=Paper=
{{Paper
|id=None
|storemode=property
|title=Fuzzy Approach to Landslide Susceptibility Zonation
|pdfUrl=https://ceur-ws.org/Vol-706/papersg01.pdf
|volume=Vol-706
|dblpUrl=https://dblp.org/rec/conf/dateso/MarjanovicC11
}}
==Fuzzy Approach to Landslide Susceptibility Zonation==
https://ceur-ws.org/Vol-706/papersg01.pdf
Fuzzy approach
Fuzzy Approach to to
landslide susceptibility
Landslide zonation
Susceptibility
Zonation
Miloš Marjanović1, Jan Caha2
MilošinMarjanović
Palacky University and Jan
Olomouc, Faculty Caha Tr. Svobody 26,
of Science,
771 46 Olomouc, Czech Republic
Palacky University in Olomouc, Faculty of Science
1milos.marjanovic01@upol.cz
Tr. Svobody 26, 771 46 Olomouc, Czech Republic
2jan.caha@klikni.cz
milos.marjanovic01@upol.cz, jan.caha@klikni.cz
Abstract. The paper addresses a landslide-prone area on Fruška Gora Mt. in
NW Serbia. It proposes a model of relative landslide susceptibility based on
fuzzy sets. Having a variety of spatial attributes (proven statistically significant)
at disposal, as well as present landslide inventory map, we conducted systemat-
ic analysis through (i) assigning fuzzy memberships to attribute categories, and
(ii) combining the memberships by means of fuzzy operators. The performance
defined by Area Under Curve parameter of the Receiver Operating Character-
istics curve, led to preference of Frequency Ratio method for assigning mem-
berships, and Fuzzy Gamma Operator for combining those memberships in 2-
level experimenting configuration. Results are also well related with previous
investigations with different approaches.
1 Introduction
Landslides and alike mass movements are one of the most widespread hazardous phe-
nomena [1]. They seem to be among the top seven natural hazards, and advancing
[19] in the world of growing needs for urbanization, land exploitation, and yet un-
stable climate conditions. Accordingly, there has been a significant ascent of interest
in landslide assessment topics, resulting in more frequent multidisciplinary case stud-
ies and rising number of scholars per investigation [11].
Common notion of landslide hazard is broadly misinterpreted in relation to its con-
ventional definition, which regards the hazard quantitatively as a function of fre-
quency of hazardous phenomena over specified area or volume [23]. Nevertheless,
even such precise scientific formulation is not entirely straightforward, since literal
hazard assessment appears to be feasible only for the limited areas with excellent data
coverage [4]. Entire range of problems is encountered in this framework, including
the input data quality, lack of evidence on previous occurrences or triggering events,
lack of consistent evaluation of the modeling results [4]. Therefore, most of the stud-
ies actually address landslide susceptibility as non-temporal variant of the landslide
hazard, which evaluates the landsliding potential in the relative scale.
Practice of landslide zonation had been illustrated in versatile techniques in various
case studies, yielding more or less reliable results depending on the complexity of the
terrain and suitability of the approach [5]. Thereto, the principle assumption imply
V. Snášel, J. Pokorný, K. Richta (Eds.): Dateso 2011, pp. 181–195, ISBN 978-80-248-2391-1.
182 Miloš Marjanović, Jan Caha
that future landslide occurrences stand in relation with the present ones [3], while
central – multi-criteria modeling idea couples different input thematic data (geologic-
al, geomorphological, environmental maps), relate them to the referent map of present
landslides, and processes a single output – hazard/susceptibility map. Techniques of
relating referent landslide map with the inputs are numerous: heuristic (expert-based),
deterministic (physically-based), statistical and probabilistic, artificial intelligence
based (neural networks, decision trees, machine learning algorithms, data mining),
fuzzy logic based, and so forth. All those equally face the non-linearity of the prob-
lem, and strong dependence on the referent landslide data, the entire input data fea-
ture space, for that matter.
