a cellular automata-based simulation tool for real fire...

Research ArticleA Cellular Automata-Based Simulation Tool forReal Fire Accident Prevention

Jacek M Czerniak 1 Hubert Zarzycki2 Aukasz Apiecionek1

WiesBaw Palczewski3 and Piotr Kardasz345

1Artificial Intelligence and Robotics Laboratory (AIRlab) Casimir the Great University in BydgoszczUl Chodkiewicza 30 85-064 Bydgoszcz Poland2University of Information Technology and Management Copernicus Ul Inowrocławska 56 53-648 Wrocław Poland3College of Management Edukacja Department of Computer Science and Quantitative MethodsUl Krakowska 56-62 50-425 Wrocław Poland4Cluster of Research Development and Innovation Ul Piłsudskiego 74 50-020 Wrocław Poland5Foundation for Research Development and Innovation Ul Legnicka 65 54-206 Wrocław Poland

Correspondence should be addressed to Jacek M Czerniak jczerniakukwedupl

Received 17 May 2017 Accepted 15 November 2017 Published 14 February 2018

Academic Editor Andrzej Swierniak

Copyright copy 2018 Jacek M Czerniak et al This 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 is properlycited

Many serious real-life problems could be simulated using cellular automata theory There were a lot of fires in public places whichkill many people Proposed method called Cellular Automata Evaluation (CAEva in short) is using cellular automata theory andcould be used for checking buildings conditions for fire accidentThe tests performed on real accident showed that an appropriatelyconfigured program allows obtaining a realistic simulation of human evacuation The authors analyze some real accidents andproved that CAEva method appears as a very promising solution especially in the cases of building renovations or temporaryunavailability of escape routes

1 Introduction

Cellular automata are used by some of the IT branchesincluding the field of artificial intelligence They consist ofa network of cells each of which is distinguished by somespecific state and a set of rules The change of the currentstate of a given cell is the outcome of the above-mentionedproperties and interrelations with the neighboring cells [12] The theory of cellular automata was first introducedby an American scientist of Hungarian descent John vonNeumann He demonstrated among others that even simplemachines show an ability to reproduce which was until thattime regarded as a fundamental feature of living organisms [34] Formany years cellular automata had been subject to theo-retical studies only With the development of computers andsoftware optimizing methods based on this approach havebeen more and more frequently studied and implementedin practice [5] Due to their versatility cellular automata are

applied in many real-life fields such as biology physics andmathematics and in various fields of IT such as cryptographyor computer graphics [6 7]

11 Application of Cellular Automata Cellular automata havebeen applied in practice for example in simulation of thestreet traffic where specifically defined cellular automatoncontrols the traffic [8ndash10] The vehicle flow is managedbasically at the specific segment of a given traffic inten-sity [11] This applies for instance to the traffic intensitycontrol on highways of the Ruhr in Germany The moni-toring centers designed exclusively for that purpose collectthe data from selected sections of the highways [12ndash16]The information thus obtained is analyzed and used forpreparing short-time simulations of the traffic intensity bymeans of cellular automata The projects websites publishthe statistical information about the studies performed onthe behavior of drivers who were prewarned about possible

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 3058241 12 pageshttpsdoiorg10115520183058241

2 Mathematical Problems in Engineering

Figure 1 Types of grids 1D 2D and 3D [source [14]]

traffic problems [17] that might occur over several followinghours [6] Another example of cellular automata applicationis demographic simulations for a given region The aim ofsuch simulations is to generate a model showing the sizeof the population at a given area in a form of a map ofthe forecasted population density Such simulations can bebased on the well-known ldquoGame of Liferdquo [18] By introducingsome modification to the algorithm it is possible to monitorthe behavior of the surrounding cells [7] Other examplesof cellular automata implementations include image process-ing generation of textures simulation of waves wind andpeople evacuation process as well as a simulation programdeveloped for the purpose of this study [19ndash23] The aimof the proposed algorithm is to generate the simulations ofpatterns of human escape from the building on fire with agiven number of exits and fire sources [24ndash27]

12 The Grid of Cellular Automata A grid or a discretespace where cellular automata evolution takes place consistsof a set of identical cells [26 30 31] Each of the cellsis surrounded by the same number of neighbors and canassume the same number of states [32ndash35] There are threestructural factors which significantly influence the grid formand as a consequence the behavior of the entire cellularautomaton [8 17 23 32ndash35]

(i) the size of the space which depends on themagnitudeof the studied problem the examples of which areshown in Figure 1 (grids 1D 2D and 3D)

(ii) the provision of regularity which requires the grid tobe filled entirely with identical cells

(iii) the number of neighbors (dependent on both above-mentioned factors)

In this article the authors present the possibility of simulatingreal fire accident to prevent huge fire accidents For thispurpose authors used Cellular Automata Evaluation methodCAEva in short This paper has following organization Sec-tion 2 presents the idea of forecasting the fire hazard two realaccidentsrsquo description and CAEva simulation method withtheir boundary conditions and transfer function Section 3presents the experiment results when the mentioned two realfire accidents were simulated Finally Section 4 consists offinal conclusions

2 Forecasting the Fire Hazard

21 Fire Accidents in Public Places Fires are one of themost uncontrollable calamities especially when they happenindoors Thus regardless of the edifices function whetherit is a residential business or any other kind of building

Mathematical Problems in Engineering 3

Table 1 Fire accidents in public places

Name Year Fatalities InjuriesStudy Club fire 1929 22 50Cocoanut Grove fire 1942 492 166Karlslust dance hall fire 1947 80ndash88 150Stardust fire 1981 48 214Alcal 20 nightclub fire 1983 82 27Ozone Disco Club fire 1996 162 95Gothenburg discothque fire 1998 63 213Volendam New Years fire 2001 14 241Canecmo Mineiro nightclub fire 2001 7 197Utopa nightclub fire 2002 25 100The Station nightclub fire 2003 100 230Wuwang Club fire 2008 43 88Santika Club fire 2009 66 222Lame Horse fire 2009 156 le160Kiss nightclub fire 2013 231 168

its design must comply with fire regulations The width ofcorridors number of emergency exits and the permissiblenumber of people staying inside at the same time have agrave impact on the safety of its users Simple presence of thedoors on floor plan is not sufficient they have to be open Inmany cases the high number of casualties stemmed from theemergency exit doors being locked In the past decades therehave been a number of disastrous fires in public places likerestaurants and nightclubs Table 1 presents some examplesof such accidents and lists the numbers of victims As youcan see from the data provided there have been many firesin entertainment clubs over the years causing many injuriesirrespective of whether they occurred decades ago (1942) orin recent times (2013)

