Multilevel Fuzzy Approach to the Risk and Disaster Management

Transcription

1 Act Polytechnic Hungric Vol. 7, No. 4, 21 Multilevel Fuzzy Approch to the Risk nd Disster Mngement Márt Tkács John von Neumnn Fculty of Informtics, Óbud University Bécsi út 96/b, H-134 Budpest, Hungry Abstrct: In this pper short generl review of the min chrcteristics of risk mngement pplictions is given, where hierrchicl, multilevel risk mngement method cn be pplied in fuzzy decision mking environment. The given cse study is trvel risk-level clcultion bsed on the presented model. In the lst section n extended model nd preliminry mthemticl description is presented, where the pirwise comprison mtrix of the grouped risk fctors expnds the previous principles. Keywords: risk mngement; fuzzy multilevel decision mking; comprison mtrix 1 Introduction The economicl crisis situtions nd the complex environmentl nd societl processes over the pst yers indicte the need for new mthemticl model constructions to predict their effects. The helth dignostic s multi-prmeter nd multi-criteri decision mking system is, s well, one of the models where, s in the previous exmples, risk model should be mnged. Himes in [1] gives n extensive overview of risk modeling, ssessment, nd mngement. The presented quntittive methods for risk nlysis in [2] re bsed on well-known mthemticl models of expert systems, quntittive optimum clcultion models, sttisticl hypothesis nd possibility theory. The cse studies present pplictions in the fields of economics nd environmentl protection. It is observble tht the sttisticl-bsed numericl resoning methods need long-term experiments nd tht they re time- nd computtionlly demnding. The complexity of the systems increses the runtime fctor, nd the system prmeter representtion is usully not user-friend. The numericl methods nd opertion reserch models re redy to give cceptble results for some finite dimensionl problems, but without mngement of the uncertinties. The complexity nd uncertinties in those systems rise the necessity of soft computing bsed models. 91

2 M. Tkács Multilevel Fuzzy Approch to the Risk nd Disster Mngement Nowdys the expert engineer s experiences re suited for modeling opertionl risks, not only in the engineering sciences, but lso for brod rnge of pplictions [13]. Wng introduces the term of risk engineering relted to the risk of costs nd schedules on project in which there is the potentil for doing better s well s worse thn expected [3]. The presented cse studies in his book re prticulrly bsed on long-term engineering experiences, for exmple on fuzzy pplictions, which offer the promised lterntive mesuring of opertionl risks nd risk mngement globlly. The use of fuzzy sets to describe the risk fctors nd fuzzy-bsed decision techniques to help incorporte inherent imprecision, uncertinties nd subjectivity of vilble dt, s well s to propgte these ttributes throughout the model, yield more relistic results. Fuzzy logic modeling techniques cn lso be used in risk mngement systems to ssess risk levels in cses where the experts do not hve enough relible dt to pply sttisticl pproches. There re even more pplictions to del with risk mngement nd bsed on fuzzy environments. Fuzzy-bsed techniques seem to be prticulrly suited to modeling dt which re scrce nd where the cuse-effect knowledge is imprecise nd observtions nd criteri cn be expressed in linguistic terms. [4] The structurl modeling of risk nd disster mngement is cse-specific, but the hierrchicl model is widely pplied. The system chrcteristics re s follows: it is multi-prmetricl, multi-criteri decision process, where the input prmeters re the mesured risk fctors, nd the multi-criteri rules of the system behviors re included in the decision process. The Anlyticl Hierrchy Process (AHP) expnds this complex system with the pirwise comprison of the fctors' importnce nd interction [5]. In this pper, fter short generl review of the min chrcteristics of risk mngement pplictions, hierrchicl, multilevel risk mngement method will be presented in fuzzy environment. The given cse study is trvel risk-level clcultion bsed on the presented model. In the lst section preliminry mthemticl description is presented bsed on pirwise comprison mtrix nd AHP expnded principles. 2 Risk Mngement Risk mngement is the identifiction, ssessment, nd prioritiztion of risks, defined s the effects of uncertinty of objectives, whether positive or negtive, followed by the coordinted nd economicl ppliction of resources to minimize, monitor, nd control the probbility nd/or impct of unfortunte events [6]. The techniques used in risk mngement hve been tken from other res of system mngement. Informtion technology, the vilbility of resources, nd 92