Weather using ordinary fuzzy sets, or fuzzy measures, or even combining fuzzy
with other statistical or classification approaches (Dampster-Shafer, K-means, Neural
Networks) the ultimate advantage is seen in logics, which provides a substantial pos-
sibility for standardization of the analysis under the consideration [12]. Thus, the pro-
cedure tends to be repeatable, adjustable and reliable. When it comes to the landslide
assessment analysis in particular, a number of researchers have applied fuzzy ap-
proach to handle the non-linearity, which is common in multi-criteria framework. In-
terestingly enough, Himalayan terrains were addressed in many investigations with
fuzzy theory background, starting from standard fuzzy set approach [15], [21], [6],
through combinations of neural-fuzzy [13] and risk-oriented fuzzy approach [14].
Most of these studies agreed that plausible susceptibility models could be obtained by
applying advanced operators, with preference toward Cosine Amplitude method for
obtaining memberships. Very similar conclusions with analogue methodology were
inferred over Iranian case studies [22], and in Turkey [7], China [24] and so forth.
The latter is also interesting in respect of harmonizing expert-based and fuzzy-driven
solutions, inferring that one does not exclude another, but supports it. Finally, Regmi
et al. [20] conducted one of the most consistent researches, where many different
fuzzy configurations were put to test. Detailed elaboration of the choice of fuzzy op-
erator type, optimal fitting of gamma operator as a method of preference, and some
suggestions on handling multi-type landslide cases, can be found in this research. In
addition, most of the researchers encourage the usage of the fuzzy method in other,
similar or entirely different ambients, worldwide.
Herein we will concentrate on fuzzy logic approach, and compare results with
some of earlier works that involved heuristic, statistical and machine learning tech-
niques over the same area, using similar datasets. Thus, the primary objective is to in-
vestigate whether the fuzzy logic approach enhances the susceptibility model and to
which extent. Optimization of the procedure, in accordance with the characteristics of
the dataset, was also one of the foci, in order to reach the best performance of the
model.
Organization of the paper goes as follows: in Chapter 2, a brief overview of all im-
plemented techniques is presented; Chapter 3 follows with very basic description of
study area; data acquisition and preparation is regarded in Chapter 4; results of sus-
ceptibility model and comparative analysis are presented and discussed in Chapter 5;
Chapter 6. concludes the paper. Appendix 1 contains very detailed modeling paramet-
ers of attributes, which were used in the procedure.
Fuzzy Approach to Landslide Susceptibility Zonation 183
All parametric calculations, were performed in MS Excel sheets, and spatial attrib-
utes were prepared and visualized with ArcGIS 9+ packages (ranged, calculated,
cross-tabulated etc.), as well as final models.
2 Methods
2.1 Feature Selection
It is recommendable to filter the set for features which are of no relevance to the ana-
lysis, if nothing, for the sake of hardware and time expenditure, thus the filtering pro-
cedure is not to be overlooked. In parlance of the latter, a statistical significance tests
needs to be run prior to the dataset utilization.
Chi-Squared statistic, parameter X2, is a significance criterion, which relates the
frequencies of observed independent variable instances φo within the dependent vari-
able classes, and their expected frequencies φe, in the following fashion:
2
q n ϕ o −ϕ ei , j (0)
Χ =∑ ∑
2 i, j
,
i=1 j=1 ϕe
i, j
where q is the number of classes within a dependent variable, and n within the inde-
pendent variable. In our case, the former represents landslide inventory classes, while
the latter disclose the classes of a particular terrain attribute, since X2 needs to be
paired with every single attribute separately. The given terrain attribute disapproves
the hypothesis of being statistically independent from the landslide inventory classes
only if it exceeds the critical X2 threshold, defined by the level of confidence (in re-
spect with the normal distribution) and degrees of freedom (defined by reduced
product of q and n, (q-1)(n-1)). In effect, this method reveals the relation of an attrib-
ute and the referent landslide inventory, but the ranking among multiple attributes is
rather relative, primarily due to the measurement scale dependence of X2 [2].
2.2 Fuzzy Set Theory
Concepts of fuzzy logic have a very long tradition in spatial analysis framework.
