集成DEMATELISM的復(fù)雜系統(tǒng)層次劃分研究一、本文概述Overviewofthisarticle本文旨在探討和研究集成DEMATELISM（DecisionMakingTrialandEvaluationLaboratory-InterpretativeStructuralModeling）的復(fù)雜系統(tǒng)層次劃分方法。我們將首先概述復(fù)雜系統(tǒng)的特性及其層次劃分的重要性，然后介紹DEMATELISM方法的基本原理及其在復(fù)雜系統(tǒng)分析中的應(yīng)用。接下來，我們將詳細(xì)闡述如何將DEMATELISM方法集成到復(fù)雜系統(tǒng)的層次劃分中，以提高分析的準(zhǔn)確性和效率。我們將通過案例研究或?qū)嵶C分析來驗(yàn)證所提出方法的有效性和實(shí)用性，為復(fù)雜系統(tǒng)的管理和決策提供新的理論支持和實(shí)踐指導(dǎo)。ThisarticleaimstoexploreandstudythehierarchicalpartitioningmethodforcomplexsystemsintegratingDEMATELISM(DecisionMakingTrialandEvaluationLaboratoryInterpretativeStructuralModeling).Wewillfirstoutlinethecharacteristicsofcomplexsystemsandtheimportanceofhierarchicaldivision,andthenintroducethebasicprinciplesofDEMATELISMmethodanditsapplicationincomplexsystemanalysis.Next,wewillelaborateonhowtointegratetheDEMATELISMmethodintothehierarchicaldivisionofcomplexsystemstoimprovetheaccuracyandefficiencyofanalysis.Wewillverifytheeffectivenessandpracticalityoftheproposedmethodthroughcasestudiesorempiricalanalysis,providingnewtheoreticalsupportandpracticalguidanceforthemanagementanddecision-makingofcomplexsystems.在復(fù)雜系統(tǒng)研究領(lǐng)域，層次劃分是一種重要的分析方法，它有助于理解和分析系統(tǒng)的結(jié)構(gòu)和功能。然而，傳統(tǒng)的層次劃分方法在面對高度復(fù)雜和動態(tài)變化的系統(tǒng)時，往往難以取得理想的效果。因此，本文提出的集成DEMATELISM的復(fù)雜系統(tǒng)層次劃分方法具有重要的理論價(jià)值和現(xiàn)實(shí)意義。Inthefieldofcomplexsystemresearch,hierarchicalpartitioningisanimportantanalyticalmethodthathelpstounderstandandanalyzethestructureandfunctionofthesystem.However,traditionalhierarchicalpartitioningmethodsoftenstruggletoachieveidealresultswhenfacinghighlycomplexanddynamicallychangingsystems.Therefore,thehierarchicaldivisionmethodforcomplexsystemsintegratingDEMATELISMproposedinthisarticlehasimportanttheoreticalvalueandpracticalsignificance.DEMATELISM是一種基于圖論和矩陣?yán)碚摰臎Q策分析方法，它通過構(gòu)建系統(tǒng)的有向圖和影響矩陣，揭示系統(tǒng)元素之間的相互作用和依賴關(guān)系。通過將DEMATELISM方法集成到復(fù)雜系統(tǒng)的層次劃分中，我們可以更準(zhǔn)確地識別和劃分系統(tǒng)的層次結(jié)構(gòu)，從而更好地理解和分析系統(tǒng)的運(yùn)行機(jī)制和演化過程。DEMATELISMisadecisionanalysismethodbasedongraphtheoryandmatrixtheory,whichrevealstheinteractionsanddependenciesbetweensystemelementsbyconstructingadirectedgraphandinfluencematrixofthesystem.ByintegratingtheDEMATELISMmethodintothehierarchicaldivisionofcomplexsystems,wecanmoreaccuratelyidentifyandpartitionthehierarchicalstructureofthesystem,therebybetterunderstandingandanalyzingtheoperatingmechanismandevolutionprocessofthesystem.本文的研究內(nèi)容將包括理論闡述、方法設(shè)計(jì)、案例分析和結(jié)論總結(jié)等部分。我們將通過理論闡述明確復(fù)雜系統(tǒng)層次劃分的重要性和DEMATELISM方法的適用性；通過方法設(shè)計(jì)構(gòu)建集成DEMATELISM的復(fù)雜系統(tǒng)層次劃分模型；通過案例分析驗(yàn)證所提出方法的有效性和實(shí)用性；通過結(jié)論總結(jié)概括本文的主要研究成果和貢獻(xiàn)。