22The Case of Kiss Nightclub Fire Accident The event calledldquoAglomeradosrdquo began on Saturday 26 January 2013 at 2300UTC at the Kiss nightclub In the club there were studentsof six universities and people from technical courses at theFederal University of Santa Maria [36] In the early morninghours of the following day conflagration took place whilethe students were holding a freshersrsquo ball and a panic brokeout Witnesses testified that the cause of the fire was eithera flare of fireworks lit by the members of a music bandplaying during the party The fire caused the roof to collapsein several parts of the building trapping many people insideFirefighters found numbers of bodies in the clubrsquos bathroomAt the moment of conflagration there were about 2000people inside the club This number doubles the buildingsmaximum capacity of 1000 At least 231 people died andhundreds more were injured in this disaster Many fatalitieswere apparently caused by smoke inhalation while othervictims were trampled in the rush for the exits Figure 2presents the scheme of the Kiss nightclub

23 The Cocoanut Grove Fire Accident The Cocoanut Grovewas a restaurant built in 1927 and located at 17 Piedmont

StageStage

WC

Bar

Figure 2 Kiss nightclub scheme [28]

Street near Park Square in downtownBostonMassachusetts[29 37] According to Prohibition it was very popular inthe 1920s The building structure was single-storey with abasement beneath The basement consists of a bar kitchenfreezers and storage areas The first floor contained a largedining room area and ballroom with a bandstand along withseveral bar areas separate from the ballroom The diningroom also had a retractable roof for use during warmweatherto allow a view of the moon and stars The main entranceto the Cocoanut Grove was via a revolving door on thePiedmont Street side of the building On Saturday November28 1942 there was a very large fire accident During thatevening a busboy had been ordered to fix a light bulb locatedat the top of an artificial palm tree in the corner of thebasement bar A moment later decorations started burningAs other furnishings ignited a fireball of flame and toxicgas raced across the room towards the stairs The revolvingdoor became jammed due to the crush of panicked patronsLots of people stuck in fire It was later estimated that morethan 1000 persons were inside the Grove at the time ofthe fire The final death count established by CommissionerReilly was 490 dead and 166 injured but the number ofinjured people was a count of those treated at a hospital andlater released while many people were injured but did notseek hospitalization Figure 3 presented the scheme of theCocoanut Grove

24 CAEva Simulation Method CAEva simulation methodis a program prepared for the purpose of rehearsing thefire escape scenarios in buildings [7] It helps to comparevarious simulation results and to draw suitable conclusionsThe program has been implemented in the C++Builderenvironment which is an object-oriented programming toolinWindows environment and is available free of charge at theAIRlab web site [38] The program allows drawing a boardof any size including the plan of a single-storey building tolocate people inside and to indicate the source of fire Theboard consists of a grid of cells Each cell can assume only


Figure 3 The Cocoanut Grove scheme [29]

Empty

FirePerson Personon fire

Wall

Figure 4 Diagram of cell states

one of the following states fire wall person person on fireor an empty cell Figure 4 presents the diagram of states for asingle cell in the fire simulation automaton

25 Boundary Conditions The discrete space where variousevolutions of cellular automata take place includes a d-dimensional theoretically infinite grid As this kind of gridcannot be implemented into computer application it isrepresented in a form of a limited table Therefore it isnecessary to set boundary conditions at the grid borders thatis at the table limits The set of basic conditions is shown inFigure 5These conditions are analogous after grid rotation of90 degrees so further arrangements were skipped as trivialThe following rules were used for the simulation of the cellmotion in the wall direction

(i) straight motion the state of the cell remains un-changed

(ii) diagonal motion the state of the cell changes into anempty one since the angle of incidence equals theangle of rebound the state of the cell in the mirrorimage shall change into the state of the cell whichinitiated the motion

(iii) motion conditions

(iv) motion is possible if the target cell is in the emptystate Otherwise the cell will not change its state

(v) the attempt of the motion of the cell in ldquopersonrdquo stateto the cell in ldquofirerdquo state increases the number of burnsof the initiating cell

A special case is an attempt of themotion from the cornerof the board A rebound in three initiating directions does notchange the state of a cell but itmay change it change as a resultof an attempt of the motion in the consecutive five directionsIt should be also noted that motion rules and conditionsapply to the cells in the ldquopersonrdquo state as well as in the ldquofirerdquostate The fields to which the motion cannot be executedare the cells in the ldquowallrdquo state Rebound conditions occurat the edge of the cellular automata grid which constitutesa barrier from which moving virtual objects rebound (invisual sense) Those conditions are used to simulate encasedempirical spaces

26 Transfer Function The evolution of cellular automatatakes place in discrete time determining consecutive process-ing cycles Each discrete moment 119905 = 0 1 2 119899 is used forupdating the state of individual cells thus each automaton isa dynamic object over time In every iteration the transferfunction can process (calculate) all the cells in the grid one byone according to specific rules Each processed cell receivesits new state based on the calculation of its current stateand states of the neighboring cells Transfer rules and thestate space as well as the defined neighborhood are inherentelements of the cellular automata evolution process Onceexecuted the programdisplaysmain screen ready to draw thebuilding plan and to arrange individual elements insideOncethe board is drawn and all the components are arranged theuser can start the configuration of fire and people parametersand setting of the group effect Fire parameters are as follows

(i) fire goes out alone if the number of neighbors is lessthan 1

(ii) fire goes out from overpopulation if the number ofneighbors is more than 3

(iii) new fire is generated when the number of neighborsis at least 3

(iv) fire is generated when the number of neighbors is lessthan or equal to 4 Parameters concerning people areas follows

