Table Of ContentInnovation in Risk Analysis
Chunbing Bao
Jianping Li
Dengsheng Wu
Risk Matrix
Rating Scheme Design and
Risk Aggregation
Innovation in Risk Analysis
SeriesEditor
JianpingLi ,SchoolofEconomicsandManagement,UniversityofChinese
AcademyofScience,Beijing,China
This book series focuses on discussing the new theories, new models, and new
methodsofriskanalysis.Moreover,thebetterriskmanagementpracticesintheareas
ofsocial,physicalandhealthsciences,engineering,publicpolicyandadministration,
andmediaandcommunicationstudieswillpriorityattention.
Thebookseriesaimstopublishthelatesttheoreticalandempiricalresearchon
the communication, regulation, and management of risk. Research that you might
wanttocontributetothebookseriescouldexplore:
(cid:129)
TheInter-relationshipsbetweenrisk,decision-makingandsociety.
(cid:129)
Howtopromotebetterriskmanagementpractices.
(cid:129)
Contributetothedevelopmentofriskmanagementmethodologiesinthedifferent
areas.
Moreinformationaboutthisseriesathttps://link.springer.com/bookseries/16914
· ·
Chunbing Bao Jianping Li Dengsheng Wu
Risk Matrix
Rating Scheme Design and Risk Aggregation
ChunbingBao JianpingLi
SchoolofManagement SchoolofEconomicsandManagement
ShandongUniversity UniversityofChineseAcademyofSciences
Jinan,China Beijing,China
DengshengWu
InstitutesofScienceandDevelopment
ChineseAcademyofSciences
Beijing,China
ISSN 2731-6254 ISSN 2731-6262 (electronic)
InnovationinRiskAnalysis
ISBN 978-981-19-1479-9 ISBN 978-981-19-1480-5 (eBook)
https://doi.org/10.1007/978-981-19-1480-5
©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature
SingaporePteLtd.2022
Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether
thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse
ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and
transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar
ordissimilarmethodologynowknownorhereafterdeveloped.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor
theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany
errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional
claimsinpublishedmapsandinstitutionalaffiliations.
ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSingaporePteLtd.
The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721,
Singapore
Contents
1 RiskMatrix:FoundationsandOverview ......................... 1
1.1 WhatIsRiskMatrix? ....................................... 2
1.1.1 WhatIsRisk? ....................................... 3
1.1.2 WhatIsRiskMeasure ................................ 3
1.1.3 Objective Risk Measure Versus Subjective Risk
Measure ............................................ 4
1.2 TheoreticalFlawsandtheTopicsinThisBook ................. 6
1.2.1 SomeTheoreticalFlawsofRiskMatrix ................. 6
1.2.2 TheTopicsinThisBook .............................. 8
References ..................................................... 10
2 DifferentTypesofRiskMatricesandTypicalApplications ......... 13
2.1 OriginandFundamentalModel ............................... 13
2.1.1 TheOriginoftheRiskMatrix ......................... 13
2.1.2 FundamentalMathematicalModelofRiskMatrix ........ 14
2.2 StructureandtheDesignofDifferentKindsofRiskMatrix ....... 15
2.2.1 QualitativeRiskMatrix ............................... 16
2.2.2 Semi-quantitativeRiskMatrices ........................ 17
2.2.3 QuantitativeRiskMatrices ............................ 18
2.3 ApplicationsinDifferentFields .............................. 19
2.3.1 FoodSafetyRiskAssessment .......................... 20
2.3.2 RiskAssessmentofPublicInfrastructureOperation ....... 21
2.3.3 MedicalandHealthRiskAssessment ................... 22
References ..................................................... 26
3 RatingSchemeDesignMethods .................................. 27
3.1 SummaryofSomeUnwrittenRules ........................... 27
3.1.1 InputClassification ................................... 27
3.1.2 MeasureofRisks .................................... 28
3.1.3 ClassificationofDifferentRisks ........................ 29
v
vi Contents
3.2 UsageofUtilityFunctionstoDesignQualitativeRiskMatrix