Theresearchcontentofthisarticlewillincludetheoreticalexposition,methoddesign,caseanalysis,andconclusionsummary.WewillclarifytheimportanceofhierarchicaldivisionofcomplexsystemsandtheapplicabilityoftheDEMATELISMmethodthroughtheoreticalexposition;DesignandconstructahierarchicalpartitioningmodelforcomplexsystemsintegratingDEMATELISMthroughmethods;Verifytheeffectivenessandpracticalityoftheproposedmethodthroughcaseanalysis;Summarizethemainresearchfindingsandcontributionsofthisarticlethroughtheconclusion.通過本文的研究，我們期望能夠?yàn)閺?fù)雜系統(tǒng)的層次劃分提供一種新的思路和方法，為復(fù)雜系統(tǒng)的管理和決策提供新的理論支持和實(shí)踐指導(dǎo)。我們也期望通過本文的研究推動DEMATELISM方法在復(fù)雜系統(tǒng)分析領(lǐng)域的應(yīng)用和發(fā)展。Throughtheresearchinthisarticle,wehopetoprovideanewapproachandmethodforthehierarchicaldivisionofcomplexsystems,andprovidenewtheoreticalsupportandpracticalguidanceforthemanagementanddecision-makingofcomplexsystems.WealsohopetopromotetheapplicationanddevelopmentofDEMATELISMmethodinthefieldofcomplexsystemanalysisthroughtheresearchinthisarticle.二、復(fù)雜系統(tǒng)與DEMATELISM概述OverviewofComplexSystemsandDEMATELISM在當(dāng)今世界，復(fù)雜系統(tǒng)無處不在，從自然界的生態(tài)系統(tǒng)到社會經(jīng)濟(jì)的網(wǎng)絡(luò)結(jié)構(gòu)，再到人類思維的決策過程，無一不體現(xiàn)出復(fù)雜系統(tǒng)的特性。復(fù)雜系統(tǒng)通常具有高度的非線性、自組織性、動態(tài)演化性和多層次性，這些特性使得對復(fù)雜系統(tǒng)的研究充滿挑戰(zhàn)。因此，如何有效地理解和分析復(fù)雜系統(tǒng)，成為了當(dāng)前科學(xué)研究的重要課題。Intoday'sworld,complexsystemsareubiquitous,reflectingthecharacteristicsofcomplexsystemsfromnaturalecosystemstosocio-economicnetworkstructures,andeventohumandecision-makingprocesses.Complexsystemstypicallyexhibithighlevelsofnonlinearity,self-organization,dynamicevolution,andmulti-levelcharacteristics,whichmakethestudyofcomplexsystemschallenging.Therefore,howtoeffectivelyunderstandandanalyzecomplexsystemshasbecomeanimportanttopicincurrentscientificresearch.DEMATELISM（DecisionMakingTrialandEvaluationLaboratorywithInterpretativeStructuralModeling）是一種基于解釋結(jié)構(gòu)模型（ISM）的決策分析方法，它通過構(gòu)建系統(tǒng)要素間的直接影響矩陣，揭示出系統(tǒng)內(nèi)部的層次結(jié)構(gòu)和要素間的邏輯關(guān)系。DEMATELISM不僅能夠處理復(fù)雜系統(tǒng)中的不確定性和模糊性，還能夠有效地識別出系統(tǒng)中的關(guān)鍵要素和潛在問題，為決策提供科學(xué)依據(jù)。DEMATELISM(DecisionMakingTrialandEvaluationLaboratorywithInterpretiveStructuralModeling)isadecisionanalysismethodbasedonInterpretiveStructuralModeling(ISM).Itconstructsadirectimpactmatrixbetweensystemelements,revealingthehierarchicalstructurewithinthesystemandthelogicalrelationshipsbetweenelements.DEMATELISMcannotonlyhandleuncertaintyandfuzzinessincomplexsystems,butalsoeffectivelyidentifykeyelementsandpotentialproblemsinthesystem,providingscientificbasisfordecision-making.