(v) probability that a person goes towards the exit indefault state is 50

(vi) number of burns resulting in death is 5(vii) group effect is OnOff

There are points in the screen simulating people escapingtowards the exit and the propagating fire All the events arerecorded in the table of statistics They include the numberof people remaining within the board saved from and diedin the fire or by crushing [39 40] That data obtained enabledrawing conclusions from the experiments [41 42]

27 Implementation of OFN Notation to Fuzzy Observationof Real Fire Accident The use of ordered fuzzy numbers in


n n + 1 n n + 1 n n + 1

Figure 5 Boundary conditions (rebound from the grid edges)

N

0 3 4 5

5

6

7

x

y

NxＪＩＭＣＮＣＰ = [3 4 5 5]N

yＪＩＭＣＮＣＰ

=[55

56

]

NxＨＡＮＣＰ = [5 4 3 3]

NyＨＡ

ＮＣＰ=

[77

76

]

Figure 6 Example of move in simulation algorithm

cellular automation seems to be a natural step There aremany notations of fuzzy numbers that are introduced byZadeh [43] Klir [44] Dubois et al [45] and Kłopotek etal [23 46 47] among others Since we have in this case atwo-dimensional apparatus in which Moorersquos neighborhoodis additionally used there are eight available moves from cells119873119894 119895 An example of this situation is shown in Figure 6

There is a part of the neighborhood that is closer tothe exit and the other part closer to the group of cells inthe human state [20 48] Thus there are two possible setsof movements for this cell in question depending on thedeterminant [27 49 50] Since each of the sets is a four-element then the notation of fuzzy numbers called orderedfuzzy numbers introduced by Kosinski is suitable for itsdescription [51 52] After the death of the creator OFNsin some works are also called Kosinskirsquos Fuzzy Numbers[23 47 48 53 54] In this notation the fuzzy number A ingeneral has the shape of a trapezoid described by coordinates[119891119860(0) 119891119860(1) 119892119860(1) 119892119860(0)] which is presented in Figure 8

Arrow in Figure 8 shows directing that reflects the orderof the individual coordinates On such fuzzy numbers it

is possible to perform arithmetic operations described inliterature [47 55]

(i) addition 119860 + 119861 = (119891 + 119890 119892 + ℎ) = 119862119862 997888rarr [119891 (0) + 119890 (0) 119891 (1) + 119890 (1) 119892 (1) + ℎ (1) 119892 (0)+ ℎ (0)] (1)

(ii) scalar multiplication 119862 = 120582119860 = (120582119891 120582119892)119862 997888rarr [120582119891 (0) 120582119891 (1) 120582119892 (1) 120582119892 (0)] (2)

(iii) subtraction 119860 minus 119861 = (119891 minus 119890 119892 minus ℎ) = 119862119862 997888rarr [119891 (0) minus 119890 (0) 119891 (1) minus 119890 (1) 119892 (1) minus ℎ (1) 119892 (0)minus ℎ (0)] (3)

(iv) multiplication 119860 lowast 119861 = (119891 lowast 119890 119892 lowast ℎ) = 119862119862 997888rarr [119891 (0) lowast 119890 (0) 119891 (1) lowast 119890 (1) 119892 (1) lowast ℎ (1) 119892 (0)lowast ℎ (0)] (4)

(v) division 119860119861 = (119891119890 119892ℎ) = 119862119862 997888rarr [119891 (0)119890 (0)

119891 (1)119890 (1) 119892 (1)ℎ (1) 119892 (0)ℎ (0) ] (5)

A given set of possible moves in Moorersquos neighborhood fromthe cell119873119894119895 to cell1198731015840(119894119895)1015840 is shown in Figure 9 Depending onthe settings of the algorithm the traffic determinant can be

(i) going towards the nearest exit(ii) getting the nearest gathering of people

The determinant will be related to the fuzzy number in theOFN notation [46]

Definition 1 Let (119873119909119873119910) be two pairs of fuzzy numbersDirecting will be positive for a subset of moves closer to theindicated determinant

119873119909positive [119894 minus 1 119894 119894 + 1 119894 + 1] 119873119910positive [119895 minus 1 119895 minus 1 119895 minus 1 119895]

(6)


Table 2 Results of simulation with CAEva method for the Kiss nightclub

Number of people

Group effectNo Yes

Probability of people heading towards the exit2500 5000 7500 2500 5000 7500

Died 649 471 325 506 455 428Trampled 127 196 208 323 250 196Saved from fire 224 333 467 171 295 376

Table 3 A comparison of the CAEva method results with actual numbers for the Kiss nightclub

Relative error []

Group effectNo Yes



A pair of coordinates that are more distant from the determi-nant will be denoted by negative directing

119873119909negative [119894 + 1 119894 119894 minus 1 119894 minus 1] 119873119910negative [119895 + 1 119895 + 1 119895 + 1 119895]

(7)

A subset of cells to which further motion can be determinedis a pair of fuzzy numbers satisfying the following rules

IF 119873119909positive lowast 119873119909negative is positive THEN 119873119909 =119873119909positive ELSE 119873119909 = 119873119909negative IF 119873119910positive lowast119873119910negative is positive THEN 119873119910 = 119873119910positive ELSE119873119910 = 119873119910negative

From this set of pairs described (1198731015840119909 1198731015840119910) which representsthe four possible moves in the next evolution of the cellularautomaton one pair of coordinates is drawn By default thefields in which the traffic is impossible must be eliminatedfrom the list If no movement is possible in any of the fourcells the cell state will not changeThis symbolizes a situationin which a person remains motionless

3 The Experiment with CAEva Method

The authors launched a simulation of the Kiss nightclubscenario in CAEva program They placed people inside andset the fire The building is comprised of seven rooms andthere was only one exit The blue points mark people andthe red ones fire Several tests were performed based on thisscheme and the assumed conditions were as follows the aimof the test was to simulate a fire of the building based on cer-tain rules and relations Setting of the following parametersselection of versions and inherent rules altogether make upan environment which affect the mortality rateThe variableswere