Design .................................................... 30
3.3 Cox’sRiskMatrixDesignAxioms ............................ 31
3.4 SequentialUpdatingApproach ............................... 33
3.4.1 PrinciplesoftheSUAtoDesignRatingSchemes
forRiskMatrices .................................... 34
3.4.2 TheUniquenessPrincipleoftheSequentialUpdating
Approach ........................................... 39
3.4.3 AGlobalRatingAlgorithm ............................ 40
3.4.4 Application:DesigntheRatingSchemeofa4×4
RiskMatrixUsingSUA ............................... 42
3.5 SummaryandComparisonoftheRatingSchemeDesign
Methods .................................................. 50
3.5.1 Summary ........................................... 50
3.5.2 Comparison ......................................... 52
References ..................................................... 54
4 RiskPerceptionsinRiskMatrix:SourcesandImpacttoRisk
MatrixDesign ................................................. 57
4.1 Introduction ............................................... 57
4.2 IdentifyingRiskPerceptioninRiskMatrices ................... 60
4.2.1 PerceptionoftheScalingofInputs ..................... 61
4.2.2 PerceptionoftheLocationofInputs .................... 63
4.2.3 PerceptionofInputCategoryMembership ............... 65
4.2.4 PerceptionoftheMeasureofRisks ..................... 66
4.2.5 PerceptionofAttitudesTowardsRisks .................. 68
4.3 ASequentialUpdatingApproachUsedtoIntegrateDifferent
Perception ................................................. 70
4.3.1 ReviewoftheSUA ................................... 71
4.3.2 IntegratingDifferentTypesofRiskPerception ........... 72
4.4 RiskMatricesIntegratingDifferentRiskPerceptions ............ 75
4.4.1 Performance of Integrating Risk Perception
ontheScalingofInputs ............................... 75
4.4.2 Performance of Integrating Risk Perception
ontheLocationofInputs .............................. 78
4.4.3 PerformanceofIntegratingRiskPerceptiononInput
CategoryMembership ................................ 81
4.4.4 Performance of Integrating Risk Perception
ontheMeasureofRisks .............................. 83
4.4.5 Performance of Integrating Risk Perception
onAttitudesTowardsRisks ............................ 84
4.5 ConclusionandDiscussions .................................. 86
References ..................................................... 87
Contents vii
5 RiskMatrixDesignAssessment:CriteriaandQuantitative
Indicators ..................................................... 89
5.1 CriteriaUsedtoAssessRiskMatrix ........................... 89
5.1.1 MonotonicityofRisks ................................ 90
5.1.2 ConsistencywiththeRiskMeasure ..................... 92
5.1.3 EffectiveResolutionofRiskRatings .................... 95
5.2 QuantitativeIndicatorsoftheCriteria ......................... 97
5.2.1 ProportionofWrongRiskPairs(PWRP) ................ 97
5.2.2 TheVolatilityofRiskMeasures(VRM) ................. 99
5.2.3 ProbabilityofaCorrectDecision(PCD) ................. 102
5.3 ApplicationsoftheCriteria .................................. 106
5.3.1 InstructionforPractitionersDesigningRiskMatrices ...... 106
5.3.2 DeterminetheRiskRatingofSomeCells ................ 107
5.3.3 Assessing Some of the Risk Matrices Used
intheLiterature ...................................... 108
References ..................................................... 113
6 RiskMatrixAggregation:AGeneralFramework ................. 115
6.1 TermExplanationofRiskMatrixAggregation .................. 115
6.2 NormalFrameworktoAggregateRiskMatrices ................. 117
6.2.1 AssessIndividualRiskAccordingtotheNormalized
QuantitativeRiskMatrices ............................ 117
6.2.2 FindtheAppropriateExpressionsoftheRatings .......... 119
6.2.3 Aggregate the Individual Risks by Composition
Methods ............................................ 121
6.2.4 TransformtheResultofAggregationintoaSpecific
Value ............................................... 122
References ..................................................... 123
7 Risk Matrix Aggregation Methods: Introduction