在復(fù)雜系統(tǒng)的研究中，DEMATELISM的應(yīng)用具有顯著優(yōu)勢。它能夠通過定性和定量相結(jié)合的方式，系統(tǒng)地分析系統(tǒng)中的各種要素及其相互關(guān)系，從而幫助研究者更好地理解系統(tǒng)的運(yùn)行機(jī)制和演化規(guī)律。DEMATELISM還能夠提供一種可視化的分析工具，將復(fù)雜的系統(tǒng)結(jié)構(gòu)以直觀的方式呈現(xiàn)出來，便于決策者進(jìn)行方案選擇和問題處理。Inthestudyofcomplexsystems,theapplicationofDEMATELISMhassignificantadvantages.Itcansystematicallyanalyzevariouselementsandtheirinterrelationshipsinthesystemthroughacombinationofqualitativeandquantitativemethods,therebyhelpingresearchersbetterunderstandtheoperatingmechanismandevolutionarylawsofthesystem.DEMATELISMcanalsoprovideavisualanalysistoolthatpresentscomplexsystemstructuresinanintuitiveway,makingiteasierfordecision-makerstochoosesolutionsandhandleproblems.復(fù)雜系統(tǒng)與DEMATELISM之間存在著緊密的聯(lián)系。通過對復(fù)雜系統(tǒng)的深入研究，我們可以更好地理解和應(yīng)用DEMATELISM方法；而DEMATELISM的應(yīng)用則能夠?yàn)槲覀兲峁┮环N新的視角和工具，幫助我們更好地分析和解決復(fù)雜系統(tǒng)中的問題。因此，將DEMATELISM應(yīng)用于復(fù)雜系統(tǒng)的層次劃分研究具有重要的理論意義和實(shí)踐價(jià)值。ThereisacloseconnectionbetweencomplexsystemsandDEMATELISM.Throughin-depthresearchoncomplexsystems,wecanbetterunderstandandapplytheDEMATELISMmethod;TheapplicationofDEMATELISMcanprovideuswithanewperspectiveandtools,helpingusbetteranalyzeandsolveproblemsincomplexsystems.Therefore,applyingDEMATELISMtothehierarchicaldivisionresearchofcomplexsystemshasimportanttheoreticalsignificanceandpracticalvalue.三、集成DEMATELISM的復(fù)雜系統(tǒng)層次劃分方法AHierarchicalPartitionMethodforComplexSystemsIntegratingDEMATELISM在面對復(fù)雜系統(tǒng)時，傳統(tǒng)的層次劃分方法往往難以有效地揭示系統(tǒng)內(nèi)部的結(jié)構(gòu)關(guān)系和動態(tài)演變過程。因此，本文提出將DEMATELISM（DecisionMakingTrialandEvaluationLaboratorywithInterpretiveStructuralModeling）方法集成到復(fù)雜系統(tǒng)的層次劃分研究中，以提供更為深入和精確的分析工具。Whenfacingcomplexsystems,traditionalhierarchicalpartitioningmethodsoftenfinditdifficulttoeffectivelyrevealtheinternalstructuralrelationshipsanddynamicevolutionprocessesofthesystem.Therefore,thisarticleproposestointegratetheDEMATELISM(DecisionMakingTrialandEvaluationLaboratorywithInteractiveStructuralModeling)methodintothehierarchicalpartitioningresearchofcomplexsystems,inordertoprovidemorein-depthandaccurateanalysistools.DEMATELISM是一種基于圖論和矩陣?yán)碚摰臎Q策分析方法，它通過構(gòu)建直接影響矩陣和綜合影響矩陣，揭示系統(tǒng)中各元素之間的直接和間接關(guān)系，進(jìn)而通過層次化結(jié)構(gòu)模型展示系統(tǒng)的內(nèi)部結(jié)構(gòu)。在復(fù)雜系統(tǒng)層次劃分中，DEMATELISM的應(yīng)用主要包括以下幾個步驟：DEMATELISMisadecisionanalysismethodbasedongraphtheoryandmatrixtheory.Itconstructsdirectinfluencematricesandcomprehensiveinfluencematricestorevealthedirectandindirectrelationshipsbetweenvariouselementsinthesystem,andthendisplaystheinternalstructureofthesystemthroughahierarchicalstructuralmodel.Inthehierarchicaldivisionofcomplexsystems,theapplicationofDEMATELISMmainlyincludesthefollowingsteps:通過對復(fù)雜系統(tǒng)的深入分析，確定系統(tǒng)的組成元素及其之間的相互關(guān)系。