StudyofHybridNeurofuzzyInferenceSystemforForecasting...

Research ArticleStudy of Hybrid Neurofuzzy Inference System for ForecastingFlood Event Vulnerability in Indonesia

Sri Supatmi 12 Rongtao Hou 1 and Irfan Dwiguna Sumitra 3

1School of Computer and Software Nanjing University of Information Science and Technology No 219 Ningliu RoadPukou Nanjing Jiangsu 210044 China2Computer Engineering Department Universitas Komputer Indonesia No 102-116 Dipati Ukur BandungWest Java 40132 Indonesia3Postgraduate of Information System Department Universitas Komputer Indonesia No 102-116 Dipati UkurBandung West Java 40132 Indonesia

Correspondence should be addressed to Sri Supatmi srisupatmiemailunikomacid

Received 18 October 2018 Accepted 15 January 2019 Published 25 February 2019

Academic Editor Carmen De Maio

Copyright copy 2019 Sri Supatmi et al )is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

An experimental investigation was conducted to explore the fundamental difference among the Mamdani fuzzy inference system(FIS) TakagindashSugeno FIS and the proposed flood forecasting model known as hybrid neurofuzzy inference system (HN-FIS))e study aims finding which approach gives the best performance for forecasting flood vulnerability Due to the importance offorecasting flood event vulnerability the Mamdani FIS Sugeno FIS and proposed models are compared using trapezoidal-typemembership functions (MFs) )e fuzzy inference systems and proposed model were used to predict the data time series from2008 to 2012 for 31 subdistricts in Bandung West Java Province Indonesia Our research results showed that the proposed modelhas a flood vulnerability forecasting accuracy of more than 96 with the lowest errors compared to the existing models

1 Introduction

Flood disaster [1] is one of the significant problems in somecountries including Indonesia Flood disaster occurs mostlyin populated areas )e high rainfall in many cities increasesthe risk of flooding )e flood occurs mainly because of ahigh rate of rainfall for extended periods in the wet season)e drainage system could not control the problem of risingwater volume in a river or a channel )e critical thing inmeteorology hydrology (eg flood warning) environ-mental policy and agriculture is the accurate measurementof rainfall [2] As a result of flood people loss their homesand their crops miss the school education and even worselose their life

In October 2016 some regions in Indonesia were af-fected by the flood and the disaster management officialsreported that the flash flood in the Bandung city causeddeath of one person and damaged thousands of homes )eNational Disaster Management Authority also known as

BNPB informed that there was 77mm of rainfall in the townin just 15 hours around midday [3 4] Most of the areas ofthe city were inundated with flood water between 120 cmand 200 cm deep [3 4] In the same month a part ofGorontalo Indonesia was affected by flood at least 1500homes were damaged and around 4500 people were forcedto evacuate their homes [5 6] In December 2016 a part ofWest Nusa Tenggara Province Indonesia was hit by twofloods in the space of days forcing over 100000 people toleave their homes BNPB informed that thousands of homeswere damaged and streets were left with flood water fromone meter to three meters deep [4 6] On January 26 2017flood hit North Sulawesi Indonesia )is flood affected 11villages in Gorontalo Utara and damaged over 700 homessome schools and agricultural land forcing more than100 people to leave their places [4 7] On March 3 2017 atleast six people died two seriously injured and thousandsdisplaced due to floods in Indonesiarsquos West SumatraProvince )e flood also caused power and communication

HindawiComputational Intelligence and NeuroscienceVolume 2019 Article ID 6203510 13 pageshttpsdoiorg10115520196203510

outage and over one hundred electrical substations wereshut down leaving almost 15000 houses without electricity[4 8]

)e answer to overcome the flood disaster by applyingthe fuzzy system is assisting predicting and deciding theseevents In 1965 Lotfi a mathematician who created thetheory of fuzzy logic derived the result of the insufficiency ofBoolean algebra for many real-world problems [9 10] Infact as most of the information is imprecise one of thehumanrsquos greatest abilities is to process inaccurate problemsand vague information efficiently )e Oxford English Dic-tionary defined the word ldquoFuzzyrdquo as blurred indistinctimprecisely defined confused or vague )e fuzzy systemsare knowledge-based or rule-based systems )e heart of afuzzy system is the so-called knowledge-based fuzzy IF-THEN rules [11]

Many researchers have argued on meteorological fore-casting with the purpose to help assessing the disasterimpact in some regions Forecasting is also used in otherareas such as detection and prediction of diseases [12 13]Asklany et al [14] proposed the probabilistic predictionusing two skill scores namely the Brier Score and FrictionScore )ose researchers mentioned that the rainfall eventprediction was highly accurate with the data aggregated bythe stations with increasing output toward the real-timeevent Otherwise the fuzzy inference system output precedesthe recorded maximum data in six hours before the rainfallLi-Chiu et al [15] introduced a model to predict the stream-flow an hour after a flood event occurs )ey also comparedthe result using a fuzzy exemplar-based inference systemwith backpropagation neural network to show that a fuzzymodel performs better than the neural network de Bryunet al [16] described a method based on fuzzy arithmetic toestimate the possible range of flow rates and water levelbased on possible rainfall events by the forcing and un-certainty model A previous research [17] explained a rainfalllevel detection system to predict the weather using theMamdani method In [18] the rainfall event was analyzedusing the defuzzification method In [19] the genetic al-gorithm (GA) was discussed to obtain a higher accuracy ofthe rainfall forecasting system In [20] the agricultural ir-rigation control using the fuzzy method for determiningwater quantities was studied In [21] the Mamdani FIS wasstudied to predict the rainfall events in the Khorasan regionIn [22] flood events were predicted using numerical weatherprediction (NWP) with improved accuracy In [23] themain objective is to predict the high-risk area by water levelusing Artificial Neural Network in Masantol Pampanga In[24] a flood event prediction model based on SVM andboosting algorithm was presented Mitra et al [25] explainedthat flood forecasting employs the Internet of )ings andartificial neural networks based on the water level in a riverbasin In [26] the flood forecasting system development inthe upper reaches of the Zhangweihe River Basin was dis-cussed In [27] the grey model for flood forecasting based onthe rainfall and the flood index in Nanjing China wasstudied All the previous studies described flood forecastingbased on different methods and employed rainfall param-eters Gilbert Brunet described meteorological forecasting

using numerical weather prediction (NWP) and obtainedresults with good quality and accuracy with the complexityof numerical computing however a certain percentage forthe accuracy was not obtained [28] Mencattini et al utilizedthe type-2 fuzzy logic system in their system which aims atmeteorological forecasting )e measurement consists ofhumidity and temperature that was obtained from theNeuronica Lab at Politecnico of Torino (Italy) )is researchachieved accurate forecasting results even many hours inadvance with a mean absolute error of 338 for humidityand 82 for temperature [29] Hansen and Riordanemployed case-base reasoning (KNN method) and fuzzy settheory to predict the airport weather )e data tested weremore than 300000 hours of airport weather observationrecorded for 36 years )e testing methods used to solve theproblem were cloud ceiling and visibility of those airportsproduced by 6-hour predictions )e result showed goodaccuracy for the airport weather prediction [30] Ding et alemployed the artificial neurofuzzy inference system (ANFIS)and clustering technique )e ANFIS was used to make sureof the minimal errors of the parameters of membershipfunctions (MFs) and the design of MFs )e result wasefficient and close to that of actual load forecasting inpractice However the result had drawbacks of the neuralnetwork and was sensitive to the noise [31] Mountis andLevermore utilized the fuzzy logic artificial neural network(ANN) and neurofuzzy method to forecast the weather atthe Manchester International Airport for the years 1982ndash1995 which examined only summer data )e accuracy ofthe forecast depends on how well its parameters are definedand adjusted by the ANN method )e results of this re-search provided satisfactory MAE values neurofuzzy 17 ANN 18 and fuzzy logic 30 [32] Ahmad et al in theirresearch employed the ANN method with the supervisedlearning technique for forecasting )e study area in thisresearch was Senai Johor Malaysia Data inputs for theforecasting were pressure time of day dry bulb temper-ature wet bulb temperature dew point wind speed winddirection cloud cover and rainfall in the past hour )eaccuracy was 78 [33] Qin et al employed ANNs with agradient descent technique RPROP with dynamic tun-neling technique to train the actual data of past 24monthsin 1999ndash2000 with the data tested of six months (20011ndash20013 20017ndash20019) from Chongqing China )eresult gave faster convergence and global optimization forforecasting )e result is close to the real data [34] In [35]the flood prediction employing artificial neural networkwas described and the flood water level was successfullypredicted 24 hours 48 hours and 72 hours ahead of time)e results showed MAE varying from 06 to 09 and RMSEvarying from 005 to 011 In 2012 in a study case inTancheon South Korea Choi et al employed neurofuzzysystem to forecast the flood [36] )e results showed theaverage RMSE was 0367

)is study proposes a hybrid approach based on theneural network and fuzzy inference system for flood eventvulnerability namely hybrid neurofuzzy inference system(HN-FIS) )e HN-FIS is a model which can automaticallylearn and also obtain the output which can present the