Main purpose of fuzzy logic is to deal with vague information and with data that con-
tain some kind of uncertainty [25]. When using fuzzy set theory or fuzzy logic, each
object or statement is given value from interval <0,1> indicating its membership to
the given set. Each object can be member of several sets with different membership
values. This concept is very helpful for categorization of data and for decision mak-
ing, because unlike Boolean logic it produces results valid with specific degree of
truth. That helps with finding not only the perfect match for a given criteria, but
184 Miloš Marjanović, Jan Caha
rather shows how much each of possibilities meet given criteria. At some specific
situations, when modeling physical geographical crisp sets, Boolean logic fail to
provide correct and quality results because of natural substance of the phenomena at
hand. In such cases, fuzzy set theory and fuzzy logic provides solutions for dealing
with imprecise and vague data, which would be hard or even impossible to process by
any other means.
2.3 Fuzzy Memberships
Membership value is determined by membership function. Membership function is a
function that maps all given elements to interval of values <0,1>.
µ A :U <0,1> , (0)
where µA is a membership function, U is a set of elements. Then for each x∈U, µA(x)
is membership value of the element x to the set A [25]. For purpose of this paper, we
use two functions for computing the fuzzy membership values: Frequency Ratio and
Cosine Amplitude.
Frequency Ratio gives proportion of landslide cells in the specific category for each
of input layers. It can be described as ratio of relative frequency of landslide cells in a
category (an attribute class) to the relative frequency of all landslide cells in the area:
N cell Li /N cell C i (0)
FR= ,
N cell L /N cell C
Where Ncell(Li) is the number of landslide cells in the category i, Ncell(Ci) is the total
number of cells in the category i, Ncell(L) is total number of landslide cells and Ncell(C)
is the total number of cells. If the result is higher than 1 it shows higher density of
landslide cells in the category then overall in the dataset. Results lower than 1, points
to categories that have density of landslide cells lower then density in the dataset. To
transform FR to membership values those outputs have to be normalized by dividing
each FR by maximal FR in the given group of classes. Then the membership values
are from the interval <0,1> and the higher the number is, the higher is the influence of
this category on landslide occurrence.
Another method for determining the membership values of categories to the set of
categories important for landslide occurrence is Cosine Amplitude method:
N cell Li (0)
CA= .
N cell C i ⋅N cell L
In this case, the membership value is calculated as ratio between number of landslide
cells in the category and the square root of its product with the total number of land-
slide pixels in the dataset. Unlike FR the output values do not have to be normalized
because they already fall in interval <0,1>.
Fuzzy Approach to Landslide Susceptibility Zonation 185
2.4 Fuzzy Operators
Several fuzzy operators exist for combining membership functions. Best-known oper-
ators are AND and OR, but both of them suffer with problem that one of combined
sets have significant impact on result of such combination while the other sets do not
have such influence. In case of operator AND minimum of all values is the one that
defines output and in case of OR operator it is the maximum value. Because of this
reasons we use other operators such as Fuzzy Algebraic Product, Fuzzy Algebraic
Sum, Gamma Operation and Weighted Average. All of them are described in detail
[2] so only short review is given here.
In Fuzzy Algebraic Product and Fuzzy Algebraic Sum the outputs are defined as:
n (0)
μ product =∏ μi ,
i=1
n (0)
μ sum=1−∏ 1−μi ,
i=1
respectively, where n is number of membership function to be combined and µA is the
i-th membership function. Fuzzy Algebraic Product tends to produce output function
lower or equal to the lowest function given, while Fuzzy Algebraic Sum is comple-
mentary to the former, so it provides output function higher than all the inputs but
never higher than 1.
Gamma Operation is defined by:
μ γ = μsum γ⋅ μ product 1−γ . (0)
The exponent γ, which is a number from <0,1> interval, allows optimization of the
membership combination. Setting it to the extremes of the interval give either Fuzzy
Algebraic Sum (γ=1) or Fuzzy Algebraic Product (γ=0).
Weighted Average is defined as:
n (0)
∑i=1 w i⋅μi
μ w= n
,
∑i=1 iw
where wi is a weight of membership function, indicating importance of the member-
ship function on result and n is a number of membership functions to be combined.