andComparativeAnalysis ...................................... 125
7.1 FuzzySet-BasedMethod .................................... 125
7.1.1 SimilaritiesBetweenRiskMatricesandFuzzySets ....... 125
7.1.2 FuzzyMembershipinRiskMatrices .................... 128
7.2 IntervalNumber-BasedMethod .............................. 136
7.3 ProbabilityDensityFunction-BasedMethod .................... 137
7.4 ComparisonofDifferentMethodstoAggregateRiskMatrices .... 138
7.4.1 AnIllustrativeExample ............................... 138
7.4.2 RobustnessofDifferentMethods ....................... 142
7.4.3 ComparisonoftheThreeAggregationMethods .......... 143
References ..................................................... 147
viii Contents
8 Three-Dimensional Risk Matrix: Theoretical Basis
andConstruction ............................................... 149
8.1 BackgroundoftheThree-DimensionalRiskMatrix .............. 149
8.2 Three-DimensionalRiskMeasureConsideringtheStrength
ofKnowledge .............................................. 151
8.3 ImpactFactorsoftheStrengthofKnowledge ................... 154
8.4 Measure of the Strength of Knowledge Based on Fuzzy
MCDM ................................................... 155
8.4.1 Multi-Attribute Decision-Making Method Based
onFuzzyMeasureandChoquetIntegral ................. 157
8.4.2 KnowledgeStrengthUnderMulti-LayerFactors .......... 165
8.4.3 KnowledgeStrengthUnderMultipleDecisionMakers ..... 166
8.5 ConstructionofThree-DimensionalRiskMatrices .............. 166
References ..................................................... 168
9 ConclusionsandFutureResearch ................................ 171
9.1 Conclusions ............................................... 171
9.2 FutureResearch ............................................ 172
Chapter 1
Risk Matrix: Foundations and Overview
At the beginning of 2020, the COVID-19 swept across China, and then spread to
the whole world. This disease made a tremendous impact on human beings’ lives,
economics,andsoon.Sofar,peoplearestillsufferingtheseriouseffectofCOVID-
19,andGovernmentsofdifferentcountriesappealtocitizenstostaycautioustoavoid
thehealthrisk.Besides,lotsofenterprisessustainedhugelossesandevencollapsed.
Thisisthebiggesteventrecentlythatmakessomanypeopledeeplyfeeltheinfluence
ofrisk,andconsidertheimportanceofriskmanagement.
So, what is “risk?” When talking about risks, people usually refer to different
issues.Forexample,riskmaybereferredtoasthepossibilityofanadverseevent’s
occurrence;riskisthecombinationoftheuncertaintyandseverityofaconsequence;
riskisthedeviationfromareferencevalue(onemayrefertoSocietyforRiskAnalysis
Glossaryformoredefinitionofrisk).Althoughpeopleusuallysayweshouldavoida
certainrisk,likethehealthrisk,riskisnotalwaysreferredtoastheadverseaspectof
anevent(ParkandGrant2005;Leeetal.2011;Orchowskietal.2012).Forexample,
marketriskinthefinancialfieldmayresultinpossiblegainorloss.However,ithas
beenshownthatpeoplecaremoreaboutthenegativesideofaneventwithuncertainty.
Andthusadoptingtherightchoicestomakepreferredconsequencesmoreprobable
iswhatweaimtodofacingarisk.Riskmanagement issuchaprocessthathelps
minimize risk level through the main steps of risk identification, risk assessment,
andriskmitigation(Zhang 2016;JohnsonandSwedlow 2021;Rostamzadeh etal.
2018). For example, in the case where people are under the threat of COVID-19,
she/he needs to identify all the possible sources that may cause the infection risk,
assessthe consequence and probability of the risk,and take appropriate actions to
mitigatetheriskaccordingtoher/hisacceptanceoftherisk.
Foracertainrisk,afairlyimportantpartisriskassessment whenriskmanage-
mentprocessisconducted,whichfocusesonmeasuringthequantitativevalueofthe
risk,mainlyansweringwhethertheriskistolerable(Aminbakhshetal.2013;Aven
2016;HegdeandRokseth2020;Lloyd-Jonesetal.2019).Theaccuracyoftherisk
assessmentresultaffectstheriskmitigationstrategiesandthenthereally-happened
©TheAuthor(s),underexclusivelicensetoSpringerNatureSingaporePteLtd.2022 1
C.Baoetal.,RiskMatrix,InnovationinRiskAnalysis,
https://doi.org/10.1007/978-981-19-1480-5_1