2 Computational Intelligence and Neuroscience

essence of fuzzy logic )e system was applied in 31 sub-districts in Bandung )e flood forecasting depends onseveral variable inputs population density altitude of thearea and rainfall in time series from 2008 to 2012 )e maincontributions of this paper are (i) presenting a hybridforecasting for flood vulnerability based on the neuralnetwork and fuzzy inference system for accurate floodforecasting employing data variables which utilized Ban-dung database for flood vulnerability forecasting and (ii)developing an effective hybrid forecasting approach for floodvulnerability with higher accuracy

2 Study Area

)is study used data collected from Bandung West JavaProvince Indonesia (Figure 1) Geographical conditions of thesubdistricts have total area cover about 17623867Ha whichlies between longitudes 107022prime and 108050prime east and latitudes6041prime and 7019prime south Most of the area of Bandung is locatedbetween the surrounding hills andmountains To the north liesMount Bukittunggul with a height of 2200meters and MountTangkuban Perahu with a height of 2076meters which bordersWest Bandung and Purwakarta On the south there is MountPatuha with a height of 2249meters Mount Malabar with aheight of 2321meters Mount Papandayan with a height of2262meters and Mount Guntur with a height of 2249metersBandung has mountainous areas with an average slope of from0ndash8 8ndash15 to above 45 Bandung has a tropical climatethat is influenced by the monsoon climate with average rainfallbetween 2000mm and 3000mm per year (Table 1) Airtemperature ranges from 12degC to 24degC which results in airhumidity of about 78 in the rainy monsoon season and 70in the hot dry season

)e primary variables (Tables 1ndash3 used to obtain theflood forecasting value were divided into four parameters(population density altitude of the area rainfall and vul-nerability of flood) )e definitions of the main parametersand the fuzzy value are presented below

(1) Population density the population density of thesubdistricts in which the people are located )evalue zero means the population density is very low(less than or equal to 50 personskm2) )e value onemeans the population density is very high (that isgreater than 400 persons per square kilometer)

(2) Altitude of the area the distance above sea level ofthe land mountain sea bed or any other place If thealtitude of an area is less than 200meters above sealevel or coastal area it is shown in fuzzy as low level(value 0) and the altitude of area greater than350meters above sea level or mountain area meansthe altitude in high level (value 1)

(3) Rainfall according to the rate of rainfall it is clas-sified as low level ldquo0rdquo light rain which happens whenthe precipitation rate is less than 20mm per hourand high level ldquo1rdquo very heavy rain which happenswhen the precipitation rate is more than 100mm perhour

(4) Vulnerability of flood the inability to resist a flood orto respond when the flood occurs 0 safe (when thearea is secured from flood) and 1 danger (when thearea is under a threat of flood)

3 Material Parameters

)e flood vulnerability in 31 subdistricts in Bandung ispredicted using the Mamdani system Sugeno system andproposed flood forecasting model (HN-FIS) It consists ofthree inputs for vulnerability of flood level populationdensity altitude of the area and rainfall )e populationdensity is in the range of 350 to 9000 peoplekm2 )e al-titude of the area is in the range of 0 to more than1000meters above sea level (masl) )e rainfall is in therange of 0 to more than 200mm All the fuzzy models in thisresearch were applied in the trapezoidal type trying to findthe best one for the prediction of the vulnerability of floodevent )e classification of fuzzy sets employed in the floodforecasting method is presented in Table 4)ere are three orfour indexes to indicate the parameters according toTables 1ndash3 respectively )e inputs have three or fourmembership functions as shown in Tables 5ndash7 presented forthe population density altitude of the area and rainfall (alsoshown in Figures 2(a)ndash2(c)) respectively )e output (thevulnerability of flood) is taken in values ranging from 0 tomore than 374 presented for three conditions (safe alertand danger) as shown in Table 8 and Figure 3

According to Table 5 the population density has fourfuzzy classifications such as very low low high and over-population respectively (Table 2)

Table 6 describes the fuzzy classification for the altitudeof the three-level fuzzy area parameters such as lowmoderate and high

In Table 7 the fuzzy classification was divided into fourlevels such as low moderate high and extreme rainfall

Table 8 provides the fuzzy classification for the output ofthe vulnerability of flood It has three levels fuzzy safe alertand danger

4 Distributed Implementation of Hybrid FloodForecasting Model

Based on the measurement and theoretical analysis bothMamdani and Sugenomodels required a significant number offorecasting to obtain a higher level of accuracy for the vul-nerability of flood)e models considered the parameters thatare in flood forecasting We present the Mamdani model andthe Sugeno model for practically distributed flood prediction

41 Mamdani Fuzzy Inference System (Mamdani FIS)Mamdani and Assilian proposed the first type of fuzzy in-ference system (FIS) in 1975 [37] A Mamdani FIS has fuzzyinputs and fuzzy output )e architecture of the MamdaniFIS to show the mapping from input space into output spacecan be seen in Figure 4 (referred from [38])

According to Figure 4 the system of the crisp inputsource is first transformed by fuzzifier into a set of linguistic

Computational Intelligence and Neuroscience 3

variables in X )e fuzzy inference engine using the inputvariables and the rules to decide on the fuzzy rule basederives a set of conclusions in V Defuzzifier purpose toconvert into a crisp number which corresponds to the outputof the system [39]

42 Sugeno Fuzzy Inference System (Sugeno FIS) Takagi andSugeno proposed the first fuzzy inference system namelySugeno FIS in 1985 [40] and by Sugeno and Kang in 1988[41] A Sugeno FIS has fuzzy inputs and a crisp output

Referring to the same assumptions as for the MamdaniFIS the architecture for the Sugeno FIS is illustrated inFigure 5 (according to [38])

In this short of fuzzy inference system only the ante-cedents of the rules are fuzzy and it means the rules act as aninference mechanism themselves [38 41] )e main dif-ference of this architecture which compared with MamdaniFIS is that the Sugeno FIS does not require a defuzzificationto obtain a crisp result output from the rules consequents)e crisp result can be obtained employing a weightedaverage of the rules crisp consequents using the firingstrength level as weights [38 41 42]

43 Proposed Flood Forecasting Model Takagi and Sugeno[40] presented an adaptive neurofuzzy inference system thatwas obtained from the neural network and fuzzy logic [43]by catching the advantages of both in one framework )eneural network has the capability of automatic learningHowever this model cannot describe how it acquires theoutput from decision making On the other hand the fuzzylogic can obtain output out of the fuzzy logic decisionHowever it does not have the ability of learning automat-ically [44] Combining neural network and fuzzy logic cangenerate input and output data pairs and it has been suc-cessfully used in diverse fields at solving nonlinear issues andindicating problems [45] In this study the Sugeno fuzzymultilayer which is equivalent to a neural network and the

Source Google Maps

Figure 1 Study area map of Bandung West Java Indonesia

Table 1 Rainfall in 31 subdistricts in Bandung

MonthRain precipitation (mm)

2008 2009 2010 2011 2012January 265 2085 3533 63 829February 166 2005 5571 767 3037March 425 3657 531 894 1555April 342 1656 93 3815 2908May 132 1838 345 1934 2571June 20 101 1919 1176 605July 242 2208 772 342August 80 05 2208 31 0September 45 24 4244 1028 27October 303 2345 2922 1036 125November 455 3182 4014 3214 537December 333 2711 2375 259 637Rainfallyear 25660 20976 38684 17887 25107


Mamdani fuzzy inference system were combined to forma hybrid neurofuzzy inference system (HN-FIS) )e ad-vantage of the proposed model is its capability of auto-matically learning and obtaining an output of fuzzy logicdecision more clearly which can exhibit human judgmentreasonably

Considering Figures 4 and 5 have the same rule base andfuzzification for the variables there are several defuzzifierswhich can be chosen for a Mamdani FIS that originatesimilar results in a Sugeno FIS which means an inevitableoverlap between both types of systems )e Mamdani FIS ismore widely used particularly for decision support appli-cations andmostly refers to the intuitive and interpretabilitynature of the rule base On the other hand the Sugeno FIS donot have a linguistic term and this interpretability is par-tially lost [41 46] However since Sugeno FIS rulersquos con-sequents can have as many parameters per rule as inputvalues this translates into more degrees of freedom in itsdesign than a Mamdani FIS thus providing more flexibility[41] Mendel reaches this conclusion by comparing thenumber of possible design parameters for bothMamdani FISand Sugeno FIS for certain choices of input and outputvariables [41]

According to that fuzzy inference system many pa-rameters can be employed in the consequents of the rules of

Table 2 Population density in 31 subdistricts in Bandung

No SubdistrictPopulation density (peoplekm2)