Weight system in this equation allows more interaction from user to the calculation,
because it allows emphasis of certain values.
186 Miloš Marjanović, Jan Caha
2.5 Performance Evaluation
Performance metrics involved Receiver Operating Characteristics (ROC), which is a
cut-off independent performance estimator [9]. It involves contingency table inspec-
tion (derived by area cross-tabulations of attribute vs. landslide inventory). ROC val-
ues are created by plotting the cumulative True Positive Rates (TPR=sensitivity)
versus False Positive Rate (FPR=1–specificity) for every model, resulting in a set of
ROC curves. The performance is evaluated by the Area Under the Curve (AUC) relat-
ive to the entire plot area, so that an AUC equal to 1 has the best performance, while
an AUC as low as 0.5 results in a very poor performance [10]. In addition, TPR is a
good measurement of performance in the landslide assessment framework, since it
takes into account instances that are not classified as landslides in the model but actu-
ally are landslides, which is more dangerous underestimation than false alarms.
3 Case Study
The study area encompasses the NW slopes of the Fruška Gora Mountain, in the vi-
cinity of Novi Sad, Serbia. The site (N 45°09’20”, E 19°32’34” – N 45°12’25”, E
19°37’46”) spreads over approximately 100 km2 of hilly landscape, but with interest-
ing dynamics and an abundance of landslide occurrences. As judged in some previous
investigations over this area [16], [17,], [18], the landslide process is chiefly governed
by geological and morphological attributes, while the triggering mechanism could be
assigned to excessive rainfall, but moderate seismic activity typical for this mountain,
could also be an option.
4 Dataset
Dataset included geological, geo-morphometric, hydrological and environmental at-
tributes, obtained from different resources, converted to raster grid format with 30 m
cell resolution. It also included landslide inventory map.
• Geological data were assembled by using geological map 1 : 50 000, photo-
geological map (Remote Sensing based interpretation of geological struc-
tures and geodynamic processes and forms) 1 : 50 000, and field survey data.
For the purpose of this research, a segment of geological map was digitized
and simplified to geo-unit attribute. Geological structures, which were used
to make a buffer geo-structures were extracted from photogeological map. In
addition, the buffer geo-boundaries was created by choosing only the bound-
aries between the units with significant difference in hydrogeological func-
tion.
• Model of the terrain surface was created from digitized contour maps at 1 :
25 000, first by calculating Triangulated Irregular Network (TIN) and then
substituting it with the Digital Elevation Model (DEM) of 30 m resolution,
Fuzzy Approach to Landslide Susceptibility Zonation 187
by means of TIN-to-raster data conversion. Given the terrain morphology,
various geo-morphometric attributes were created as first order derivates of
DEM: aspect, elevation, slope angle, slope length, profile and planar
curvature.
• Hydrological attributes are represented by topographic wetness index (TWI)
as the second order derivate of DEM, and buffer stream calculated after auto-
matic generation of drainage pattern using DEM.
• Land cover, as an environmental attribute, was desirable in order to delineate
deforested and cultivated areas as more convenient for the development of
landslides than vegetated areas. The attribute was created by Landsat TM
band ratioing (particularly red and near infrared bands, due to the authentic
spectral behavior of vegetation). Several vegetation indices were considered,
and Normalized Difference Vegetation Index (NDVI) seemed like the optim-
al solution, due to its simplicity and accuracy. Since the area of the interest is
not very populated, urban influences were not considered. Classification of
NDVI into land cover categories was semi-supervised, i.e. visual, but aided
by K-means classification to four different entities (Appendix 1).
• Landslide inventory map was essential requirement to make a susceptibility
assessment evaluated for performance. The map was created by extracting
landslide forms from photogeological map. Subsequently, it was simplified
to binary attribute (TRUE and FALSE landslide categories). It is important
to mention constrains of such map, since it considered only earth slides [23]
of rotational, translational and complex type, with two stages of the activity
(dormant and active). This is understandable regarding the scale of the study
(1 : 50 000) and the nature of the dominating landslide phenomena within the
area of interest. According to this binary map, total of 10% of the area fall
into landslide category (about 10 km2).