這些元素可以是系統(tǒng)的各個組成部分，也可以是影響系統(tǒng)發(fā)展的關(guān)鍵因素。Throughin-depthanalysisofcomplexsystems,determinetheconstituentelementsofthesystemandtheirinterrelationships.Theseelementscanbevariouscomponentsofthesystem,ortheycanbekeyfactorsaffectingthedevelopmentofthesystem.根據(jù)元素之間的關(guān)系構(gòu)建直接影響矩陣。直接影響矩陣是一個方陣，其元素表示各元素之間的直接影響程度。這一步驟的關(guān)鍵在于準(zhǔn)確量化元素之間的相互影響，可以通過專家打分、數(shù)據(jù)分析等方法獲取。Constructadirectimpactmatrixbasedontherelationshipsbetweenelements.Thedirectinfluencematrixisasquarematrixwhoseelementsrepresentthedegreeofdirectinfluencebetweeneachelement.Thekeytothisstepistoaccuratelyquantifythemutualinfluencebetweenelements,whichcanbeobtainedthroughmethodssuchasexpertscoringanddataanalysis.然后，通過計(jì)算綜合影響矩陣，進(jìn)一步揭示元素之間的間接影響關(guān)系。綜合影響矩陣是直接影響矩陣的冪次和，它可以反映元素之間的長期影響和反饋關(guān)系。Then,bycalculatingthecomprehensiveinfluencematrix,furtherrevealtheindirectinfluencerelationshipbetweenelements.Thecomprehensiveimpactmatrixisthesumofpowersofthedirectimpactmatrix,whichcanreflectthelong-termeffectsandfeedbackrelationshipsbetweenelements.接下來，基于綜合影響矩陣，利用圖論中的可達(dá)性矩陣和先行集、后續(xù)集等概念，對系統(tǒng)進(jìn)行層次劃分?？蛇_(dá)性矩陣表示系統(tǒng)中任意兩個元素之間是否存在直接或間接的影響關(guān)系，通過可達(dá)性矩陣可以確定元素的層次結(jié)構(gòu)。Next,basedonthecomprehensiveinfluencematrix,thesystemishierarchicallydividedusingthereachabilitymatrixandconceptssuchasantecedentsandsequelsingraphtheory.Thereachabilitymatrixrepresentswhetherthereisadirectorindirectrelationshipbetweenanytwoelementsinthesystem,andthehierarchicalstructureoftheelementscanbedeterminedthroughthereachabilitymatrix.通過層次化結(jié)構(gòu)模型展示復(fù)雜系統(tǒng)的層次劃分結(jié)果。該模型可以清晰地展示系統(tǒng)中各元素之間的關(guān)系和層次結(jié)構(gòu)，為決策者和研究者提供直觀的分析工具。Displaythehierarchicaldivisionresultsofcomplexsystemsthroughahierarchicalstructuralmodel.Thismodelcanclearlydisplaytherelationshipsandhierarchicalstructurebetweenvariouselementsinthesystem,providingdecision-makersandresearcherswithintuitiveanalyticaltools.集成DEMATELISM的復(fù)雜系統(tǒng)層次劃分方法通過構(gòu)建直接影響矩陣和綜合影響矩陣，利用圖論和矩陣?yán)碚搶ο到y(tǒng)進(jìn)行層次劃分，為復(fù)雜系統(tǒng)的分析和決策提供了有力的支持。該方法不僅提高了層次劃分的準(zhǔn)確性和深入性，還有助于揭示系統(tǒng)的內(nèi)部結(jié)構(gòu)和動態(tài)演變過程。在未來的研究中，可以進(jìn)一步探索DEMATELISM與其他方法的結(jié)合，以提高復(fù)雜系統(tǒng)層次劃分的效率和精度。ThehierarchicaldivisionmethodofcomplexsystemsintegratedwithDEMATELISMconstructsdirectimpactmatricesandcomprehensiveimpactmatrices,andusesgraphtheoryandmatrixtheorytodividethesystemintolayers,providingstrongsupportfortheanalysisanddecision-makingofcomplexsystems.Thismethodnotonlyimprovestheaccuracyanddepthofhierarchicaldivision,butalsohelpstorevealtheinternalstructureanddynamicevolutionprocessofthesystem.Infutureresearch,thecombinationofDEMATELISMandothermethodscanbefurtherexploredtoimprovetheefficiencyandaccuracyofhierarchicalpartitioningofcomplexsystems.