2008 2009 2010 2011 20121 Ciwidey 1613 1643 1465 1490 15002 Rancabali 355 359 324 330 3323 Pasirjambu 342 346 334 339 3414 Cimaung 1357 1377 1328 1355 13785 Pangalengan 734 748 710 723 7286 Kertasari 463 466 432 428 4307 Pacet 1139 1151 1100 1120 11298 Ibun 1391 1406 1389 1417 14289 Paseh 2026 2055 2053 2098 211810 Cikancung 1936 1954 2028 2084 212311 Cicalengka 3030 3093 3059 3123 315212 Nagreg 1005 1022 985 1008 101813 Rancaekek 3634 3691 3675 3760 379514 Majalaya 6284 6399 5976 6079 612515 Solokan Jeruk 3353 3390 3230 3289 332416 Ciparay 3266 3306 3270 3336 336917 Baleendah 4532 4602 5364 5580 573018 Arjasari 1421 1444 1401 1429 144719 Banjaran 2618 2638 2667 2726 275520 Cangkuang 2456 2479 2640 2743 281221 Pameungpeuk 4552 4591 4757 4876 496122 Katapang 4109 4193 4682 4866 499723 Soreang 2034 2075 2068 2123 215724 Kutawaringin 5963 6102 6126 6295 637425 Margaasih 7100 7245 7482 7728 789526 Margahayu 11655 11788 11417 11607 1168727 Dayeuhkolot 10905 10993 10278 10388 1039628 Bojongsoang 3071 3120 3804 3983 413329 Cileunyi 4211 4254 5197 5482 570930 Cilengkrang 1436 1458 1559 1613 164831 Cimenyan 1833 1871 1971 2031 2078

Table 3 Altitude of the areas in 31 subdistricts in Bandung

No Subdistrict Altitude of the area (masl)1 Ciwidey 700ndash12002 Rancabali 1200ndash15503 Pasirjambu 1000ndash12004 Cimaung 765ndash10575 Pangalengan 984ndash15716 Kertasari 1250ndash18127 Pacet 700ndash11168 Ibun 700ndash12009 Paseh 600ndash80010 Cikancung 600ndash120011 Cicalengka 667ndash85012 Nagreg 715ndash94813 Rancaekek 608ndash68614 Majalaya 681ndash79615 Solokan Jeruk 671ndash70016 Ciparay 678ndash80517 Baleendah 600ndash71518 Arjasari 550ndash100019 Banjaran 750ndash80020 Cangkuang 700ndash71021 Pameungpeuk 650ndash67522 Katapang 675ndash70023 Soreang 700ndash82524 Kutawaringin 500ndash110025 Margaasih 60026 Margahayu 70027 Dayeuhkolot 60028 Bojongsoang 681ndash68729 Cileunyi 600ndash70030 Cilengkrang 600ndash170031 Cimenyan 750ndash1300

Table 4 Example of fuzzy sets in flood forecasting

Populationdensity

Altitude ofthe area Rainfall Vulnerability

of floodVery low Low Low SafeLow Moderate Moderate AlertHigh High High DangerOver Extreme

Table 5 Fuzzy classification of population density

Population densityrating Very low Low High Over

Population density(peoplekm2) lt350 [350 3350] [3500 9000] gt9000

Table 6 Fuzzy classification of the altitude of the area

Altitude of area rating Low Moderate HighAltitude of the area (masl) lt500 [500 1000] gt1000

Table 7 Fuzzy classification of rainfall

Rainfall rating Low Moderate High ExtremeRainfall value (mm) [0 50] [50 100] [100 200] gt200


a Sugeno FIS which reasonably approximates a MamdaniFIS is session described how the proposed ood fore-casting model (hybrid neurofuzzy inference system (HN-FIS)) works

e Takagi-Sugeno (Sugeno) fuzzy model and Mam-dani fuzzy model are two great fuzzy rule-based inferencesystems e Sugeno fuzzy inference system works wellwith linear techniques and guarantees continuity of theoutput surface [40 47] However the Sugeno fuzzy modelhas diculties in dealing with the multiparameter syntheticevaluation It has diculties in assigning weight to eachinput and fuzzy rule e Mamdani fuzzy model has hadsome advantages such as its intuitive widespread accep-tance and well suitable to human cognition [37 48 49]e researchers employed the Mamdani model and theSugeno model as a proposed ood forecasting model(hybrid neurofuzzy inference system) which shows theadvantages of those models in the output statement whichis more readibility and easy to understand even by thelayperson

A function needs to be assigned to specify the operationof the Mamdani fuzzy model entirely with the followingsteps

0 05 1 15 2 25 3

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es

Crisp population density values (timeslowast104 personskm2)

Very lowLow

HighVery high

(a)

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es

0 2 4 8 10 14 16Crisp altitude of area values (timeslowast102 masl)

6 12 18

LowMiddleHigh

(b)

Crisp rainfall values (timeslowast102 mm)

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es

ModerateLight Heavy

Very heavy

0 1 2 3 4 5 6

(c)

Figure 2 Membership function curves of ood forecasting fuzzy variable premises

Table 8 Fuzzy classication of the vulnerability of ood

Vulnerability of ood rating Safe Alert DangerVulnerability of ood lt248 [248 374] gt374

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es

100 150 200 250Crisp vulnerability of flood

300 350 400

SafelyAlertDanger

Figure 3 Membership function curves of ood forecasting fuzzyvariable output


Fuzzy rule baseR1 if A1 is P1 AND hellip AND Am is Pn THEN Z is V1

Rn if A1 is Pn AND hellip AND Am is Pnm THEN Z is Vn

Fuzzifier steps Defuzzifier steps

Fuzzy inference engine

Fuzzy sets in X Fuzzy sets in V

A in XZ in V

if A is P then Z is VA is Plowast Z is Vlowast

Figure 4 Mamdani fuzzy inference system architecture

R1 if A1 is P1 AND hellip AND Am is Pn THEN Z = C0 + C1V1 + CmVm

Rn if A1 is Pn AND hellip AND Am is Pnm THEN Z = C0n + CnVn + CmnVmn

Fuzzifier Weighted average

β1 Z1

βn Zn

Figure 5 e architecture of the Sugeno fuzzy inference system

P

A

P1

P2

P3

P4

A1

A2

A3

R

R1

R2

R3

R4

Π

Π

Π

Π

B1

B2

B3

Bn

Σg

w1

w2

w3

wn

Figure 6 Proposed ood forecasting model (HN-FIS) architecture


(1) Operator OR or operator AND to the rule firingstrength computation with ORrsquoed or ANDrsquoedreferences

(2) Consequent membership function calculated fromthe implication operator based on a given firingstrength

(3) Aggregate operator used to produce overall outputmembership function by combining the aggregatedqualified consequents

(4) Defuzzification operator aims to transform an out-put membership function to a crisp single outputvalue

If the first step is the AND operator the second step is aproduct the third step is the sum and the fourth step is thecentroid of the area (COA) [50 51] we can derive thefollowing equations )e advantage of applying hybridneurofuzzy inference system (HN-FIS) model is the ability oflearning because of differentiability during computation

Equations (1) and (2) [37] provide the sum-productcomposition )e final crisp output when using centroiddefuzzification is equal to the weighted average of thecentroid of consequent membership functions

δ ri( 1113857 w ri( 1113857 times α (1)

where δ(ri) is the weighted factor of ri ri is the ith fuzzy rulew(ri) is the firing strength of ri and α is the area of theconsequent membership functions of ri

ZCOA 1113938

n

Zi1μBprime(z)z dz

1113938n

Zi1μBprime(z) dz

w1α1z1 + + wnαnzn

w1α1 + + wnαn

(2)

where αi and zi are the area and the center of the consequentmembership function μBi(z) respectively

)e rules of the HN-FIS model are given as follows

Rule 1(r1) if P is P1 A is A1 and R is R1 then ZB1Rule 2 (r2) if P is P2 A is A2 and R is R2 then ZB2

Rule n(rn) if P is Pn A is An and Rf is Rfn then ZBn

According to the rules the HN-FIS model can beexpressed as shown in Figure 6

P A and R represent the inputs which are popula-tion density (Table 5) altitude of the area (Table 6) andrainfall (Table 7) P1 P2 P3 and P4 represent themembership functions of population density A1 A2 andA3 represent the membership functions of the altitude ofthe area R1 R2 R3 and R4 represent the membershipfunctions of rainfall )e firing strength denoted as w1w2 wn B1 B2 Bn represents the following pa-rameters which need to be adjusted )e consequentparameter B is a multiplication of αi and zi (according to(2)) )e membership function of the vulnerability outputis denoted as g

)e HN-FIS architecture is composed of five layers andFigure 6 illustrates the output of each layer

First layer fuzzification layer

L1i μPi(P) i 1 2 3 4

L1i μAiminus4(A) i 5 6 7

L1i μRiminus7(R) i 8 9 10 11

(3)

)e membership function is the generalized trapezoidalfunction denoted as follows

μPi(P)

0 Plt si

Pminus si

ti minus si

si lePle ti

1 ti lePle ui

vi minusP

vi minus ui

ui lePle vi

0 vi leP

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μAi(A)

0 Alt si

Aminus si

ti minus si

si leAle ti

1 ti leAle ui

vi minusA

vi minus ui

ui leAle vi

0 vi leA

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μRi(R)

0 Rlt si

Rminus si

ui minus si

si leRle ui

1 ti leRle ui

vi minusR

vi minus ui

ui leRle vi

0 vi leR

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)

P is the crisp value (real value) of population densityA isthe crisp value of altitude of the area and R is the crisp valueof rainfall si ti ui vi is the premise parameter or the setparameter which is used to denote the membership func-tions in this model