Apparently, dataset involved continual numeric data, but categorical attributes as
well. The methodological approach required ranging of continual attributes to cat-
egorical data, prior to their processing, and several solutions were regarded. Finally,
ranging by means of Natural break cut-offs was the method of choice, which was ap-
plied to all continual attributes. Different continual attributes were ranged by appro-
priate number of intervals (Appendix 1), due to differences in pixel frequencies
among attributes. In favor of selected approach of preparing the data, feature selection
parameter proved that all attributes had statistical dependence to referent landslide in-
ventory, having the values significantly higher than critical (Appendix 1).
5 Results and Discussion
Given the categorized (ranged) raster attributes and the referent landslide inventory
map, we first calculated the memberships of each category in each attribute. Two par-
allel variants of the experiment were driven: EXPERIMENT 1 used Cosine Amp-
litude, while EXPERIMENT 2 used Frequency Ratio to obtain the memberships.
188 Miloš Marjanović, Jan Caha
Both experiments had exactly the same course, thus the following manipulations took
place in each.
5.1 Susceptibility Model
In order to combine memberships by different operators we undertook a small inter-
vention to exclude too many extreme membership values (0 and 1) by replacing them
with close approximations (0.0001 and 0.9999). We proposed 2-level fuzzy combina-
tions based on a priory knowledge of the phenomena (Fig. 1), i.e. the pairs of attrib-
utes of similar origin were grouped together. Continual Susceptibility Model was ob-
tained after the second level combination. The final susceptibility model was gener-
ated by ranging the continual values into five standard categories of relative suscept-
ibility: Very Low – VL, Low – L, Moderate – M, High – H, Very High - VH [8]. Re-
garding the distribution of the pixels in Continual Susceptibility Model, it was justifi-
able to adopt the quantile interval cut-offs for afore mentioned categorization. Only
the highest susceptibility class VH was regarded for performance evaluation (AUC)
against the referent landslide inventory (Table 1). This was instructed by the fact that
determined landslides should be marked as a priority zone (preferably as VH class).
Fig. 1. Flowchart of the experiment configuration.
To remain consistent, we kept the same type of the operator at both combination
levels. Initial results in both experiments gave preference to Fuzzy Gamma Operator,
so we directed further fitting toward optimization of parameter γ. Cases of γ=0 (Fuzzy
Product) and γ=1 (Fuzzy Sum) were already regarded, so we tested several choices
within that interval (0.25, 0.5, 0.75). It turned that the best performance (AUC) was
Fuzzy Approach to Landslide Susceptibility Zonation 189
achieved by γ=0.5, making it a parameter of choice for our final susceptibility model.
Finally, EXPERIMENT 2 gave slightly better performance over EXPERIMENT 1,
meaning that Frequency Ratio could be preferred over Cosine Amplitude for assign-
ing memberships.
Table 1. Performance evaluation of different fuzzy experiments configurations (1-Cosine Amp-
litude, 2-Frequency Ratio memberships), and other landslide susceptibility models (shaded)
Model AUC TPR
EXPERIMENT 1 (Weighted Average) 0.65 0.37
EXPERIMENT 1 (Gamma Operator, γ=0.5) 0.70 0.53
EXPERIMENT 2 (Weighted Average) 0.71 0.56
EXPERIMENT 2 (Gamma Operator, γ=0.5) 0.72 0.58
AHP 0.67 0.48
CP 0.72 0.60
SVM 0.85 0.77
Distribution of relative susceptibility classes goes as follows: VL – 53%, L – 14%,
M – 12%, H – 11%, and VH – 10%. Dominance of the VL class characterizes the ter-
rain as mostly stable, while similarly as in the referent inventory map, the most ad-
verse zones occupy about 10% of the area. Furthermore, a majority of the actual land-
slide instances fall into the VH and H classes (37% and 23% of all landslides, respect-
ively), while M, L and VL classes occupy mostly non-landslide instances (75% of
non-landslide instances in total for all three classes).