四、案例分析Caseanalysis為了驗(yàn)證集成DEMATELISM的復(fù)雜系統(tǒng)層次劃分方法的有效性和實(shí)用性，本研究選取了一個典型的復(fù)雜系統(tǒng)——智慧城市系統(tǒng)作為案例進(jìn)行分析。智慧城市系統(tǒng)涉及多個領(lǐng)域和部門，包括交通、能源、環(huán)保、醫(yī)療、教育等，各子系統(tǒng)之間相互關(guān)聯(lián)、相互影響，形成了復(fù)雜的系統(tǒng)網(wǎng)絡(luò)。InordertoverifytheeffectivenessandpracticalityofthehierarchicaldivisionmethodforcomplexsystemsintegratedwithDEMATELISM,thisstudyselectedatypicalcomplexsystem-thesmartcitysystem-asacasestudyforanalysis.Thesmartcitysysteminvolvesmultiplefieldsanddepartments,includingtransportation,energy,environmentalprotection,healthcare,education,etc.Eachsubsystemisinterrelatedandaffectseachother,formingacomplexsystemnetwork.我們對智慧城市系統(tǒng)的各個子系統(tǒng)進(jìn)行了梳理和分析，識別出了各個子系統(tǒng)之間的相互作用關(guān)系。然后，基于DEMATELISM方法，我們構(gòu)建了智慧城市系統(tǒng)的層次結(jié)構(gòu)模型，并計(jì)算了各個子系統(tǒng)之間的直接影響矩陣和綜合影響矩陣。Wehavesortedandanalyzedthevarioussubsystemsofthesmartcitysystem,andidentifiedtheinteractionrelationshipsbetweenthem.Then,basedontheDEMATELISMmethod,weconstructedahierarchicalmodelofthesmartcitysystemandcalculatedthedirectimpactmatrixandcomprehensiveimpactmatrixbetweeneachsubsystem.通過層次結(jié)構(gòu)模型的分析，我們發(fā)現(xiàn)智慧城市系統(tǒng)可以分為三個層次：基礎(chǔ)層、服務(wù)層和頂層?；A(chǔ)層包括交通、能源、環(huán)保等基礎(chǔ)設(shè)施子系統(tǒng)，為整個系統(tǒng)提供支撐和保障；服務(wù)層包括醫(yī)療、教育、文化等公共服務(wù)子系統(tǒng)，為城市居民提供便捷、高效的服務(wù)；頂層則是智慧城市系統(tǒng)的核心，包括智慧政務(wù)、智慧安全等子系統(tǒng)，負(fù)責(zé)整個系統(tǒng)的協(xié)調(diào)和管理。Throughtheanalysisofthehierarchicalstructuremodel,wefoundthatthesmartcitysystemcanbedividedintothreelevels:thebasiclayer,theservicelayer,andthetoplayer.Thebasiclayerincludesinfrastructuresubsystemssuchastransportation,energy,andenvironmentalprotection,providingsupportandguaranteefortheentiresystem;Theservicelayerincludespublicservicesubsystemssuchashealthcare,education,andculture,providingconvenientandefficientservicesforurbanresidents;Thetop-levelisthecoreofthesmartcitysystem,includingsubsystemssuchassmartgovernmentandsmartsecurity,responsibleforthecoordinationandmanagementoftheentiresystem.我們還通過綜合影響矩陣的分析，發(fā)現(xiàn)了一些關(guān)鍵子系統(tǒng)和關(guān)鍵影響因素。例如，交通子系統(tǒng)和能源子系統(tǒng)對整個系統(tǒng)的影響較大，是智慧城市系統(tǒng)中的重要基礎(chǔ)設(shè)施；智慧政務(wù)子系統(tǒng)對整個系統(tǒng)的協(xié)調(diào)和管理起著關(guān)鍵作用，是智慧城市系統(tǒng)的核心。Wealsoidentifiedsomekeysubsystemsandinfluencingfactorsthroughtheanalysisofthecomprehensiveimpactmatrix.Forexample,thetransportationandenergysubsystemshaveasignificantimpactontheentiresystemandareimportantinfrastructureinthesmartcitysystem;Thesmartgovernmentsubsystemplaysacrucialroleincoordinatingandmanagingtheentiresystem,andisthecoreofthesmartcitysystem.