3 Act Polytechnic Hungric Vol. 7, No. 4, 21 other fcts hve helped to develop the new risk mngement with the methods to identify, mesure nd mnge the risks, thereby reducing the potentil for unexpected loss or hrm [7]. Generlly, risk mngement process involves the following min stges. The first step is the identifiction of risks nd potentil risks to the system opertion t ll levels. Evlution, the mesure nd structurl systemtiztion of the identified risks, is the next step. Mesurement is defined by how serious the risks re in terms of consequences nd the likelihood of occurrence. It cn be qulittive or quntittive description of their effects on the environment. Pln nd control re the next stges to prepre the risk mngement system. This cn include the development of response ctions to these risks, nd the pplied decision or resoning method. Monitoring nd review, s the next stge, is importnt if we re to hve system with feedbck, nd the risk mngement system is open to improvement. This will ensure tht the risk mngement process is dynmic nd continuous, with correct verifiction nd vlidity control. The review process includes the possibility of new dditionl risks nd new forms of risk description. In the future the role of complex risk mngement will be to try to increse the dmging effects of risk fctors. 2.1 Fuzzy Risk Mngement Risk mngement is complex, multi-criteri nd multi-prmetricl system full of uncertinties nd vgueness. Generlly the risk mngement system in its preliminry form contins the identifiction of the risk fctors of the investigted process, the representtion of the mesured risks, nd the decision model. The system cn be enlrged by monitoring nd review in order to improve the risk mesure description nd decision system. The models for solving re knowledgebsed models, where linguisticlly communicted modeling is needed, nd objective nd subjective knowledge (definitionl, cusl, sttisticl, nd heuristic knowledge) is included in the decision process. Considering ll these conditions, fuzzy set theory helps mnge complexity nd uncertinties nd gives userfriendly visuliztion of the system construction nd working model. Fuzzy-bsed risk mngement models ssume tht the risk fctors re fuzzified (becuse of their uncertinties or linguistic representtion); furthermore the risk mngement nd risk level clcultion sttements re represented in the form of if premises then conclusion rule forms, nd the risk fctor clcultion or output decision (summrized output) is obtined using fuzzy pproximte resoning methods. Considering the fuzzy logic nd fuzzy set theory results, there re further possibilities to extend fuzzy-bsed risk mngement models modeling risk fctors with type-2 fuzzy sets, representing the level of the uncertinties of the membership vlues, or using specil, problem-oriented types of opertors in the fuzzy decision mking process. 93

4 M. Tkács Multilevel Fuzzy Approch to the Risk nd Disster Mngement The hierrchicl or multilevel construction of the decision process, the grouped structurl systemtiztion of the fctors, with the possibility of gining some subsystems, depending on their importnce or other significnt environment chrcteristics or on lying emphsis on risk mngement ctors, is possible wy to mnge the complexity of the system. Crr nd Th describe common hierrchicl-risk brekdown structure for developing knowledge-driven risk mngement, which is suitble for the fuzzy pproch [8]. Strting with simple definition of the risk s the dverse consequences of n event, such events nd consequences re full of uncertinty, nd inherent precutionry principles, such s sufficient certinty, prevention, nd desired level of protection. All of these cn be represented s fuzzy sets. The strtegy of the risk mngement my be viewed s simplified exmple of precutionry decision process bsed on the principles of fuzzy logic decision mking [9]. 3 Grouped, Weighted Fuzzy Model Bsed on the min ides from [8] risk mngement system cn be built up s hierrchicl system of risk fctors (inputs), risk mngement ctions (decision mking system) nd direction or directions for the next level of risk sitution solving lgorithm. Actully, those directions re risk fctors for the ction on the next level of the risk mngement process. To sum this up: risk fctors in complex system re grouped to the risk event where they figure. The risk event determintes the necessry ctions to clculte nd/or increse the negtive effects. Actions re described by if then type rules. With the output those components frme one unit in the whole risk mngement system, where the items re ttched on the principle of the time-scheduling, significnce or other criteri (Fig. 1). Input Risk Fctors (RF) grouped nd ssigned to the current ction re described by the Fuzzy Risk Mesure Sets (FRMS) such s low, norml, high, nd so on. Some of the risk fctor groups, risk fctors or mngement ctions hve different weighted role in the system opertion. The system prmeters re represented with fuzzy sets, nd the grouped risk fctors vlues give intermitted results [14]. Considering some system input prmeters, which determine the risk fctors role in the decision mking system, intermitted results cn be weighted nd forwrded to the next level of the resoning process. 94