Highest overall performance in EXPERIMENT 2 (AUC=0.72) could be acknow-
ledged as plausible, which is also supported visually (Fig. 2a-b), since VH class cor-
responds very well with the spatial trends of landslide scarps. Apparent influence of
intermediate layer Geo Buffer caused several outliers by underestimating some land-
slide scarps. A considerable drawback is relatively low TPR in both experiments
(Table 1) which is inconvenient for any hazard-related analysis, since the model tends
to underestimate actual landslide instances (claiming class other than VH for an actu-
al landslide instance). However, the actual performance is somewhat better, since we
regarded only VH class for cross-tabulation. Thus, H or even M class could be fair re-
placements for VH class, as they buffer-out around it, which if included in cross-tabu-
lation might reduce the number of False Negatives, thus increasing TPR.
5.2 Comparison
In order to determine the true practicality of our results, we related proposed model to
other available results including: Analytical Hierarchy Process (AHP) model [16],
Conditional Probability (CP) model [18], and machine learning with Support Vector
Machine (SVM) model [17]. When comparing the best fuzzy-based result with the
other models the same policy of comparing only VH class holds, due to compatibility
issue. Namely, some of the comparison models, such as SVM, are discrete in their
190 Miloš Marjanović, Jan Caha
nature and cannot follow (standardized) relative susceptibility categorization (VL–
VH).
Fig. 2. Landslide susceptibility models based on EXPERIMENT 1 (CA, γ=0.5) a), and EX-
PERIMENT 2 (FR, γ=0.5) b). Bold contours outline the landslide scarps from the landslide in-
ventory. Legend depicts relative susceptibility classes.
Expectedly, SVM approach outperformed fuzzy-based models by far (Table 1).
Ease of handling continual and categorical data most likely enables such dominance
of SVM model over other results. On the other hand, fuzzy approach turned practic-
ally as successful as statistical one (CP model), but with more subjectivity involved in
the modeling procedure (in ranging the input intervals, but also in selecting the oper-
ators and numbers of combination levels). It outperformed AHP model, not as much
in the overall performance (AUC) as in considerably higher TPR, giving itself a slight
preference for safer assessment (Table 1).
6 Conclusion
In present paper, we regarded fuzzy set approach in the landslide susceptibility frame-
work, having different input attributes and referent landslide inventory at disposal.
Subjectivity in ranging input attributes was inevitable, due to incapability of the ap-
proach to handle continual numerical variables (in the stage of assigning member-
ships). Another subjective intervention regarded proposing the number of levels for
fuzzy combination, and grouping the attributes with similar origin at level 1. We pro-
posed two configurations of generating memberships of input attribute categories,
EXPERIMENT 1 (CA) and EXPERIMENT 2 (FR), and led further optimization to-
ward the choice of fuzzy operators for combination task. The best performance was
reached with Fuzzy Gamma Operator with γ=0.5. The resulting Landslide Susceptib-
Fuzzy Approach to Landslide Susceptibility Zonation 191
ility Model turns plausible, and seems improved when compared to some previous
models designed for the same study area, particularly heuristic one.
Further refinement, left for the future work, should involve combining of fuzzy ap-
proach with some other techniques. The latter primarily address merging with heurist-
ic expert decisions, while fuzzyfication in machine learning approach is also to be
challenged. Another improvement could be recognized in reducing the subjectivity in
experiment design, and configure the experiment structure on statistical basis or in-
formation theory basis.
To conclude, our research came up with suitable model, while the procedure re-
mained simple, semi-automated and re-operable in GIS environment. The resulting
map could serve preliminary levels of risk or disaster management, landscape (re-
gional) planning, route selection, insurance management and so forth.
Acknowledgement
This work was supported by the Czech Science Foundation (Grant No. 205/09/079).