(i) the layout of the building floors including the num-ber and location of doors

(ii) distribution of a defined number of people inside thebuilding at specified places

(iii) setting the fire parameters

(a) the fire goes out alone if there are no neighbors(b) the fire goes out because of overpopulation if

there are more than 3 neighbors(c) new fire is generated when there are at least 3

neighbors but not more than 4

(iv) setting of the parameters for people (live cells)

(a) number of burns resulting in death is by defaultset to 5

(v) location of the fire source on the board(vi) specifying the probability of people heading towards

the exit (three options) 25 50 and 75(vii) specifying whether people move towards the exit in

groups (two options) with or without a group effect

Figure 10 presents Kiss nightclub schema before thesimulation process was startedThe red squares represent firewhile the blue ones represent people Figure 11 presents Kissnightclub schema after completing the simulation Figure 12presents Cocoanut Grove schema before the simulation pro-cess was startedThe red squares represent fire while the blueones represent people Figure 13 presents Cocoanut Groveschema after completing the simulation The simulation wasmade two hundred times for each condition there weresix conditions which give 1200 simulations for one fireaccident Table 2 presents the average results of the performedsimulation Taking into account the real data concerning thenumber of fatalities in the Kiss nightclub fire the outcomewhich was closest to the actual death toll was achieved using75 probability of people going towards the exit and withgroup effect off Table 3 compares the average results with realnumbers


Table 4 Results of simulation with CAEva method for the Cocoanut Grove nightclub

Number of people

Group effectNo Yes



Table 5 A comparison of the CAEva method results with actual numbers for the Cocoanut Grove nightclub

Number of people

Group effectNo Yes



As you can see in Table 2 the increase in the proba-bility of people heading to the exit reduces the number ofpeople who die as a result of fire The number of victimsdecreases only when the group effect is on Furthermorethe overall number of people who have survived a fire alsoincreases as the probability of people moving towards the exitincreases

As shown in the Table 3 the smallest relative errorwas obtained in the absence of group effect and at thevalue of 75 of the people heading to the exit The biggesterrors were achieved with the group effect enabled andwith the 25 probability of people going to the exit Thiscould mean that in the event of this fire the group effectdid not work and people were looking for a way out bythemselves

As you can see in Table 4 here also the increase in theprobability of going to the exit of the premises has reducedthe number of people who died in the fire Table 5 comparesthe average results with real numbers The smallest error wasobtained for the disabled group effect but with a value of50 of people heading to the exit This may mean that in theevent of a fire in this club group effect also did not work butpeople did not hurry to leave the club which caused a tragiceffect

The mortality rate depends on the place of the fireoutbreak If the fire blocks any room then the people stayingthere are not able to escape and to reach the exit even ifthey move towards it with 100 probability The group effectused in the program does not necessarily help in escape ofpeople from the building It can generate crowd as peopleare looking for others to form groups and thus tramplingcan occur When a person does not have any direction whenheshe could move heshe is trampled In Figures 6ndash9 theplace of fire and the fire spread are marked in red In contrast

blue indicates the location of people at the start of an event afire

4 Conclusions

As one can see performed simulations can help understandhow people behaved at the time of the fire whether theyfollowed the crowd in search of an exit whether they wereacting alone or were they determined enough to find a wayout In one case people showed a higher level of determi-nation (75 probability of going towards the exit) whilein the second case the level was lower (50) Simulationscan be used as a warning during security level analysis butalso as an element of a detailed analysis of the events thatoccurred

The comparison of the proposed method with actualcase demonstrated that it is extremely difficult to createa simulation of fire escape scenario The most challengingelement is the people behavior whichmay become stochasticand unpredictable The authors of this study managed torecreate the scenario of the escape of people from a build-ing by means of cellular automata the implementation ofwhich was the object of this paper Using an appropriateconfiguration of the program determining the probabilityof a person heading towards the exit the fire parametersand onoff setting of the group effect allow to drawing thefollowing conclusions When the group effect is applied inthe program the number of people who die as a resultof trampling is larger than in the case when this effect isdisabled The mortality rate rises when people are not ableto move in any direction which is a result of individu-als gathering in groups that create areas of high densitywhere trampling often occurs The results which proved tobe closest to the actual numbers were achieved when the


x

55545435325

0

02

04

06

08

1

y=

(x

)

[3 4 5 5]

(a)

x

555 65645

0

02

04

06

08

1

y=

(x

)

[5 5 5 6]

(b)

x

55545435325

0

02

04

06

08

1

y=

(x

)

[5 4 3 3]

(c)

x

55 7656 75

0

02

04

06

08

1

y=

(x

)

[7 7 7 6]

(d)

Figure 7 The OFN visualization of Nx-positive (a) Ny-positive (b) Nx-negative (c) and Ny-negative (d)

1

0 2 4 6 8 10

A(x

)

fA(0) fA(1) gA(1) gA(0)

Figure 8 Fuzzy number with the extension


0

x

y

xi

yj

i minus 1 j minus 1

i minus 1 j

i minus 1 j + 1

i j minus 1

i j

i j + 1

i + 1 j minus 1

i + 1 j

i + 1 j + 1

Figure 9 Possible move

Figure 10 Kiss nightclub schema with people and fire in CAEvaprogram

value of probability with which people escape was around50ndash75 The hindrances that affect the decision makingprocess during the evacuation include among others limitedvisibility due to the smoke resulting from combustion offlammable materials high temperature and toxic gases Theresult achieved in the CAEva method can provide valuableinformation for architects and building constructors Theresults obtained from the program confirm the thesis thatinsouciant or unlawful blocking of escape routes inside

Figure 11 CAEva program after simulating fire in Kiss nightclub

buildings may have tragic consequences at each stage ofthe building operation The people who are responsible forfire safety and structural safety inspections may apply suchtools to justify their decisions that sometimes could seem tobe too strict To make the simulation even more realisticit is worth considering the option of automatic change ofthe parameter related to the probability of a person movingtowards the exit during the simulation Adding furtherconditions in order to provide more accurate results is also