Second layer the layer of rule or the layer ofinference


L2i wi μPi(P) x μAi(A) x μRi(R) i 1 2 3 4

(5)

In this layer the product method is generated for thefiring strength wi

ird layer implication layer

L3i wi ∘Bi i 1 2 3 48 (6)

)e product of this layer comes from the implicationoperator

Fourth layer aggregation layer

L4i O1 1113944n48

i1wi ∘Bi i 1 2 3 48 (7)

)e result of this layer is the sum of all implicationoperators in the implication layer )e following parametersare denoted by Bi

Fifth layer defuzzification layer

L5 O2 g D ∘O1 (8)

)e defuzzification (D) method and center of the area(COA) were achieved to produce the crisp output g

In this paper the trapezoidal functions generalized wereused for the type of membership functions (MFs) of the

inputs and had four nonlinear parameters to be adjusted (siti ui vi))eMFs of population density have four nonlinearparameters (shown in Table 5 and Figure 2(a)) )e MFs ofthe altitude of the area have three nonlinear parameters(shown in Table 6 and Figure 2(b)) )e MFs of rainfall havefour nonlinear parameters (shown in Table 7 andFigure 2(c)) In this model premise parameters are 48 andfollowing parameters are 96 Hence the total number of thenonlinear parameter is 140

44 Evaluation Criteria for Model Performance If Mi is themeasured value for the number of subdistricts and Pi is theprediction value in the same subdistricts then the error (Ei)is defined as

Ei Mi minusPi (9)

Since there are measured values and predictions for nsubdistricts there will be n error terms and the standardstatistical measures can be defined as follows

Mean absolute error (MAE) is the average of all absoluteerrors meaning the amount of all absolute errors divided bythe number of errors )e equation of MAE is as follows

MAE 1n

1113944

n

i1Ei

11138681113868111386811138681113868111386811138681113868

11139741113972

times 100 (10)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alue

s of v

ulne

rabi

lity

of fl

ood

31 subdistricts in Bandung Regency

M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(a)

500

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(b)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(c)

Figure 7 Vulnerability values of flood (a) proposedmodel (HN-FIS) (b) Mamdani model and (c) Sugeno model in 2008 2009 2010 2011and 2012 respectively


Root mean square error (RMSE) is the square root of theaverage of squared dierences between the measured valueand the predicted value shown in the following equation

RMSE 1n

sumn

i1Ei∣∣∣∣∣∣∣∣2

radicradic

times 100 (11)

e mean absolute error is dened by rst making eacherror positive by taking its absolute value and then averaging

the result in the square root e RMSE is dened by thesimilar idea of the mean absolute error In RMSE the errorsare made positive by squaring each one and then thesquared root errors are averaged e MAE has the ad-vantage of being more interpretable and easier to describenonspecialists e RMSE has the advantage of being easierto handle mathematical problems Each of these statisticsdeals with measures of accuracy whose size depends on thescale of the data [32 52]

Proposed modelSugenoMamdani

Erro

r (

)

3

2

1

0

ndash10 10 20

31 subdistricts in Bandung Regency30 40

(a)


Erro

r (

)

2

15

1

05

00 10 20


(b)


4

2

Erro

r (

)

0

ndash20 10 20


(c)


Erro

r (

)

10

0

ndash10

ndash20

ndash300 10 20


(d)


3

2

1

Erro

r (

)

0

ndash10 10 20


(e)

Figure 8 Comparing error of the Mamdani model Sugeno model and proposed model (HN-FIS) in (a) 2008 (b) 2009 (c) 2010 (d) 2011and (e) 2012


5 Results and Discussion

)e discussion of the results begins with explanation of theperformance of the proposed vulnerability of the floodforecastingmodel based on the neurofuzzy system approachnamely HN-FIS )e flood forecasting models are developedemploying MATLAB 2017 software [53] )e results arepresented as follows

In our experiment three graphics illustrated in Figure 7are the result of the vulnerability of flood forecastingemploying three models Mamdani Sugeno and HN-FISrespectively applied in 31 subdistricts in Bandung Indonesia)ose models have used to design of experiment to find thebest model which could affect the accuracy of flood vul-nerability forecasting Figure 7 shows also that all of themodels have similar values from the measured data andpredicted data Further analysis showed that the high accuracyachieved by three models to decide the vulnerability of floodin Bandung (shown in Figure 8) is based on Equation (10)

In order to evaluate the performance of the proposedmodel other commonly used techniques such as the Mam-dani model and the Sugeno model were employed forcomparison purposes )e forecasting errors obtained arepresented in Table 9 For MAE measurement the averageerror is 17797 14035 and 12556 for the Mamdanimodel the Sugeno model and the proposed flood forecastingmodel (HN-FIS) respectively )ese average values in RMSEmeasurement are 00382 19479 and 00371 for the

Mamdani model the Sugeno model and the proposed model(HN-FIS) respectively )e results showed that the proposedmodel reduces on flood vulnerability forecasting errorsconsiderably in 31 subdistricts in Bandung indicating thegreat improvement in flood vulnerability forecasting accuracy

Figure 9 illustrates MAE and RMSE values in threemodels for flood vulnerability forecasting )e proposedmodel outperforms the other models and forecasted valuescorrectly following the trend of flood variation

Compared with the other methods presented in theliterature using other databases the proposed hybrid modelprovides reliable flood vulnerability forecasting as shown inTable 9 In [35] the accuracy obtained in terms of MAE from0627 to 09357 and RMSE from 00523 to 01154 for floodprediction of 24 hours to 72 hours ahead of time In [36] theaccuracy of the average RMSE was 0367 for flood fore-casting in Tancheon Basin in Korea )e RMSE obtainedwith the proposedmodel varies from 00126 to 00548 forflood vulnerability forecasting It means if an error is smallthen accuracy will be close to real data and the model willgive better flood vulnerability forecasting result )e pro-posed model achieved improvement in accuracy comparedto the existing algorithms

6 Conclusions

Neural network adopts a linear equation in the consequentpart which cannot present human assessment reasonably In

Table 9 MAE and RMSE of the Mamdani model the Sugeno Model and the proposed flood forecasting model (HN-FIS)

Forecasting modelMAE () RMSE ()

2008 2009 2010 2011 2012 2008 2009 2010 2011 2012Mamdani 08496 15693 11420 40662 12714 00302 00628 00354 00154 00473Sugeno 02425 10729 08213 40499 08307 07519 42681 15261 04739 27197HN-FIS 03489 05825 07382 40950 05133 00126 00477 00548 00294 00410

Data time series in 2008ndash2012

Mea

n ab

solu

te er

ror (

)

0

1

3

2

4

5

ndash12008 2009 2010 2011 2012

MAE-proposed modelMAE-SugenoMAE-Mamdani

(a)


Root

mea

n sq

uare

erro

r (

)0

1

3

2

4

5

2008 2009 2010 2011 2012

RMSE-proposed modelRMSE-SugenoRMSE-Mamdani

(b)

Figure 9 (a) MAE and (b) RMSE between Mamdani vs Sugeno vs proposed model (HN-FIS)


this case we propose the hybrid model based on neuralnetwork and fuzzy inference system (HN-FIS) which hasgreater advantages in the following part and intuitive part offuzzy reasoning )e proposed model has been constructedby a hybrid technique of the Mamdani model and Sugenomodel based on the neurofuzzy inference system approach)e HN-FIS model can show its readability and un-derstandability and present the essence of fuzzy logic moreclearly )e current study aimed to determine and optimizethe performance of the proposed model (HN-FIS) Assupported by measurement and the predicted values basedon simulation the proposed model compares favorably withthe Mamdani model and the Sugeno model in the capa-bilities of predicting the vulnerability of flood in 31 sub-districts in Bandung Indonesia )e most apparent findingto emerge from this study is that three model flood fore-casting (Mamdani Sugeno and proposed model) achievedthe performance of more than 96 However the proposedmodel (HN-FIS) achieved the lowest error rate in bothRMSE and MAE (00371 and 12556 respectively) andobtained the best performance in flood vulnerability fore-casting compared with existing models

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)ere are no conflicts of interest to declare in this paper

Acknowledgments

)e authors thank Prof Hou Rongtao and Dr Irfan Dwi-guna Sumitra for their support in this research

References

[1] I D Sumitra R Hou and S Supatmi ldquoDesign and de-ployment of wireless sensor networks for flood detection inIndonesiardquo in Proceeding of International Conference onCloud Computing and Security 2017 (ICCCS2017) CloudComputing and Security Nanjing China October 2017

[2] P R Jagannadha P M Bhacya V Sridevi and UshaRanildquoDetection of rain fall and wind direction using wirelessmobile multi-node energy efficient sensor networkrdquo In-ternational Journal of Applied Information Systems (IJAIS)vol 3 no 9 2012

[3] R Davies ldquoAsia news Indonesia-floods in Bandung WestJava leave 1 deadrdquo March 2018 httpfloodlistcomasiaindonesia-floods-bandung-west-java-leave-1-dead