5 Act Polytechnic Hungric Vol. 7, No. 4, 21 Risk event nd ctions (if.. then rules)1 Risk Fctor11 (the output signl of risk ction 21) () Risk Fctor 1n Risk event nd ctions (if.. then rules)21 Risk Fctor21/1 Risk Fctor21/2 Figure 1 The hierrchicl risk mngement construction 3.1 Disster Mngement - Cse Studies Disster event monitoring s one of the steps in risk nd crisis mngement is very complex system with uncertin input prmeters. Fuzzified inputs, the fuzzy rule bse, which is constructed using objective nd subjective definitionl, cusl, sttisticl, nd heuristic knowledge, is ble to present the problem in userfriendly form. The complexity of the system cn be mnged by the hierrchiclly-structured resoning model, with themticlly-grouped, nd if necessry, gined risk fctor structure. Crisis or disster event monitoring provides bsic informtion for mny decisions in tody s socil life. The disster recovery strtegies of countries, the finncil investments plns of investors, or the level of the tourism ctivities ll depend on different groups of disster or crisis fctors. A disster cn be defined s n unforeseen event tht cuses gret dmge, destruction nd humn suffering, evolved from nturl or mn-mde event tht negtively ffects life, property, livelihood or industry. A disster is the strt of crisis, nd often results in permnent chnges to humn societies, ecosystems nd the environment. Bsed on the experts observtions [11], [12], the risk fctors which prejudice disster sitution cn be clssified s follows: - nturl dissters; - mn-mde dissters (unintended events or willful events). Nturl dissters rise without direct humn involvement, but my often occur, becuse of humn ctions prior, during or fter the disster itself (for exmple, hurricne my cuse flooding by rin or by storm surge). The nturl dissters cn lso be grouped primrily bsed on the root cuse: - hydro-meteorologicl dissters: floods, storms, nd droughts; 95

6 M. Tkács Multilevel Fuzzy Approch to the Risk nd Disster Mngement - geophysicl dissters: erthqukes, tsunmis nd volcnic eruptions; - biologicl dissters: epidemics nd insect infesttions; or they cn be structured hierrchiclly, bsed on sequentil supervention. The exmple, presented in this pper, is constructed bsed on the first principle, with fuzzified inputs nd hierrchiclly-constructed rule bse system (Figure 2). The risk or disster fctors, s the inputs of one subsystem of the globl fuzzy decision mking system, give outputs for the next level of decision, where the min nturl disster clsses result is the totl impct of this risk ctegory. Figure 2 Hierrchiclly constructed rule bse system This pproch llows dditionl possibilities to hndle the set of risk fctors. It is esy to dd one fctor to fctors-subset; the complexity of the rule bse system is chnged only in the ffected subsystem. In different sesons, environmentl situtions etc., some of the risk groups re more importnt for the globl conclusion thn others, nd this cn be chieved with n importnce fctor (number from the [,1]). Mn-mde dissters hve n element of humn intent or negligence. However, some of those events cn lso occur s the result of nturl disster. Mn-mde fctors nd dissters cn be structured in mnner similr to the nturl risks nd events. One of the possible clssifictions of the bsic mn-mde risk fctors or disster events (pplied in our exmple) is s follows: 1. unintended events: - Industril ccidents (chemicl spills, collpses of industril infrstructures); - Trnsport or telecommuniction ccidents (by ir, ril, rod or wter mens of trnsport); 96

7 Act Polytechnic Hungric Vol. 7, No. 4, 21 - Economic crises (growth collpse, hyperinfltion, nd finncil crisis); 2. willful events (violence, terrorism, civil strife, riots, nd wr). In the investigted exmple, the effects of mn-mde dissters s inputs in the decision mking process re represented with their reltive frequency, nd the premises of the relted fuzzy rules re very often represented with the membership functions: never, rrely, frequently, etc. 1 The input prmeters re represented on the unit universe [,1] with tringulr or trpezoidl membership functions describing the linguistic vribles such s the frequency of the floods, for exmple: "low", "medium" or "high" (Fig. 3). The system ws built in the Mtlb Fuzzy Toolbox nd Simulink environment. Figure 3 Membership functions of the flood frequencies The risk nd disster fctors re grouped in two min groups: humn- nd nturebsed group. The inputs re crisp, but the rule bse system is hierrchiclly constructed (Fig. 4), nd the decision mking is Mmdni type pproximte resoning with bsic min nd mx opertors. 1 The Mtlb Fuzzy Toolbox nd Simulink elements were in the preliminry, prtil form constructed by Attil Krnis, student of the Óbud University s the project on the course "Fuzzy systems for engineers". 97