Figure 12 The Cocoanut Grove schema with people and fire inCAEva program

Figure 13 CAEva program after simulating fire in The CocoanutGrove

possible The future experiments should take this fact intoaccount

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] E Mikolajewska and D Mikolajewski ldquoExoskeletons in neu-rological diseases - current and potential future applicationsrdquoAdvances in Clinical and Experimental Medicine vol 20 no 2pp 227ndash232 2011

[2] E Mikolajewska and D Mikolajewski ldquoE-learning in theeducation of people with disabilitiesrdquo Advances in Clinical andExperimental Medicine vol 20 no 1 pp 103ndash109

[3] X Yang B Wang and Z Qin ldquoFloor field model based oncellular automata for simulating indoor pedestrian evacuationrdquoMathematical Problems in Engineering vol 2015 Article ID820306 10 pages 2015

[4] E A Lim andWC Tan ldquoSimulating evacuations with obstaclesusing a modified dynamic cellular automata modelrdquo Journalof Applied Mathematics vol 2012 Article ID 765270 17 pages2012

[5] JM CzerniakWDobrosielski H Zarzycki and Ł ApiecionekldquoA proposal of the new owlANT method for determining thedistance between terms in ontologyrdquo Advances in IntelligentSystems and Computing vol 323 pp 235ndash246 2014

[6] B Płaczek ldquoPerformance evaluation of road traffic control usinga fuzzy cellular modelrdquo Lecture Notes in Computer Science(including subseries Lecture Notes in Artificial Intelligence andLectureNotes in Bioinformatics) Preface vol 6679 no 2 pp 59ndash66 2011

[7] J M Czerniak L Apiecionek H Zarzycki and D EwaldldquoProposed CAEva simulation method for evacuation of peoplefrom a buildings on firerdquo in Novel Developments in UncertaintyRepresentation and Processing pp 315ndash326 Springer 2016

[8] V Terrier ldquoTwo-dimensional cellular automata and their neigh-borhoodsrdquo Theoretical Computer Science vol 312 no 2-3 pp203ndash222 2004

[9] S Wolfram A New Kind of Science Wolfram Media Cham-paign Ill USA 2002

[10] I Rojek M Kowal and A Stoic ldquoPredictive compensationof thermal deformations of ball screws in cnc machines usingneural networksrdquo Tehnicki Vjesnik vol 24 no 6 2017

[11] [link] URL httpwwwautobahnnrwde[12] D Chowdhury L Santen and A Schadschneider ldquoStatistical

physics of vehicular traffic and some related systemsrdquo PhysicsReports vol 329 no 4ndash6 pp 199ndash329 2000

[13] N Yu G de RooM de Jong and S Storm ldquoDoes the expansionof a motorway network lead to economic agglomerationevidence from Chinardquo Transport Policy vol 45 pp 218ndash2272016

[14] K Nagel and M A Schreckenberg ldquoCellular automaton modelfor freeway trafficrdquo Journal de Physique vol 2 pp 2221ndash22291992

[15] S-C Lo and C-H Hsu ldquoCellular automata simulation formixedmanual and automated control trafficrdquoMathematical andComputer Modelling vol 51 no 7-8 pp 1000ndash1007 2010

[16] M Burzynski W Cudny and W Kosinski ldquoTraffic flow sim-ulation cellular automata with fuzzy rules approachrdquo in ChAdvances in Soft Computing Proc of the Sixth Int Conferenceon Neural Network and Soft Computing pp 808ndash813 ZakopanePoland 2003

[17] SMaerivoet andBDeMoor ldquoCellular automatamodels of roadtrafficrdquo Physics Reports vol 419 no 1 pp 1ndash64 2005

[18] P Prokopowicz ldquoFlexible and simple methods of calculationson fuzzy numbers with the ordered fuzzy numbers modelrdquo inArtificial Intelligence and Soft Computing vol 7894 of LectureNotes in Computer Science pp 365ndash375 Springer BerlinHeidelberg 2013

[19] R Kozik M Choras A Flizikowski M Theocharidou VRosato and E Rome ldquoAdvanced services for critical infrastruc-tures protectionrdquo Journal of Ambient Intelligence and Human-ized Computing vol 6 no 6 pp 783ndash795 2015

[20] E Velizarova E Sotirova K Atanassov P Vassilev and SFidanova ldquoOn the game method for the forest fire spreadmodelling with considering the wind effectrdquo in Proceedings ofthe 2012 6th IEEE International Conference Intelligent SystemsIS pp 216ndash220 Bulgaria 2012

[21] S Darlington M Brocchetto and D Ford Fire rips throughcrowded brazil nightclub killing 233 httpseditioncnncom20130127worldamericasbrazil-nightclub-fireindexhtml

[22] S Darlington and C J Carter Brazil nightclub fire rsquolike awar zonersquo with bodies piled httpeditioncnncom20130128worldamericasbrazil-nightclub-fireindexhtml

[23] T Vince J Molnar and R Bucko ldquoA survey of urban vehicularsensing platformsrdquo Transactions of KMOSU vol 4 no 1 pp150ndash153 2010


[24] A Stachowiak KDyczkowski AWojtowicz P Zywica andMWygralak ldquoA bipolar view on medical diagnosis in OvaExpertsystemrdquo Advances in Intelligent Systems and Computing vol400 pp 483ndash492 2016

[25] K Dyczkowski ldquoA less cumulative algorithm of mining linguis-tic browsing patterns in the world wide webrdquo in Proceedings ofthe 5th EUSFLAT Conference Ostrava Czech Republic 2007

[26] J Czerniak H Zarzycki and D Ewald AAO as a new strategyin modeling and simulation of constructional problems optimiza-tion Simulation Modelling Practice andTheory 2017

[27] J Czerniak G Smigielski D Ewald and M Paprzycki ldquoNewproposed implementation of ABC method to optimization ofwater capsule flightrdquo in Federated Conference on ComputerScience and Information Systems IEEE Digital Library ACSIS 5pp 489ndash493