[4] National Disaster Management Authority (BNPB) March2018 httpbnpbgoid

[5] R Davies ldquoAsia news Indonesia-floods in Gorontalo forcethousands to evacuaterdquo March 2018 httpfloodlistcomasiaindonesia-floods-gorontalo-october-2016

[6] R Davies ldquoAsia news Indonesia-100000 evacuate floods inWest Nusa Tenggarardquo March 2018 httpfloodlistcomasiaindonesia-floods-bima-west-nusa-tenggara

[7] R Davies ldquoAsia news Indonesia-7000 affected by floods inSulawesi and Belitungrdquo March 2018 httpfloodlistcomasiaindonesia-7000-affected-floods-sulawesi-belitung

[8] R Davies ldquoAsia news Indonesia-6 killed in floods andlandslides in West Sumatrardquo March 2018 httpfloodlistcomasiaindonesia-floods-landslides-west-sumatra-march-2017

[9] N Dunstan ldquoGenerating domain-specific web-based expertsystemsrdquo Expert Systems with Applications vol 35 pp 686ndash690 2008

[10] B Kishan V Chada and C Maini ldquoA review of developmentand application of expert systemrdquo International Journal ofAdvanced Research in Computer Science and Software Engi-neering vol 2 pp 319ndash325 2012

[11] A K Deb ldquoObject-oriented expert system estimated lineampacityrdquo IEEE Computer Applications in Power vol 8 no 3pp 30ndash35 1994

[12] M K Priyan and U D Gandhi ldquoA novel three-tier Internet of)ings architecture with machine learning algorithm for earlydetection of heart diseasesrdquo Computers and Electrical Engi-neering vol 65 pp 222ndash235 2018

[13] M K Priyan S Lokesh R Varatharajan G C Babu andP Parthasarathy ldquoCloud and IoT based disease predictionand diagnosis system for healthcare using Fuzzy neuralclassifierrdquo Future Generation Computers Systems vol 86pp 527ndash534 2018

[14] S A Asklany K Elhelow I K Youssef and M El-WahabldquoRainfall events prediction using rule-based fuzzy inferencesystemrdquo Atmospheric Research vol 101 pp 28ndash236 2011

[15] C Li-Chiu C Fi-John and T Ya-Hsin ldquoFuzzy exemplar-based inference system for flood forecastingrdquoWater ResourcesResearch vol 41 2005

[16] B de Bryun L Fayet and F Laborie ldquoAssessing floodforecasting uncertainty with fuzzy arithmeticrdquo in Proceedingsof FLOOD Risk-3rd European Conference on Flood RiskManagement European Lyon France October 2016

[17] A Y Ardiansyah R Sarno and O Giandi ldquoRain detectionsystem for estimate weather level using Mamdani fuzzy in-ference systemrdquo in Proceedings of International Conference onInformation and Communication Technology (ICOIACT)Yogyakarta Indonesia March 2018

[18] K K Uraon and S Kumar ldquoAnalysis of defuzzificationmethod for rainfall eventrdquo International Journal of ComputerScience andMobile Computing vol 5 no 1 pp 341ndash354 2016

[19] N Fhira and Adiwijaya ldquoA rainfall forecasting using fuzzysystem based on genetic algorithmrdquo in Proceedings of In-ternational Conference of Information and CommunicationTechnology (ICoICT) Bandung Indonesia March 2013

[20] A A Alfin and R Sarno ldquoSoil irrigation fuzzy estimate ap-proach based on decision making in sugarcane industryrdquo inProceedings of International Conference of Information andCommunication Technology (ICoICT) Indonesia October 2017

[21] G A Fallah M M Baygi and M H Nokhandan ldquoAnnualrainfall forecasting by using Mandani inference systemrdquoResearch Journal of Environmental Sciences vol 5 no 1pp 341ndash354 2009

[22] J TanZouak N Bame B Yenke and I Sarr ldquoA system toimprove the accuracy of numeric weather prediction (NWP)for flood forecasting systemrdquo in Proceedings of 13th In-ternational Conference on Signal-Image Technology andInternet-Based System(SITIS) 2017

[23] M A Sahagun J C Dela Cruz and R G Garcia ldquoWirelesssensor nodes for flood forecasting using artificial neuralnetworkrdquo in Proceedings of 2017 IEEE 9th InternationalConference on Humanoid Nanotechnology Information


Technology Communication and Control Environment andManagement (HNICEM) Pasay City Philippines December2017

[24] S Li M A Kaikai Z Jin and Y Zhu ldquoA new flood fore-casting model based on SVM and boosting learning algo-rithmsrdquo in Proceedings of IEEE Congress on EvolutionaryComputation (CEC) Vancouver Canada July 2016

[25] P Mitra R Ray and R Chatterjee ldquoFlood forecasting usinginternet of things and artificial neural networkrdquo in Proceedingsof 2016 IEEE 7th Annual Information Technology Electronicsand Mobile Communication Conference (IEMCON) Vancou-ver BC Canada November 2016

[26] J Sun and W Liao ldquoDevelopment of a flood forecastingsystem and its application to upper reaches of ZhangweiheRiver Basinrdquo in Proceedings of 2012 International Symposiumon Geomatics for Integrated Water Resource ManagementLanzhou China October 2012

[27] Y Zhengwei and L Zonghua ldquoGrey model used flood riskyears forecasting in Nanjing Chinardquo in Proceedings of 2ndConference on Environmental Science and Information Ap-plication Technology IEEE Wuhan China July 2010

[28] B Gilbert ldquo)e first hundred years of numerical weatherprediction recherche en prevision numerique environmentCanadardquo in Proceedings of 19th International Symposium onHigh Performance Computing System and Applications(HPCSrsquo05) Guelph Canada May 2005

[29] A Mencattini M Salmeri S Bertazzoni R LojaconoE Pasero and W Moniaci ldquoLocal meteorological forecastingby type-2 fuzzy systems time series predictionrdquo in Proceedingsof IEEE International Conference on Computational In-telligence for Measurement Systems and Applications GiardiNaxos Italy July 2005

[30] B K Hansen and D Riordan ldquoWeather prediction usingcase-base reasoning and fuzzy set theoryrdquo MS )esisTechnical University of Nova Scotia Halifax Nova ScotiaCanada 2005

[31] W Ding F-G Dong and S-D Yang ldquoLoad forecasting basedon clustering analysis using fuzzy logicrdquo in Proceedings of GeFourth International Conference on Machine Learning andCybernetics pp 18ndash21 Guangzhou China August 2005

[32] A Mountis and G Levermore ldquoWeather prediction forfeedforward control working on the summer datardquo IEEEpp 334ndash340 2005

[33] A M Ahmad C S Chuan and F Mohamad ldquoWeatherprediction using artificial neural networkrdquo in Proceedings ofGe International Conference on CircuitsSystems Computers2002

[34] Z Qin J Yang HWang and J Zou ldquoNeural network based ondynamic tunneling technique for weather forecastrdquo in Pro-ceedings of 11th Pacific Rim International Symposium on De-pendable Computing (PRDCrsquo05) Hunan China December2005

[35] A Paul and P Das ldquoFlood prediction model using artificialneural networkrdquo International Journal of Computer Appli-cations Technology and Research vol 3 no 7 pp 473ndash4782014

[36] C Choi J Ji M Yu T Lee M Kang and J Yi ldquoUrban floodforecasting using a neuro-fuzzy techniquerdquo Urban Watervol 122 pp 249ndash259 2012

[37] E H Mamdani and S Assillian ldquoAn experimental in lin-guistic synthesis with a fuzzy logic controllerrdquo InternationalJournal of Man-Machine Studies vol 7 no 1 pp 1ndash13 1975

[38] L-X Wang Adaptive Fuzzy System and Control Design andStability Analysis Prentice-Hall Upper Saddle River NJUSA 1994

[39] A M Sirwan and B S Sattar ldquoA comparison ofMamdani andSugeno fuzzy inference systems based on block chipperevaluationrdquo International Journal of Scientific and Engi-neering Research vol 4 no 12 2013

[40] T Takagi and M Sugeno ldquoFuzzy identification of system andits application to modeling and controlrdquo IEEE Transaction onSystems man and Cybernetics vol 15 no 1 pp 116ndash1321985

[41] J Mendel Uncertain Rule-based Fuzzy Inference SystemsIntroduction and New Directions Prentice-Hall Upper SaddleRiver NJ USA 2001

[42] T J Ross Fuzzy Logic with Engineering Applications JohnWilley and Sons Ltd Hoboken NJ USA 2004

[43] J-S R Jang ldquoANFIS-adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[44] W Phootrakornchai and S Jiriwibhakorn ldquoOnline criticallearning time estimation using an adaptive neuro-fuzzy in-ference system (ANFIS)rdquo International Journal of ElectricalPower and Energy Systems vol 73 pp 170ndash181 2015

[45] M Rezakazemi A Dasthi M Asghari and S Shirazian ldquoH2-selective mixed matrix membranes modeling using ANFISPSO-ANFIS GA-ANFISrdquo International Journal of HydrogenEnergy vol 42 no 22 pp 15211ndash15225 2017

[46] J Jassbi S H Alavi J A Paulo and A R Rita ldquoTrans-formation of Mamdani FIS to first order Sugeno FISrdquo inProceedings of IEEE International Fuzzy Systems ConferenceLondon UK June 2007

