development projects, especially in mountainous areas.
... dalam sistem yang telah dibuat, (9) melakukan perhitungan manual, (10) membandingkan hasil output sistem dengan data yang ada, (11) menghitung tingkat kesalahan dari sistem yang dibuat, (12) menarik kesimpulan dari hasil pengolahan data. ...
Article
Full-text available
Kemiskinan adalah suatu keadaan yang menyangkut ketidakmampuan dalam menghadapi tantangan kehidupan yang paling minimum, khususnya dari aspek konsumsi dan pendapatan. Jumlah penduduk miskin di Indonesia hingga saat ini masih tergolong banyak sehingga pemerintah masih terus memberikan bantuan sosial secara berkala kepada penduduk miskin. Namun, keluarga yang tergolong miskin masih kurang maksimal sehingga menyebabkan bantuan yang diberikan menjadi kurang tepat sasaran. Penelitian ini bertujuan untuk menerapkan sistem inferensi fuzzy metode Mamdani dalam menentukan keluarga miskin yang layak menerima bantuan sosial pemerintah menggunakan GUI Matlab. Logika fuzzy digunakan untuk menerjemahkan suatu besaran yang diekspresikan menggunakan bahasa (linguistik). Logika fuzzy dapat menyajikan setiap keadaan atau mewakili pemikiran manusia. Dalam logika fuzzy, keanggotaan elemen berada dalam interval [0, 1]. Logika fuzzy digunakan untuk menggambarkan ketidakjelasan. Kelebihan bahasa fuzzy adalah kemampuannya dalam proses penalaran secara sehingga dalam perancangannya tidak memerlukan persamaan matematik yang rumit. Variabel input yang digunakan dalam penelitian ini berasal dari 14 Kriteria keluarga miskin menurut Badan Pusat Statistik, sedangkan variabel output-nya adalah Status Keluarga. Penelitian ini menggunakan data sekunder dari Dinas Sosial Kota Kupang dan Pemerintah Kelurahan Fontein.
... Fuzzy logic was initially proposed by Zadeh (1965) [12] as a strategy to mimic the human approach in understanding data-generating processes and logical decision making, where factors in the decision-making process may be subject to vagueness and uncertainty. It has subsequently been applied to a variety of practical applications, from inventory control [13] to analysis of landslide susceptibility [14], due to its flexibility and efficiency in modeling nonlinear processes [15]. In human medical research, fuzzy logic algorithms have been evaluated for their use in disease classification based on genomic markers [16,17]. ...
Article
Full-text available
The high dimensionality of genotype data available for genomic evaluations has presented a motivation for developing strategies to identify subsets of markers capable of increasing the accuracy of predictions compared to the current commercial single nucleotide polymorphism (SNP) chips. In this simulation study, an algorithm for combining statistics used in the preselection and prioritization of SNP markers from a high-density panel (1.3 million SNPs) into a composite “fuzzy” ranking score based on a Sugeno-type fuzzy inference system (FIS) was developed and evaluated for performance in preselection for genomic predictions. FST scores, and p-values were evaluated as inputs for the FIS. The accuracy of genomic predictions for fuzzy-score-preselected panel sizes of 1–50 k SNPs ranged from −0.4–11.7 and −0.3–3.8% higher than FST and p-value preselection, respectively. Though gains in prediction accuracies using only two inputs to the FIS were modest, preselection based on fuzzy scores yielded more accurate predictions than both FST scores and p-values for the majority of evaluated panel sizes under all genetic architectures. FIS have the potential to aggregate information from multiple criteria that reflect SNP-trait associations and biological relevance in a flexible and efficient way to yield higher quality genomic predictions.
... Sun et al. 2021;Xing et al. 2021), Random Forest (RF) (Abu El-Magd et al. 2021;Zhou et al. 2021), Naïve Bayes (NB) (Hu et al. 2021;Nguyen and Kim 2021), Support Vector Machines (SVM) (Kamran et al. 2021;C. Xi et al. 2022) and Mamdani Fuzzy Inference Systems (Lucchese et al. 2021;Peethambaran et al. 2019;Pinto et al. 2021;C. Xi et al. 2022) are being used for better landslide susceptibility modeling and mapping. ...
Article
Landslide susceptibility map is considered as one of the important steps in assessing vulnerability of an area to landslide hazard. In this study, the main objective is to propose ensemble machine learning models: BF, DF and RSSF which are a combination of Fuzzy Unordered Rules Induction algorithm (F) and three optimization techniques namely Bagging, Decorate, and Random Subspace, respectively for landslide susceptibility mapping. In addition, two other single models namely F and Support Vector Machines (SVM) were also applied for the comparison of performance of the proposed models. For this purpose, the Sin Ho district, Lao Cai Province, Vietnam was selected as the study area. For the development of models, database of 850 present and historical landslides of this province including ten landslide affecting input parameters namely slope, curvature, elevation, aspect, Topographic Wetness Index (TWI), deep division, river density, fault density, aquifer, and geology were used. Validation of the models was done using various popular statistical indicators including Area Under the Receiver Operating Characteristics (AUC) curve. The results show that the BF model (AUC = 0.923) is the best model for accurate landslide susceptibility mapping (LSM) in comparison to other models namely DF (AUC = 0.899), RSSF (AUC = 0.893), SVM (AUC = 0.840), and F (AUC = 0.862). The study revealed that LSM map constructed using BF model can be used for better land use planning and proper landslide hazard management.