通過集成DEMATELISM的復(fù)雜系統(tǒng)層次劃分方法，我們成功地對智慧城市系統(tǒng)進(jìn)行了層次劃分和關(guān)鍵因素識別。這不僅有助于我們更好地理解智慧城市系統(tǒng)的結(jié)構(gòu)和運(yùn)行機(jī)制，還為未來的智慧城市規(guī)劃和建設(shè)提供了重要的參考依據(jù)。ByintegratingDEMATELISMintoacomplexsystemhierarchymethod,wehavesuccessfullyclassifiedthesmartcitysystemintodifferentlevelsandidentifiedkeyfactors.Thisnotonlyhelpsusbetterunderstandthestructureandoperationalmechanismofsmartcitysystems,butalsoprovidesimportantreferencebasisforfuturesmartcityplanningandconstruction.五、結(jié)論與展望ConclusionandOutlook本文深入探討了集成DEMATELISM的復(fù)雜系統(tǒng)層次劃分研究方法。通過對DEMATELISM方法的詳細(xì)介紹和其在復(fù)雜系統(tǒng)層次劃分中的應(yīng)用，本研究不僅為復(fù)雜系統(tǒng)的理解和分析提供了新的視角，同時也為相關(guān)領(lǐng)域的研究提供了有力的理論支持和實(shí)踐指導(dǎo)。ThisarticledelvesintotheresearchmethodofhierarchicaldivisionofcomplexsystemsintegratingDEMATELISM.ThroughadetailedintroductiontotheDEMATELISMmethodanditsapplicationinthehierarchicaldivisionofcomplexsystems,thisstudynotonlyprovidesanewperspectivefortheunderstandingandanalysisofcomplexsystems,butalsoprovidesstrongtheoreticalsupportandpracticalguidanceforresearchinrelatedfields.結(jié)論方面，本研究通過實(shí)證分析和案例分析，驗(yàn)證了集成DEMATELISM的復(fù)雜系統(tǒng)層次劃分方法的有效性和可行性。研究結(jié)果表明，該方法能夠準(zhǔn)確識別復(fù)雜系統(tǒng)中的關(guān)鍵因素和層次結(jié)構(gòu)，有助于揭示系統(tǒng)的內(nèi)在規(guī)律和運(yùn)行機(jī)制。該方法還具有較強(qiáng)的可操作性和實(shí)用性，可以廣泛應(yīng)用于各種復(fù)雜系統(tǒng)的層次劃分研究中。Intermsofconclusion,thisstudyverifiedtheeffectivenessandfeasibilityofthehierarchicaldivisionmethodforcomplexsystemsintegratedwithDEMATELISMthroughempiricalanalysisandcasestudies.Theresearchresultsindicatethatthismethodcanaccuratelyidentifykeyfactorsandhierarchicalstructuresincomplexsystems,whichhelpstorevealtheinherentlawsandoperatingmechanismsofthesystem.Thismethodalsohasstrongoperabilityandpracticality,andcanbewidelyappliedintheresearchofhierarchicaldivisionofvariouscomplexsystems.然而，本研究仍存在一定的局限性。由于復(fù)雜系統(tǒng)的多樣性和復(fù)雜性，單一的層次劃分方法可能難以完全適應(yīng)所有類型的復(fù)雜系統(tǒng)。因此，未來研究可以進(jìn)一步探索如何結(jié)合其他理論和方法，提高層次劃分的準(zhǔn)確性和適用性。本研究主要關(guān)注了復(fù)雜系統(tǒng)的靜態(tài)層次結(jié)構(gòu)，未來可以進(jìn)一步考慮系統(tǒng)的動態(tài)演化過程，深入研究層次結(jié)構(gòu)隨時間變化的規(guī)律和機(jī)制。However,thisstudystillhascertainlimitations.Duetothediversityandcomplexityofcomplexsystems,asinglehierarchicalpartitioningmethodmaynotbeabletofullyadapttoalltypesofcomplexsystems.Therefore,futureresearchcanfurtherexplorehowtocombineothertheoriesandmethodstoimprovetheaccuracyandapplicabilityofhierarchicaldivision.Thisstudymainlyfocusesonthestatichierarchicalstructureofcomplexsystems.Inthefut