[47] T Takagi and M Sugeno ldquoDerivation of Fuzzy Control rulesfrom Human Operators Control Actionsrdquo in Proceedings ofIFAC Symposium on Fuzzy Information Knowledge Pre-sentation and Decision Analysis pp 55ndash60 New York NYUSA July 1983

[48] F Esragh and E H Mamdani A General Approach to Lin-guistic Approximation Fuzzy Reasoning and its ApplicationAcademic Press Cambridge MA USA 1981

[49] E H Mamdani ldquoApplication of fuzzy logic to approximatereasoning using linguistic synthesisrdquo IEEE Transactions onComputers vol 26 no 12 pp 1182ndash1191 1997

[50] R R Yager and D P Pilev ldquoSLIDE a simple adaptivedefuzzification methodrdquo IEEE Transaction on Fuzzy Systemsvol 1 no 1 pp 69ndash78 1992

[51] P Mahalakshmi and K Ganesan ldquoMamdani fuzzy rule-basedmodel to classify sites for aquaculture developmentrdquo IndianJournal of Fisheries vol 62 no 1 pp 110ndash115 2015

[52] A Shahi A B Rodziah and M D Nasir ldquoAn effective fuzzyC-mean and type-2 fuzzy logic for weather forecastingrdquoJournal of Georetical and Applied Information Technologypp 556-557 2009

[53] MATLAB software January 2018 httpschmathworkscomcampaignsproducts


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Submit your manuscripts atwwwhindawicom

outage and over one hundred electrical substations wereshut down leaving almost 15000 houses without electricity[4 8]

)e answer to overcome the flood disaster by applyingthe fuzzy system is assisting predicting and deciding theseevents In 1965 Lotfi a mathematician who created thetheory of fuzzy logic derived the result of the insufficiency ofBoolean algebra for many real-world problems [9 10] Infact as most of the information is imprecise one of thehumanrsquos greatest abilities is to process inaccurate problemsand vague information efficiently )e Oxford English Dic-tionary defined the word ldquoFuzzyrdquo as blurred indistinctimprecisely defined confused or vague )e fuzzy systemsare knowledge-based or rule-based systems )e heart of afuzzy system is the so-called knowledge-based fuzzy IF-THEN rules [11]

Many researchers have argued on meteorological fore-casting with the purpose to help assessing the disasterimpact in some regions Forecasting is also used in otherareas such as detection and prediction of diseases [12 13]Asklany et al [14] proposed the probabilistic predictionusing two skill scores namely the Brier Score and FrictionScore )ose researchers mentioned that the rainfall eventprediction was highly accurate with the data aggregated bythe stations with increasing output toward the real-timeevent Otherwise the fuzzy inference system output precedesthe recorded maximum data in six hours before the rainfallLi-Chiu et al [15] introduced a model to predict the stream-flow an hour after a flood event occurs )ey also comparedthe result using a fuzzy exemplar-based inference systemwith backpropagation neural network to show that a fuzzymodel performs better than the neural network de Bryunet al [16] described a method based on fuzzy arithmetic toestimate the possible range of flow rates and water levelbased on possible rainfall events by the forcing and un-certainty model A previous research [17] explained a rainfalllevel detection system to predict the weather using theMamdani method In [18] the rainfall event was analyzedusing the defuzzification method In [19] the genetic al-gorithm (GA) was discussed to obtain a higher accuracy ofthe rainfall forecasting system In [20] the agricultural ir-rigation control using the fuzzy method for determiningwater quantities was studied In [21] the Mamdani FIS wasstudied to predict the rainfall events in the Khorasan regionIn [22] flood events were predicted using numerical weatherprediction (NWP) with improved accuracy In [23] themain objective is to predict the high-risk area by water levelusing Artificial Neural Network in Masantol Pampanga In[24] a flood event prediction model based on SVM andboosting algorithm was presented Mitra et al [25] explainedthat flood forecasting employs the Internet of )ings andartificial neural networks based on the water level in a riverbasin In [26] the flood forecasting system development inthe upper reaches of the Zhangweihe River Basin was dis-cussed In [27] the grey model for flood forecasting based onthe rainfall and the flood index in Nanjing China wasstudied All the previous studies described flood forecastingbased on different methods and employed rainfall param-eters Gilbert Brunet described meteorological forecasting

using numerical weather prediction (NWP) and obtainedresults with good quality and accuracy with the complexityof numerical computing however a certain percentage forthe accuracy was not obtained [28] Mencattini et al utilizedthe type-2 fuzzy logic system in their system which aims atmeteorological forecasting )e measurement consists ofhumidity and temperature that was obtained from theNeuronica Lab at Politecnico of Torino (Italy) )is researchachieved accurate forecasting results even many hours inadvance with a mean absolute error of 338 for humidityand 82 for temperature [29] Hansen and Riordanemployed case-base reasoning (KNN method) and fuzzy settheory to predict the airport weather )e data tested weremore than 300000 hours of airport weather observationrecorded for 36 years )e testing methods used to solve theproblem were cloud ceiling and visibility of those airportsproduced by 6-hour predictions )e result showed goodaccuracy for the airport weather prediction [30] Ding et alemployed the artificial neurofuzzy inference system (ANFIS)and clustering technique )e ANFIS was used to make sureof the minimal errors of the parameters of membershipfunctions (MFs) and the design of MFs )e result wasefficient and close to that of actual load forecasting inpractice However the result had drawbacks of the neuralnetwork and was sensitive to the noise [31] Mountis andLevermore utilized the fuzzy logic artificial neural network(ANN) and neurofuzzy method to forecast the weather atthe Manchester International Airport for the years 1982ndash1995 which examined only summer data )e accuracy ofthe forecast depends on how well its parameters are definedand adjusted by the ANN method )e results of this re-search provided satisfactory MAE values neurofuzzy 17 ANN 18 and fuzzy logic 30 [32] Ahmad et al in theirresearch employed the ANN method with the supervisedlearning technique for forecasting )e study area in thisresearch was Senai Johor Malaysia Data inputs for theforecasting were pressure time of day dry bulb temper-ature wet bulb temperature dew point wind speed winddirection cloud cover and rainfall in the past hour )eaccuracy was 78 [33] Qin et al employed ANNs with agradient descent technique RPROP with dynamic tun-neling technique to train the actual data of past 24monthsin 1999ndash2000 with the data tested of six months (20011ndash20013 20017ndash20019) from Chongqing China )eresult gave faster convergence and global optimization forforecasting )e result is close to the real data [34] In [35]the flood prediction employing artificial neural networkwas described and the flood water level was successfullypredicted 24 hours 48 hours and 72 hours ahead of time)e results showed MAE varying from 06 to 09 and RMSEvarying from 005 to 011 In 2012 in a study case inTancheon South Korea Choi et al employed neurofuzzysystem to forecast the flood [36] )e results showed theaverage RMSE was 0367

)is study proposes a hybrid approach based on theneural network and fuzzy inference system for flood eventvulnerability namely hybrid neurofuzzy inference system(HN-FIS) )e HN-FIS is a model which can automaticallylearn and also obtain the output which can present the



2 Study Area























Source Google Maps















Populationdensity














0 05 1 15 2 25 3

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


Very lowLow

HighVery high

(a)

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


6 12 18

LowMiddleHigh

(b)


1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es

ModerateLight Heavy

Very heavy

0 1 2 3 4 5 6

(c)




1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


300 350 400

SafelyAlertDanger








A in XZ in V






β1 Z1

βn Zn


P

A

P1

P2

P3

P4

A1

A2

A3

R

R1

R2

R3

R4

Π

Π

Π

Π

B1

B2

B3

Bn

Σg

w1

w2

w3

wn









δ ri( 1113857 w ri( 1113857 times α (1)


ZCOA 1113938

n

Zi1μBprime(z)z dz

1113938n

Zi1μBprime(z) dz

w1α1z1 + + wnαnzn

w1α1 + + wnαn

(2)









L1i μPi(P) i 1 2 3 4



(3)


μPi(P)

0 Plt si

Pminus si

ti minus si

si lePle ti

1 ti lePle ui

vi minusP

vi minus ui

ui lePle vi

0 vi leP

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μAi(A)

0 Alt si

Aminus si

ti minus si

si leAle ti

1 ti leAle ui

vi minusA

vi minus ui

ui leAle vi

0 vi leA

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μRi(R)

0 Rlt si

Rminus si

ui minus si

si leRle ui

1 ti leRle ui

vi minusR

vi minus ui

ui leRle vi

0 vi leR

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)





(5)



L3i wi ∘Bi i 1 2 3 48 (6)



L4i O1 1113944n48

i1wi ∘Bi i 1 2 3 48 (7)



L5 O2 g D ∘O1 (8)





Ei Mi minusPi (9)



MAE 1n

1113944

n

i1Ei

11138681113868111386811138681113868111386811138681113868

11139741113972

times 100 (10)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alue

s of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(a)

500

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(b)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(c)




RMSE 1n

sumn

i1Ei∣∣∣∣∣∣∣∣2

radicradic

times 100 (11)