[28] [link] URL httpenwikipediaorgwikiKiss nightclub firemediaviewerKissnightclubsvg

[29] [link] URL httpenwikipediaorgwikiCocoanut Grove fireThe club

[30] I Zolotova and R Hosak ldquoObjects for visualization of processdata in supervisory controlrdquo in Aspects of Computational Intel-ligence Theory and Applications vol 2 of Topics in IntelligentEngineering and Informatics pp 51ndash61 Springer Berlin Ger-may 2013

[31] E Mikołajewska and D Mikołajewski ldquoNon-invasive EEG-based brain-computer interfaces in patients with disorders ofconsciousnessrdquo Military Medical Research vol 1 no 1 p 142014

[32] C Burstedde K Klauck A Schadschneider and J ZittartzldquoSimulation of pedestrian dynamics using a two-dimensionalcellular automatonrdquo Physica A Statistical Mechanics and itsApplications vol 295 no 3-4 pp 507ndash525 2001

[33] A Kirchner and A Schadschneider ldquoSimulation of evacuationprocesses using a bionics-inspired cellular automatonmodel forpedestrian dynamicsrdquo Physica A Statistical Mechanics and itsApplications vol 312 no 1-2 pp 260ndash276 2002

[34] A SchadschneiderWKlingschH Klupfel T Kretz C Rogschand A Seyfried ldquoEvacuation dynamics empirical resultsmodeling and applicationsrdquo in Encyclopedia of complexity andsystems science pp 3142ndash3176 Springer 2009

[35] Y Suma D Yanagisawa and K Nishinari ldquoAnticipation effectin pedestrian dynamics modeling and experimentsrdquo Physica AStatistical Mechanics and its Applications vol 391 no 1-2 pp248ndash263 2012

[36] [link] URL httpeditioncnncom20130128worldameri-casbrazil-nightclub-fire

[37] [link] URL httpwwwbostonfirehistoryorgfirestory11281942html

[38] G Smigielski R Dygdała H Zarzycki and D LewandowskildquoReal-time system of delivering water-capsule for firefightingrdquoAdvances in Intelligent Systems andComputing vol 534 pp 102ndash111 2017

[39] F E PetryM A Cobb D Ali et al ldquoFuzzy Spatial Relationshipsand Mobile Agent Technology in Geospatial Information Sys-temsrdquo in Applying Soft Computing in Defining Spatial Relationsvol 106 of Studies in Fuzziness and Soft Computing pp 123ndash155Physica-Verlag HD Heidelberg 2002

[40] R A Angryk and F E Petry ldquoMining multi-level associationswith fuzzy hierarchiesrdquo inConference Fuzzy Systems FUZZ rsquo05The 14th IEEE International pp 785ndash790 2005

[41] A Marszal ek and T Burczynski ldquoModeling and forecastingfinancial time series with ordered fuzzy candlesticksrdquo Informa-tion Sciences vol 273 pp 144ndash155 2014

[42] A Marszałek and T Burczynski ldquoModelling financial highfrequency data using ordered fuzzy numbersrdquo in ArtificialIntelligence and Soft Computing vol 7894 of Lecture Notes inComputer Science pp 345ndash352 Springer Berlin Heidelberg2013

[43] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[44] G J Klir ldquoChapter 2 Fuzzy logicrdquo in Soft Computing andIntelligent Data Analysis in Oil Exploration F A M Nikraveshand L Zadeh Eds vol 51 ofDevelopments in Petroleum Sciencepp 33ndash49 Elsevier 2003

[45] D Dubois H Prade and G Richard ldquoMultiple-valued exten-sions of analogical proportionsrdquo Fuzzy Sets and Systems vol292 pp 193ndash202 2016

[46] M A Kłopotek S T Wierzchon and M Michalewicz inFuzzy reals with algebraic operations algorithmic approach pp311ndash320 the IISrsquo2002 Symposium on Intelligent InformationSystems 2002

[47] W Kosinski ldquoEvolutionary algorithm determining defuzzyfi-cation operatorsrdquo Engineering Applications of Artificial Intelli-gence vol 20 no 5 pp 619ndash627 2007

[48] W T Dobrosielski J M Czerniak J Szczepanski and HZarzycki ldquoTriangular expanding a new defuzzificationmethodon ordered fuzzy numbersrdquo Advances in Intelligent Systems andComputing vol 642 pp 605ndash619 2017

[49] Y Zheng B Jia X G Li and N Zhu ldquoEvacuation dynamicswith fire spreading based on cellular automatonrdquo Physica AStatistical Mechanics and its Applications vol 390 no 18-19 pp3147ndash3156 2011

[50] J Hu H Sun G Gao J Wei and L You ldquoThe group evac-uation behavior based on fire effect in the complicated three-dimensional spacerdquoMathematical Problems in Engineering vol2014 Article ID 949280 7 pages 2014

[51] J Czerniak W Dobrosielski and I Filipowicz ldquoSome cases ofcomparing fuzzy numbers using defuzzificators on the catalogof ofn shapesrdquo in Theory and Applications of Ordered FuzzyNumbers A Tribute to Professor Witold Kosinski P Prokopow-icz J Czerniak D Mikolajewski L Apiecionek and D SlezakEds vol 356 of Studies in Fuzziness and Soft Computin pp 99ndash134 Springer 2017

[52] J Czerniak ldquoThe OFNAnt method based on ant colony opti-mization used to solve the tsprdquo in Theory and Applications ofOrdered Fuzzy Numbers A Tribute to Professor Witold KosinskiP Prokopowicz J Czerniak D Mikolajewski L Apiecionekand D Slezak Eds vol 356 of Studies in Fuzziness and SoftComputing pp 209ndash224 Springer 2017

[53] T Saelao and S Patvichaichod ldquoThe computational fluiddynamic simulation of fire evacuation from the student dormi-toryrdquoAmerican Journal of Applied Sciences vol 9 no 3 pp 429ndash435 2012