... Therefore, in the recent time, several kinds of Machine Learning Algorithms (MLAs) have been widely used in this perspective to describe the non-linear relationship between the environmental factors and landslide susceptibility indexes Merghadi et al., 2020). Popular A c c e p t e d M a n u s c r i p t MLAs like "Credal Decision Tree (CDT) (Arabameri et al., 2020;He et al., 2019), Boosted Regression Tree (BRT) (Park and Kim, 2019), Support Vector Machines (SVM) (Kamran et al., 2021;Sharma et al., 2021), Artificial Neural Networks (ANN) (Mehrabi and Moayedi, 2021;Pham et al., 2021b), Fuzzy Inference Systems (FIS) (Lucchese et al., 2021;Razavi-Termeh et al., 2021) and Random Forests (RF) (Sun et al., 2021;Tanyu et al., 2021)" etc. have been used in landslide studies in recent past. Literature study indicates that stand-alone MLA also has a few disadvantages in optimal prediction analysis (Allocca et al., 2021). ...
Article
Full-text available
In geomorphological hazard studies, selecting DEM data with the proper spatial resolution is necessary for optimal analysis of prediction performance. Henceforth, accurate resolution of DEM data in landslide susceptibility study is also crucial in this perspective. This study determines the scale effects of DEM derived hydro-topographic factors in LS mapping in the Rangpo river basin, Sikkim Himalaya, India. Five different DEM data i.e., ALOS (12.5 m), and AW3D30, SRTM, ASTER and Cartosat-1 with each 30 m resolution, were used in this study. Three neural network algorithms were applied to produce LSM. The results of this investigation revealed that, among the three employed neural network techniques, the deep learning algorithm with ALOS DEM data performed the best. The proposed unique approach i.e., combination of scale effects and deep learning algorithm can be useful to produce precise LSMs in hilly areas around the globe, and will be helpful for sustainable development.
Article
Full-text available
The challenging geological conditions in hilly mountainous areas, combined with intensive human engineering activities, have led to a high frequency of landslide disasters. This is particularly true in karst mountainous areas where the geology is complex and characterized by distinct karst phenomena influenced by stratigraphy and severe terrain cutting. Therefore, it is crucial to initiate the eval uation of landslide risk in typical karst mountainous areas and establish a sound evaluation system. In this study, the landslide risk in the Jianshi County was evaluated using the Information value method with the county as the evaluation scale , and the eight categories of elevation, slope, aspect, distance from road, distance from river, distance from structure, vegetation cover and engineering rock group are established as the main causative factors to evaluate the landslide susceptibility, and the two categories of land use and rainfall as the main predisposing factors to evaluate the landslide hazard. Meanwhile, the study highlights the important finding that in typical karst areas, high susceptibility areas and high vulnerability areas tend to overlap, resulting in a concentration of high-risk landslide areas. The evaluation factors identified in this study can serve as typical factors for evaluating landslide risk in similar karst mountainous areas. Furthermore, the risk distribution characteristics observed in this study can guide landslide risk assessments in other comparable regions. These insights can aid in the development of effective landslide risk management strategies in karst mountainous areas.
Article
Landslide susceptibility map is considered as one of the important steps in assessing vulnerability of an area to landslide hazard. In this study, the main objective is to propose ensemble machine learning models: BF, DF, and RSSF which are a combination of Fuzzy Unordered Rules Induction algorithm (F) and three optimization techniques namely Bagging, Decorate, and Random Subspace, respectively for landslide susceptibility mapping. In addition, two other single models namely F and Support Vector Machines (SVM) were also applied for the comparison of performance of the proposed models. For this purpose, the Sin Ho district, Lao Cai Province, Vietnam was selected as the study area. For the development of models, database of 850 present and historical landslides of this province including ten landslide affecting input parameters namely slope, curvature, elevation, aspect, Topographic Wetness Index (TWI), deep division, river density, fault density, aquifer, and geology were used. Validation of the models was done using various popular statistical indicators including Area Under the Receiver Operating Characteristics (AUC) curve. The results show that the BF model (AUC =0.923) is the best model for accurate Landslide Susceptibility Mapping (LSM) in comparison to other models namely DF (AUC =0.899), RSSF (AUC =0.893), SVM (AUC =0.840), and F (AUC =0.862). The study revealed that LSM map constructed using BF model can be used for better land use planning and proper landslide hazard management.
Article
Full-text available
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.
Article
Full-text available
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.
Article
Full-text available
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.
Article
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.
Article
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.
Book
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.
Article
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%).