8 M. Tkács Multilevel Fuzzy Approch to the Risk nd Disster Mngement ertfreq intensity FLC erthq vulcnctivity FLC nturea FLC vulcn FLC Nture floodctivity FLC flood hurricnct FLC ntureb FLC hurricn.6667 plguehistory rebelfreq FLC rebel FLC All7 ri skl evel higienlevel FLC plgue helthinsurenc honourmesure FLC conflicts FLC honour ethnicconflict gykorisg FLC ethnicconf robberfreq murderfreq FLC welthcrime FLC Humn securitylevel FLC crime FLC lifecrime viloncemes terrorismct FLC terrorism FLC power wrct FLC wrzone dicttship FLC dictture Figure 4 The system construction for the effects of dissters to clculte the trvel risk level in country The finl conclusion bsed on both dissters' s risk fctors' groups is shown in Figure 5. Figure 5 The finl conclusion bsed on both dissters' s risk fctors' groups 98

9 Act Polytechnic Hungric Vol. 7, No. 4, 21 4 First Step to the Fuzzy AHP Model for Groupbsed Risk Mngement Model Let X 1, X 2,..., X n be the set of elements in decision mking system. It is nturl wy to use the frmework of A n n squre mtrix to represent the pirwise comprisons of the dominnce nd interction of those elements. Anlyticl Hierrchy Process (AHP) is method for estimting the preference vlues from the pirwise comprison mtrix. APH llows for the considertion of both qulittive nd quntittive spects of the decision, expnding the decision with the one-to-one comprison of the objectives, criteri, constrints or lterntives in the system model. The pirwise comprison in the AHP ssume tht the decision-mker cn compre ny two elements, for exmple X i nd X j t the sme level of the hierrchy in the system nd provide numericl vlue ij for the rtio of their importnce. Sty suggests using scle 1 to 9 to describe the preference mesures [5], but in different pplictions there re presented other possible scles too [1]. Let ij > 1 if the element X i is preferred to property = 1 for i=1,2,...n, j=1,2,...n. ji ij X j, correspondingly, the reciprocl ( ) n n 1 Ech set of comprisons for level with n elements requires judgments, 2 which re further used to construct positive reciprocl mtrix A n n of pirwise comprisons [1]. Let us interpret the comprison mtrix A n n s the mtrix of the dominnce mesures regrding the set of risk fctors in risk mngement system. If the fctors re grouped, nd the groups re more or less independent, the comprison mtrix hs the block digonl mtrix form, nd this llows us to pre down the computtion complexity. Exmple. Let X 1, X 2,..., X n be the set of risk fctors grouped in p groups, nd let it contin the first fctors group the fctors X 1, X 2, X3. The pirwise comprison of them is represented with the 3 3 dimensionl sub-mtrix A 11. The further representtions re similr to this, so the next to lst group contins two fctors: X n 2, X n 1, with the 2 2 dimensionl sub-mtrix A p 1, p 1, the lst group holds only one fctor. 99