Erro

r (

)

3

2

1

0

ndash10 10 20


(a)


Erro

r (

)

2

15

1

05

00 10 20


(b)


4

2

Erro

r (

)

0

ndash20 10 20


(c)


Erro

r (

)

10

0

ndash10

ndash20

ndash300 10 20


(d)


3

2

1

Erro

r (

)

0

ndash10 10 20


(e)










6 Conclusions






Mea

n ab

solu

te er

ror (

)

0

1

3

2

4

5

ndash12008 2009 2010 2011 2012


(a)


Root

mea

n sq

uare

erro

r (

)0

1

3

2

4

5

2008 2009 2010 2011 2012


(b)




Data Availability




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





2 Study Area























Source Google Maps















Populationdensity














0 05 1 15 2 25 3

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


Very lowLow

HighVery high

(a)

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


6 12 18

LowMiddleHigh

(b)


1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es

ModerateLight Heavy

Very heavy

0 1 2 3 4 5 6

(c)




1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


300 350 400

SafelyAlertDanger








A in XZ in V






β1 Z1

βn Zn


P

A

P1

P2

P3

P4

A1

A2

A3

R

R1

R2

R3

R4

Π

Π

Π

Π

B1

B2

B3

Bn

Σg

w1

w2

w3

wn









δ ri( 1113857 w ri( 1113857 times α (1)


ZCOA 1113938

n

Zi1μBprime(z)z dz

1113938n

Zi1μBprime(z) dz

w1α1z1 + + wnαnzn

w1α1 + + wnαn

(2)









L1i μPi(P) i 1 2 3 4



(3)


μPi(P)

0 Plt si

Pminus si

ti minus si

si lePle ti

1 ti lePle ui

vi minusP

vi minus ui

ui lePle vi

0 vi leP

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μAi(A)

0 Alt si

Aminus si

ti minus si

si leAle ti

1 ti leAle ui

vi minusA

vi minus ui

ui leAle vi

0 vi leA

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μRi(R)

0 Rlt si

Rminus si

ui minus si

si leRle ui

1 ti leRle ui

vi minusR

vi minus ui

ui leRle vi

0 vi leR

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)





(5)



L3i wi ∘Bi i 1 2 3 48 (6)



L4i O1 1113944n48

i1wi ∘Bi i 1 2 3 48 (7)



L5 O2 g D ∘O1 (8)





Ei Mi minusPi (9)



MAE 1n

1113944

n

i1Ei

11138681113868111386811138681113868111386811138681113868

11139741113972

times 100 (10)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alue

s of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(a)

500

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(b)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(c)




RMSE 1n

sumn

i1Ei∣∣∣∣∣∣∣∣2

radicradic

times 100 (11)




Erro

r (

)

3

2

1

0

ndash10 10 20


(a)


Erro

r (

)

2

15

1

05

00 10 20


(b)


4

2

Erro

r (

)

0

ndash20 10 20


(c)


Erro

r (

)

10

0

ndash10

ndash20

ndash300 10 20


(d)


3

2

1

Erro

r (

)

0

ndash10 10 20


(e)










6 Conclusions






Mea

n ab

solu

te er

ror (

)

0

1

3

2

4

5

ndash12008 2009 2010 2011 2012


(a)


Root

mea

n sq

uare

erro

r (

)0

1

3

2

4

5

2008 2009 2010 2011 2012


(b)




Data Availability




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in









Source Google Maps















Populationdensity














0 05 1 15 2 25 3

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


Very lowLow

HighVery high

(a)

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


6 12 18

LowMiddleHigh

(b)


1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es

ModerateLight Heavy

Very heavy

0 1 2 3 4 5 6

(c)




1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


300 350 400

SafelyAlertDanger








A in XZ in V






β1 Z1

βn Zn


P

A

P1

P2

P3

P4

A1

A2

A3

R

R1

R2

R3

R4

Π

Π

Π

Π

B1

B2

B3

Bn

Σg

w1

w2

w3

wn









δ ri( 1113857 w ri( 1113857 times α (1)


ZCOA 1113938

n

Zi1μBprime(z)z dz

1113938n

Zi1μBprime(z) dz

w1α1z1 + + wnαnzn

w1α1 + + wnαn

(2)









L1i μPi(P) i 1 2 3 4



(3)


μPi(P)

0 Plt si

Pminus si

ti minus si

si lePle ti

1 ti lePle ui

vi minusP

vi minus ui

ui lePle vi

0 vi leP

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μAi(A)

0 Alt si

Aminus si

ti minus si

si leAle ti

1 ti leAle ui

vi minusA

vi minus ui

ui leAle vi

0 vi leA

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μRi(R)

0 Rlt si

Rminus si

ui minus si

si leRle ui

1 ti leRle ui

vi minusR

vi minus ui

ui leRle vi

0 vi leR

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)





(5)



L3i wi ∘Bi i 1 2 3 48 (6)



L4i O1 1113944n48

i1wi ∘Bi i 1 2 3 48 (7)



L5 O2 g D ∘O1 (8)





Ei Mi minusPi (9)



MAE 1n

1113944

n

i1Ei

11138681113868111386811138681113868111386811138681113868

11139741113972

times 100 (10)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alue

s of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(a)

500

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(b)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(c)




RMSE 1n

sumn

i1Ei∣∣∣∣∣∣∣∣2

radicradic

times 100 (11)




Erro

r (

)

3

2

1

0

ndash10 10 20


(a)


Erro

r (

)

2

15

1

05

00 10 20


(b)


4

2

Erro

r (

)

0

ndash20 10 20


(c)


Erro

r (

)

10

0

ndash10

ndash20

ndash300 10 20


(d)


3

2

1

Erro

r (

)

0

ndash10 10 20


(e)










6 Conclusions






Mea

n ab

solu

te er

ror (

)

0

1

3

2

4

5

ndash12008 2009 2010 2011 2012


(a)


Root

mea

n sq

uare

erro

r (

)0

1

3

2

4

5

2008 2009 2010 2011 2012


(b)




Data Availability




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in













Populationdensity














0 05 1 15 2 25 3

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


Very lowLow

HighVery high

(a)

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


6 12 18

LowMiddleHigh

(b)


1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es

ModerateLight Heavy

Very heavy

0 1 2 3 4 5 6

(c)




1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


300 350 400

SafelyAlertDanger








A in XZ in V






β1 Z1

βn Zn


P

A

P1

P2

P3

P4

A1

A2

A3

R

R1

R2

R3

R4

Π

Π

Π

Π

B1

B2

B3

Bn

Σg

w1

w2

w3

wn









δ ri( 1113857 w ri( 1113857 times α (1)


ZCOA 1113938

n

Zi1μBprime(z)z dz

1113938n

Zi1μBprime(z) dz

w1α1z1 + + wnαnzn

w1α1 + + wnαn

(2)









L1i μPi(P) i 1 2 3 4



(3)


μPi(P)

0 Plt si

Pminus si

ti minus si

si lePle ti

1 ti lePle ui

vi minusP

vi minus ui

ui lePle vi

0 vi leP

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μAi(A)

0 Alt si

Aminus si

ti minus si

si leAle ti

1 ti leAle ui

vi minusA

vi minus ui

ui leAle vi

0 vi leA

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μRi(R)

0 Rlt si

Rminus si

ui minus si

si leRle ui

1 ti leRle ui

vi minusR

vi minus ui

ui leRle vi

0 vi leR

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)





(5)



L3i wi ∘Bi i 1 2 3 48 (6)



L4i O1 1113944n48

i1wi ∘Bi i 1 2 3 48 (7)



L5 O2 g D ∘O1 (8)





Ei Mi minusPi (9)



MAE 1n

1113944

n

i1Ei

11138681113868111386811138681113868111386811138681113868

11139741113972

times 100 (10)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alue

s of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(a)

500

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(b)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(c)




RMSE 1n

sumn

i1Ei∣∣∣∣∣∣∣∣2

radicradic

times 100 (11)




Erro

r (

)

3

2

1

0

ndash10 10 20


(a)


Erro

r (

)

2

15

1

05

00 10 20


(b)


4

2

Erro

r (

)

0

ndash20 10 20


(c)


Erro

r (

)

10

0

ndash10

ndash20

ndash300 10 20


(d)


3

2

1

Erro

r (

)

0

ndash10 10 20


(e)










6 Conclusions






Mea

n ab

solu

te er

ror (

)

0

1

3

2

4

5

ndash12008 2009 2010 2011 2012


(a)


Root

mea

n sq

uare

erro

r (

)0

1

3

2

4

5

2008 2009 2010 2011 2012


(b)




Data Availability




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in







0 05 1 15 2 25 3

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


Very lowLow

HighVery high

(a)

1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


6 12 18

LowMiddleHigh

(b)


1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es

ModerateLight Heavy

Very heavy

0 1 2 3 4 5 6

(c)




1

08

06

04

02

0

Mem

bers

hip

func

tion

valu

es


300 350 400

SafelyAlertDanger








A in XZ in V






β1 Z1

βn Zn


P

A

P1

P2

P3

P4

A1

A2

A3

R

R1

R2

R3

R4

Π

Π

Π

Π

B1

B2

B3

Bn

Σg

w1

w2

w3

wn









δ ri( 1113857 w ri( 1113857 times α (1)