[54] H Zarzycki J Czerniak and W Dobrosielski ldquoAplication ofordered fuzzy numbers to detect trends in the nasdaq compositeindexrdquo inTheory and Applications of Ordered Fuzzy Numbers ATribute to ProfessorWitoldKosinski P Prokopowicz J CzerniakD Mikolajewski L Apiecionek D Slezak and P the nasdaqcomposite index Eds vol 356 of Studies in Fuzziness and SoftComputing pp 197ndash208 Springer 2017


[55] W Dobrosielski J Czerniak H Zarzycki and J SzczepanskildquoFuzzy numbers applied to a heat furnace controlrdquo in The-ory and Applications of Ordered Fuzzy Numbers A Tributeto Professor Witold Kosinski P Prokopowicz J Czerniak DMikolajewski L Apiecionek and D Slezak Eds vol 356 ofStudies in Fuzziness and Soft Computing pp 271ndash290 Springer2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

Journal of


Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


Figure 1 Types of grids 1D 2D and 3D [source [14]]

traffic problems [17] that might occur over several followinghours [6] Another example of cellular automata applicationis demographic simulations for a given region The aim ofsuch simulations is to generate a model showing the sizeof the population at a given area in a form of a map ofthe forecasted population density Such simulations can bebased on the well-known ldquoGame of Liferdquo [18] By introducingsome modification to the algorithm it is possible to monitorthe behavior of the surrounding cells [7] Other examplesof cellular automata implementations include image process-ing generation of textures simulation of waves wind andpeople evacuation process as well as a simulation programdeveloped for the purpose of this study [19ndash23] The aimof the proposed algorithm is to generate the simulations ofpatterns of human escape from the building on fire with agiven number of exits and fire sources [24ndash27]

12 The Grid of Cellular Automata A grid or a discretespace where cellular automata evolution takes place consistsof a set of identical cells [26 30 31] Each of the cellsis surrounded by the same number of neighbors and canassume the same number of states [32ndash35] There are threestructural factors which significantly influence the grid formand as a consequence the behavior of the entire cellularautomaton [8 17 23 32ndash35]

(i) the size of the space which depends on themagnitudeof the studied problem the examples of which areshown in Figure 1 (grids 1D 2D and 3D)

(ii) the provision of regularity which requires the grid tobe filled entirely with identical cells

(iii) the number of neighbors (dependent on both above-mentioned factors)

In this article the authors present the possibility of simulatingreal fire accident to prevent huge fire accidents For thispurpose authors used Cellular Automata Evaluation methodCAEva in short This paper has following organization Sec-tion 2 presents the idea of forecasting the fire hazard two realaccidentsrsquo description and CAEva simulation method withtheir boundary conditions and transfer function Section 3presents the experiment results when the mentioned two realfire accidents were simulated Finally Section 4 consists offinal conclusions

2 Forecasting the Fire Hazard

21 Fire Accidents in Public Places Fires are one of themost uncontrollable calamities especially when they happenindoors Thus regardless of the edifices function whetherit is a residential business or any other kind of building







StageStage

WC

Bar






Empty


Wall




















n n + 1 n n + 1 n n + 1


N

0 3 4 5

5

6

7

x

y



=[55

56

]

NxＨＡＮＣＰ = [5 4 3 3]

NyＨＡ

ＮＣＰ=

[77

76

]










(v) division 119860119861 = (119891119890 119892ℎ) = 119862119862 997888rarr [119891 (0)119890 (0)

119891 (1)119890 (1) 119892 (1)ℎ (1) 119892 (0)ℎ (0) ] (5)






(6)



Number of people

Group effectNo Yes




Relative error []

Group effectNo Yes





(7)




















Number of people

Group effectNo Yes




Number of people

Group effectNo Yes








4 Conclusions




x

55545435325

0

02

04

06

08

1

y=

(x

)

[3 4 5 5]

(a)

x

555 65645

0

02

04

06

08

1

y=

(x

)

[5 5 5 6]

(b)

x

55545435325

0

02

04

06

08

1

y=

(x

)

[5 4 3 3]

(c)

x

55 7656 75

0

02

04

06

08

1

y=

(x

)

[7 7 7 6]

(d)


1

0 2 4 6 8 10

A(x

)

fA(0) fA(1) gA(1) gA(0)



0

x

y

xi

yj

i minus 1 j minus 1

i minus 1 j

i minus 1 j + 1

i j minus 1

i j

i j + 1

i + 1 j minus 1

i + 1 j

i + 1 j + 1












References

































































Journal of












Journal of







Volume 2018






Volume 2018














StageStage

WC

Bar






Empty


Wall




















n n + 1 n n + 1 n n + 1


N

0 3 4 5

5

6

7

x

y



=[55

56

]

NxＨＡＮＣＰ = [5 4 3 3]

NyＨＡ

ＮＣＰ=

[77

76

]










(v) division 119860119861 = (119891119890 119892ℎ) = 119862119862 997888rarr [119891 (0)119890 (0)

119891 (1)119890 (1) 119892 (1)ℎ (1) 119892 (0)ℎ (0) ] (5)






(6)



Number of people

Group effectNo Yes




Relative error []

Group effectNo Yes





(7)




















Number of people

Group effectNo Yes




Number of people

Group effectNo Yes








4 Conclusions




x

55545435325

0

02

04

06

08

1

y=

(x

)

[3 4 5 5]

(a)

x

555 65645

0

02

04

06

08

1

y=

(x

)

[5 5 5 6]

(b)

x

55545435325

0

02

04

06

08

1

y=

(x

)

[5 4 3 3]

(c)

x

55 7656 75

0

02

04

06

08

1

y=

(x

)

[7 7 7 6]

(d)


1

0 2 4 6 8 10

A(x

)

fA(0) fA(1) gA(1) gA(0)



0

x

y

xi

yj

i minus 1 j minus 1

i minus 1 j

i minus 1 j + 1

i j minus 1

i j

i j + 1

i + 1 j minus 1

i + 1 j

i + 1 j + 1












References

































































Journal of












Journal of







Volume 2018






Volume 2018










Empty


Wall




















n n + 1 n n + 1 n n + 1


N

0 3 4 5

5

6

7

x

y



=[55

56

]