10 M. Tkács Multilevel Fuzzy Approch to the Risk nd Disster Mngement A = n 2, n 2 n 1, n 2 n 2, n 1 n 1, n 1 A = nn 11 A p 1, p 1 Ap, p It is nturl tht the comprison vlues ii re units, ii = 1 for ll i=1,2,...n. Let x ( x1, x2,..., x n ) X ( X X,..., ) = be the ctul input vector of the risk fctors' vector = 1, 2 X n. The influence of the pirwise dominnce comprison of the fctors on the ctul input vector cn be represented s trnsformtion described T with the mtrix opertion A x. The gol is to forwrd weighted input vector to the system, where the weight-multiplier λ holds up the informtion bout the pirwise dominnce comprison of the input fctors: T T A x = λ x. The method for computing the λ multiplier cn be the eigenvlue method. On prcticl score only rel eigenvlues cn be ccepted. If there re not rel eigenvlues in the set of solutions, the multiplier λ is unit one, λ =1. If there exists more thn one solution with the proposed conditions, the chosen one should be the eigenvlue which keep the input vectors in their universe, but permits the highest efficiency of the decision. The AHP should be pplied before the risk level clcultion or decision mking process. The open problems re: to find the best wy to crete pirwise comprison of the fctors, becuse the vlues re the judgments obtined from n pproprite semntic scle. In prctice the decision-mkers usully give some or ll pir-topir comprison vlues with n uncertinty degree rther thn precise rtings; to djust the scle of the comprison vlues to keep the weighted input vector in their universe, but permitting the highest efficiency of the decision; to build up fuzzy AHP model for the preliminry comprison of the risk fctors in the risk mngement system. Conclusions Risk mngement pplictions re complex, multi-criteri nd usully multilevel decision systems, required to mnge uncertinties. The fuzzy environment is ble 1

11 Act Polytechnic Hungric Vol. 7, No. 4, 21 to represent the mbiguous risk fctors nd rules in n cceptble form, where the risk fctors re grouped bsed on their roles in the decision-mking system. The given cse study is trvel risk-level clcultion bsed on the presented model. The pirwise comprison mtrix is the first step in introducing the fuzzy AHP model for the multilevel, hierrchiclly-structured risk mngement system, with further open problems nd the possibility for fine tuning in the resoning process. Acknowledgement This work ws supported by the Óbud University nd Vojvodin Acdemy of Science nd Art (project title: Mthemticl Models for Decision Mking under Uncertin Conditions nd Their Applictions). References [1] Himes, Y. Y., Risk Modeling, Assessment, nd Mngement. 3 rd Edition. John Wiley & Sons (29) [2] Vose, D., Risk Anlysis: Quntittive Guide, 3 rd Edition. John Wiley & Sons (29) [3] Wng, J. X., Roush, M. L., pf_rd_p= &pf_rd_s=lpo-top-stripe- 1&pf_rd_t=21&pf_rd_i= X&pf_rd_m=ATVPDKIKXDER&p f_rd_r=1newtg6pbe2qgghkfgty Wht Every Engineer Should Know About Risk Engineering nd Mngement, Mrcel Dekker Inc, (2)[4] Kleiner, Y., Rjni, B., Sdiq, R., Filure Risk Mngement of Buried Infrstructure Using Fuzzy-bsed Techniques, Journl of Wter Supply Reserch nd Technology: Aqu, Vol. 55, No. 2, pp , Mrch (26) [5] Sty, T. L., Vrgs, L. G. Models, Methods, Concepts nd Applictions of the Anlytic Hierrchy Process, Kluwer Acdemic press, (21) [6] Dougls, H. The Filure of Risk Mngement: Why It's Broken nd How to Fix It. John Wiley & Sons. p. 46 (29) [7] [8] Crr, J. H. M., Th, V.: A Fuzzy Approch to Construction Project Risk Assessment nd Anlysis: Construction Project Risk Mngement System, Advnces in Engineering Softwre, Volume 32, Number 1, pp (11) October (21) [9] Cmeron, E., Peloso, G. F. Risk Mngement nd the Precutionry Principle: A Fuzzy Logic Model, Risk Anlysis, Vol. 25, No. 4, pp , August (25) 11

12 M. Tkács Multilevel Fuzzy Approch to the Risk nd Disster Mngement [1] Mikhilov, L., Deriving Priorities from Fuzzy Pirwise Comprison Judgements, Fuzzy Sets nd Systems Vol. 134, pp , (23) [11] Ysuyuki Swd, The Impct of Nturl nd Mnmde Dissters on Household Welfre, [12] Diddster Definition, [13] Németh-Erdődi, K., Risk Mngement nd Loss Optimiytion t Design Process of Products, Act Polytechnic Hungric, Vol. 5, No. 3 (28) [14] Tkács, M., Structured Risk Mngement Model with Fuzzy Bckground, Proc. of FSTA 21, Tenth Interntionl Conference On Fuzzy Set Theory And Applictions, Liptovský Ján, Slovk Republic, Februry (21) 12