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Fuzzy Approach to Landslide Susceptibility Zonation 193
Apendix 1– Table of Attributes
Input attributes, their class memberships in EXPERIMENT 1 configuration (µFR) and EXPERI-
MENT 2 configuration (µCA), and their statistical dependence (X2) on landslide inventory (de-
pendent variable)
attribute name (type, group) µFR µCA X2
categories (X2critical)
buffer geo-structure (continual, geo-buffer) 1949.6
0 - 134 0.051 0.781 (27.9)
134 - 276 0.092 0.770
276 - 426 0.141 0.805
426 - 582 0.260 1
582 - 755 0.261 0.812
755 - 942 0.178 0.445
942 - 1159 0.024 0.077
1159 - 1418 0 0
1418 - 1758 0.262 0.197
1758 – 2305 m 1 0.568
buffer geo-boundary (continual, geo-buffer) 306.3
0 - 94 0.275 1 (27.9)
94 - 218 0.038 0.630
218 - 342 0.107 0.499
342 - 458 0 0.372
458 - 589 0.040 0.295
589 - 726 0.484 0.429
726 - 878 0.579 0.313
878 - 1050 1 0.332
1050 - 1244 0.458 0.105
1244 – 1749 m 0.682 0
buffer stream (continual, hydro) 2381.6
0 - 94 0.550 0.643 (27.9)
94 - 212 0.900 1
212 - 324 0.780 0.809
324 - 432 0.453 0.431
432 - 543 0.346 0.305
543 - 660 0.218 0.165
660 - 797 0 0
797 - 966 0.024 0.002
966 - 1173 0.362 0.100
1173 – 1542 m 1 0.214
TWI (continual, hydro) 4947,6
7.5 - 9.3 0 0 (26.1)
9.3 - 10.3 0.172 0.261
10.3 - 11.4 0.696 1
11.4 - 12.8 1 0.955
12.8 - 14.3 0.811 0.575
14.3 - 16.2 0.821 0.442
16.2 - 18.3 0.781 0.320
18.3 - 20.8 0.506 0.176
20.8 - 22.5 0.131 0.079
194 Miloš Marjanović, Jan Caha
aspect (categorical, topo) 1091.0
flat 0 0 (26.1)
N 0.594 0.701
NE 0.552 0.688
E 1 1
SE 0.889 0.490
S 0.278 0.140
SW 0.645 0.638
W 0.494 0.571
NW 0.414 0.433
elevation (continual, topo) 7515.7
78 - 102 0.660 0.619 (27.9)
102 - 138 1 1
138 - 173 0.828 0.838
173 - 209 0.530 0.499
209 - 248 0.158 0.147
248 - 287 0.141 0.118
287 - 329 0.018 0.013
329 - 376 0 0
376 - 426 0 0
426 – 540 m 0 0
slope angle (continual, topo) 4453.1
0 - 4.2 0.300 0.243 (18.5)
4.2 - 9.5 1 1
9.5 - 14.8 0.473 0.403
14.8 - 21.1 0.119 0.086
21.1 - 40.1º 0 0
slope length (continual, topo) 1346.8
0 - 60 0.435 1 (27.9)
60 - 181 0.591 0.964
181 - 353 0.937 0.960
353 - 602 1 0.667
602 - 981 0.650 0.261
981 - 1506 0.301 0.080
1506 - 2196 0.178 0.033
2196 - 3094 0.427 0.061
3094 - 4392 0.187 0.019
4392 – 6499 m 0 0
plan curvature (continual, topo) 989.4
concave 0 0 (18.5)
- 0.657 0.333
flat 1 1
- 0.626 0.419
convex 0.149 0.059
profile curvature (continual, topo) 1214.0
concave 0 0.009 (18.5)
- 0.414 0.287
flat 1 1
- 0.741 0.366
convex 0.081 0
geo-units (categorical, geo-units) 8319.3
al' - Danube's inundation plane 0.100 0.099 (29.6)
al - aluvium 0.211
dl - deluvium cover 0.807 1
t - terrace sediments 1 0.785
Fuzzy Approach to Landslide Susceptibility Zonation 195
l - loess 0.338 0.334
Pl - clay 0.858 0.847
M2 - marlstone 0.133 0.083
M1 - limestone, sandstone 0.469 0.880
Se - ultra-mafic rocks 0 0
J - limestone 0 0
Pz - schists 0.002 0.003
land cover (categorical, land cover) 6316.2
water 0 0 (16.2)
arable land 1 1
grass land 0.992 0.852
forest 0.132 0.168