NxＨＡＮＣＰ = [5 4 3 3]

NyＨＡ

ＮＣＰ=

[77

76

]










(v) division 119860119861 = (119891119890 119892ℎ) = 119862119862 997888rarr [119891 (0)119890 (0)

119891 (1)119890 (1) 119892 (1)ℎ (1) 119892 (0)ℎ (0) ] (5)






(6)



Number of people

Group effectNo Yes




Relative error []

Group effectNo Yes





(7)




















Number of people

Group effectNo Yes




Number of people

Group effectNo Yes








4 Conclusions




x

55545435325

0

02

04

06

08

1

y=

(x

)

[3 4 5 5]

(a)

x

555 65645

0

02

04

06

08

1

y=

(x

)

[5 5 5 6]

(b)

x

55545435325

0

02

04

06

08

1

y=

(x

)

[5 4 3 3]

(c)

x

55 7656 75

0

02

04

06

08

1

y=

(x

)

[7 7 7 6]

(d)


1

0 2 4 6 8 10

A(x

)

fA(0) fA(1) gA(1) gA(0)



0

x

y

xi

yj

i minus 1 j minus 1

i minus 1 j

i minus 1 j + 1

i j minus 1

i j

i j + 1

i + 1 j minus 1

i + 1 j

i + 1 j + 1












References

































































Journal of












Journal of







Volume 2018






Volume 2018









n n + 1 n n + 1 n n + 1


N

0 3 4 5

5

6

7

x

y



=[55

56

]

NxＨＡＮＣＰ = [5 4 3 3]

NyＨＡ

ＮＣＰ=

[77

76

]










(v) division 119860119861 = (119891119890 119892ℎ) = 119862119862 997888rarr [119891 (0)119890 (0)

119891 (1)119890 (1) 119892 (1)ℎ (1) 119892 (0)ℎ (0) ] (5)






(6)



Number of people

Group effectNo Yes




Relative error []

Group effectNo Yes





(7)




















Number of people

Group effectNo Yes




Number of people

Group effectNo Yes








4 Conclusions




x

55545435325

0

02

04

06

08

1

y=

(x

)

[3 4 5 5]

(a)

x

555 65645

0

02

04

06

08

1

y=

(x

)

[5 5 5 6]

(b)

x

55545435325

0

02

04

06

08

1

y=

(x

)

[5 4 3 3]

(c)

x

55 7656 75

0

02

04

06

08

1

y=

(x

)

[7 7 7 6]

(d)


1

0 2 4 6 8 10

A(x

)

fA(0) fA(1) gA(1) gA(0)



0

x

y

xi

yj

i minus 1 j minus 1

i minus 1 j

i minus 1 j + 1

i j minus 1

i j

i j + 1

i + 1 j minus 1

i + 1 j

i + 1 j + 1












References

































































Journal of












Journal of







Volume 2018






Volume 2018










Number of people

Group effectNo Yes




Relative error []

Group effectNo Yes





(7)




















Number of people

Group effectNo Yes




Number of people

Group effectNo Yes








4 Conclusions




x

55545435325

0

02

04

06

08

1

y=

(x

)

[3 4 5 5]

(a)

x

555 65645

0

02

04

06

08

1

y=

(x

)

[5 5 5 6]

(b)

x

55545435325

0

02

04

06

08

1

y=

(x

)

[5 4 3 3]

(c)

x

55 7656 75

0

02

04

06

08

1

y=

(x

)

[7 7 7 6]

(d)


1

0 2 4 6 8 10

A(x

)

fA(0) fA(1) gA(1) gA(0)



0

x

y

xi

yj

i minus 1 j minus 1

i minus 1 j

i minus 1 j + 1

i j minus 1

i j

i j + 1

i + 1 j minus 1

i + 1 j

i + 1 j + 1












References

































































Journal of












Journal of







Volume 2018






Volume 2018










Number of people

Group effectNo Yes




Number of people

Group effectNo Yes








4 Conclusions




x

55545435325

0

02

04

06

08

1

y=

(x

)

[3 4 5 5]

(a)

x

555 65645

0

02

04

06

08

1

y=

(x

)

[5 5 5 6]

(b)

x

55545435325

0

02

04

06

08

1

y=

(x

)

[5 4 3 3]

(c)

x

55 7656 75

0

02

04

06

08

1

y=

(x

)

[7 7 7 6]

(d)


1

0 2 4 6 8 10

A(x

)

fA(0) fA(1) gA(1) gA(0)



0

x

y

xi

yj

i minus 1 j minus 1

i minus 1 j

i minus 1 j + 1

i j minus 1

i j

i j + 1

i + 1 j minus 1

i + 1 j

i + 1 j + 1












References

































































Journal of












Journal of







Volume 2018






Volume 2018









x

55545435325

0

02

04

06

08

1

y=

(x

)

[3 4 5 5]

(a)

x

555 65645

0

02

04

06

08

1

y=

(x

)

[5 5 5 6]

(b)

x

55545435325

0

02

04

06

08

1

y=

(x

)

[5 4 3 3]

(c)

x

55 7656 75

0

02

04

06

08

1

y=

(x

)

[7 7 7 6]

(d)


1

0 2 4 6 8 10

A(x

)

fA(0) fA(1) gA(1) gA(0)



0

x

y

xi

yj

i minus 1 j minus 1

i minus 1 j

i minus 1 j + 1

i j minus 1

i j

i j + 1

i + 1 j minus 1

i + 1 j

i + 1 j + 1












References

































































Journal of












Journal of







Volume 2018






Volume 2018









0

x

y

xi

yj

i minus 1 j minus 1

i minus 1 j

i minus 1 j + 1

i j minus 1

i j

i j + 1

i + 1 j minus 1

i + 1 j

i + 1 j + 1












References

































































Journal of












Journal of







Volume 2018






Volume 2018














References

































































Journal of












Journal of







Volume 2018






Volume 2018

















































Journal of












Journal of







Volume 2018






Volume 2018








a cellular automata-based simulation tool for real fire...

Documents