ZCOA 1113938

n

Zi1μBprime(z)z dz

1113938n

Zi1μBprime(z) dz

w1α1z1 + + wnαnzn

w1α1 + + wnαn

(2)









L1i μPi(P) i 1 2 3 4



(3)


μPi(P)

0 Plt si

Pminus si

ti minus si

si lePle ti

1 ti lePle ui

vi minusP

vi minus ui

ui lePle vi

0 vi leP

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μAi(A)

0 Alt si

Aminus si

ti minus si

si leAle ti

1 ti leAle ui

vi minusA

vi minus ui

ui leAle vi

0 vi leA

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μRi(R)

0 Rlt si

Rminus si

ui minus si

si leRle ui

1 ti leRle ui

vi minusR

vi minus ui

ui leRle vi

0 vi leR

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)





(5)



L3i wi ∘Bi i 1 2 3 48 (6)



L4i O1 1113944n48

i1wi ∘Bi i 1 2 3 48 (7)



L5 O2 g D ∘O1 (8)





Ei Mi minusPi (9)



MAE 1n

1113944

n

i1Ei

11138681113868111386811138681113868111386811138681113868

11139741113972

times 100 (10)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alue

s of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(a)

500

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(b)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(c)




RMSE 1n

sumn

i1Ei∣∣∣∣∣∣∣∣2

radicradic

times 100 (11)




Erro

r (

)

3

2

1

0

ndash10 10 20


(a)


Erro

r (

)

2

15

1

05

00 10 20


(b)


4

2

Erro

r (

)

0

ndash20 10 20


(c)


Erro

r (

)

10

0

ndash10

ndash20

ndash300 10 20


(d)


3

2

1

Erro

r (

)

0

ndash10 10 20


(e)










6 Conclusions






Mea

n ab

solu

te er

ror (

)

0

1

3

2

4

5

ndash12008 2009 2010 2011 2012


(a)


Root

mea

n sq

uare

erro

r (

)0

1

3

2

4

5

2008 2009 2010 2011 2012


(b)




Data Availability




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in









A in XZ in V






β1 Z1

βn Zn


P

A

P1

P2

P3

P4

A1

A2

A3

R

R1

R2

R3

R4

Π

Π

Π

Π

B1

B2

B3

Bn

Σg

w1

w2

w3

wn









δ ri( 1113857 w ri( 1113857 times α (1)


ZCOA 1113938

n

Zi1μBprime(z)z dz

1113938n

Zi1μBprime(z) dz

w1α1z1 + + wnαnzn

w1α1 + + wnαn

(2)









L1i μPi(P) i 1 2 3 4



(3)


μPi(P)

0 Plt si

Pminus si

ti minus si

si lePle ti

1 ti lePle ui

vi minusP

vi minus ui

ui lePle vi

0 vi leP

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μAi(A)

0 Alt si

Aminus si

ti minus si

si leAle ti

1 ti leAle ui

vi minusA

vi minus ui

ui leAle vi

0 vi leA

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μRi(R)

0 Rlt si

Rminus si

ui minus si

si leRle ui

1 ti leRle ui

vi minusR

vi minus ui

ui leRle vi

0 vi leR

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)





(5)



L3i wi ∘Bi i 1 2 3 48 (6)



L4i O1 1113944n48

i1wi ∘Bi i 1 2 3 48 (7)



L5 O2 g D ∘O1 (8)





Ei Mi minusPi (9)



MAE 1n

1113944

n

i1Ei

11138681113868111386811138681113868111386811138681113868

11139741113972

times 100 (10)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alue

s of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(a)

500

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(b)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(c)




RMSE 1n

sumn

i1Ei∣∣∣∣∣∣∣∣2

radicradic

times 100 (11)




Erro

r (

)

3

2

1

0

ndash10 10 20


(a)


Erro

r (

)

2

15

1

05

00 10 20


(b)


4

2

Erro

r (

)

0

ndash20 10 20


(c)


Erro

r (

)

10

0

ndash10

ndash20

ndash300 10 20


(d)


3

2

1

Erro

r (

)

0

ndash10 10 20


(e)










6 Conclusions






Mea

n ab

solu

te er

ror (

)

0

1

3

2

4

5

ndash12008 2009 2010 2011 2012


(a)


Root

mea

n sq

uare

erro

r (

)0

1

3

2

4

5

2008 2009 2010 2011 2012


(b)




Data Availability




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in










δ ri( 1113857 w ri( 1113857 times α (1)


ZCOA 1113938

n

Zi1μBprime(z)z dz

1113938n

Zi1μBprime(z) dz

w1α1z1 + + wnαnzn

w1α1 + + wnαn

(2)









L1i μPi(P) i 1 2 3 4



(3)


μPi(P)

0 Plt si

Pminus si

ti minus si

si lePle ti

1 ti lePle ui

vi minusP

vi minus ui

ui lePle vi

0 vi leP

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μAi(A)

0 Alt si

Aminus si

ti minus si

si leAle ti

1 ti leAle ui

vi minusA

vi minus ui

ui leAle vi

0 vi leA

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

μRi(R)

0 Rlt si

Rminus si

ui minus si

si leRle ui

1 ti leRle ui

vi minusR

vi minus ui

ui leRle vi

0 vi leR

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)





(5)



L3i wi ∘Bi i 1 2 3 48 (6)



L4i O1 1113944n48

i1wi ∘Bi i 1 2 3 48 (7)



L5 O2 g D ∘O1 (8)





Ei Mi minusPi (9)



MAE 1n

1113944

n

i1Ei

11138681113868111386811138681113868111386811138681113868

11139741113972

times 100 (10)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alue

s of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(a)

500

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(b)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(c)




RMSE 1n

sumn

i1Ei∣∣∣∣∣∣∣∣2

radicradic

times 100 (11)




Erro

r (

)

3

2

1

0

ndash10 10 20


(a)


Erro

r (

)

2

15

1

05

00 10 20


(b)


4

2

Erro

r (

)

0

ndash20 10 20


(c)


Erro

r (

)

10

0

ndash10

ndash20

ndash300 10 20


(d)


3

2

1

Erro

r (

)

0

ndash10 10 20


(e)










6 Conclusions






Mea

n ab

solu

te er

ror (

)

0

1

3

2

4

5

ndash12008 2009 2010 2011 2012


(a)


Root

mea

n sq

uare

erro

r (

)0

1

3

2

4

5

2008 2009 2010 2011 2012


(b)




Data Availability




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





(5)



L3i wi ∘Bi i 1 2 3 48 (6)



L4i O1 1113944n48

i1wi ∘Bi i 1 2 3 48 (7)



L5 O2 g D ∘O1 (8)





Ei Mi minusPi (9)



MAE 1n

1113944

n

i1Ei

11138681113868111386811138681113868111386811138681113868

11139741113972

times 100 (10)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alue

s of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(a)

500

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(b)

450

400

350

250

300

2000 5 10 15 20 25 30 35V

alues

of v

ulne

rabi

lity

of fl

ood


M-2008M-2009M-2010M-2011

M-2012P-2008P-2009

P-2010P-2011P-2012

(c)




RMSE 1n

sumn

i1Ei∣∣∣∣∣∣∣∣2

radicradic

times 100 (11)




Erro

r (

)

3

2

1

0

ndash10 10 20


(a)


Erro

r (

)

2

15

1

05

00 10 20


(b)


4

2

Erro

r (

)

0

ndash20 10 20


(c)


Erro

r (

)

10

0

ndash10

ndash20

ndash300 10 20


(d)


3

2

1

Erro

r (

)

0

ndash10 10 20


(e)










6 Conclusions






Mea

n ab

solu

te er

ror (

)

0

1

3

2

4

5

ndash12008 2009 2010 2011 2012


(a)


Root

mea

n sq

uare

erro

r (

)0

1

3

2

4

5

2008 2009 2010 2011 2012


(b)




Data Availability




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





RMSE 1n

sumn

i1Ei∣∣∣∣∣∣∣∣2

radicradic

times 100 (11)




Erro

r (

)

3

2

1

0

ndash10 10 20


(a)


Erro

r (

)

2

15

1

05

00 10 20


(b)


4

2

Erro

r (

)

0

ndash20 10 20


(c)


Erro

r (

)

10

0

ndash10

ndash20

ndash300 10 20


(d)


3

2

1

Erro

r (

)

0

ndash10 10 20


(e)










6 Conclusions






Mea

n ab

solu

te er

ror (

)

0

1

3

2

4

5

ndash12008 2009 2010 2011 2012


(a)


Root

mea

n sq

uare

erro

r (

)0

1

3

2

4

5

2008 2009 2010 2011 2012


(b)




Data Availability




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in











6 Conclusions






Mea

n ab

solu

te er

ror (

)

0

1

3

2

4

5

ndash12008 2009 2010 2011 2012


(a)


Root

mea

n sq

uare

erro

r (

)0

1

3

2

4

5

2008 2009 2010 2011 2012


(b)




Data Availability




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





Data Availability




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




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