331
1 INTRODUCTION
The ship navigation safety is one of the most
important contents of water traffic. Based on the
navigationenvironmentandtheship’scharacteristics,
the comprehensive evaluation of ship navigation
adaptabilitycannotonlyevaluate theadaptabilityof
the environment for the ship, but also assess the
statusoftheshipnavigationsafety.
Nowadays, the comprehensive evaluation
methods are mainly the fuzzy comprehensive
evaluation method, analyt
ic hierarchy process, grey
theory, expert scoring method, and other new
methods that integrate two or more comprehensive
methods
(LiZ.F. etal.2013& LiuF‐H.F.et al.2005&
Ho W. 2008). The comprehensive fuzzy evaluation
andanalytichierarchprocessareappliedtoevaluate
power generation projects’ quality for providing
theoreticalsupportforselectiondecision(LiangZ.H.
et al. 2006). Grey system theory is put into use to
evaluate the degree of air qualit
y affected by traffic
and take Japan as an example to verify the method
(PaiT.Y.etal.2007).Improvedcomprehensivefuzzy
evaluation method which uses entropy method to
correctsubjective weightisappliedinevaluatingthe
risk of waterway near Qingdao port (Nie X.L. et al.
2013 ). The fuzzy ma
tter‐element model based on
entropy weight is used to comprehensively evaluate
waterquality(ZhangX.Q.etal.2005).Amethodof
grey system based on entropy weight is made the
evaluation of ship suppliers system (Liu L.G. et al.
2012 ). The entropy weight method in extension
theoryisappliedtoevaluategasgradeoftenthrough
thetunnelofcoalseam(HuangR.D.etal.2012).
According to the analysis of comprehensive
evaluationmethods, wecanfind tha
tthesemethods
can provide a certain reference value for ship
navigation adaptability evaluation, but they rely on
Comprehensive Evaluation
Cloud Model for Ship
Navigation Adaptability
M.Zhu,Y.Q.Wen,C.H.Zhou& C.S.Xiao
HubeiInlandShippingTechnologyKeyLaboratory&SchoolofNavigation,WuhanUniversityofTechnology,Wuhan,
Hubei,China
ABSTRACT:Inthispaper,usingcloudmodelandDelphi,webuild acomprehensiveevaluationcloudmodelto
solvetheproblemsofqualitativedescriptionandquantitativetransformationinshipnavigationadaptability
comprehensiveevaluation.Inthemodel,thenormalcloudgeneratorisusedtofindoptimalcloudmodelsof
reviewsandevaluationfact
ors.TheweightofeachevaluationfactorisdeterminedbycloudmodelandDelphi.
Thefloatingcloudalgorithmisappliedtoaggregatethebottomlevel’sevaluationfactors,andcomprehensive
cloud algorithm is used toaggregate the highestlevel’s evaluation fact
ors to get comprehensive evaluation
cloudmodel.Finally,evaluationresultisgotbymatchingcomprehensiveevaluationcloudmodelandoptimal
cloudmodelofreviews.Ascasestudy,themodelisappliedtothesmallLNGship’snavigationadaptabilityin
SoutheastAsia.Comparedwiththefuzzycomprehensiveevaluationmethod,themodelproposedinthi
spaper
ismoreintuitiveandreliableincomprehensiveevaluationofthesmallLNGship’snavigationadaptability.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 8
Number 3
September 2014
DOI:10.12716/1001.08.03.01
332
mathematical model of a precise operation in
evaluation process or use a threshold to classify
evaluation results, regardless of the uncertainty
(including fuzziness and randomness) appearing in
theevaluationprocess.Cloudmodelisanimportant
theoretical model of uncertainty in artificial
intelligence, which can integrate fuzziness and
randomnessofthe
spatialentitiestogether.Sowecan
seethatcloudmodel can overcomethe limitationof
theabovemethods(LiD.Y.etal.2004&ChenH.etal.
2011).Inthispaper,wewillmakedeeplyanalysison
thefactorsaffectingtheshipnavigationadaptability,
and propose a comprehensive evaluation method
based on cloud model for ship navigation
adaptability.
2 CLOUDMODEL
Cloudmodelisaqualitativetransformationmodelfor
uncertainty, which can well deal with the
transformationbetweenone’squalitativeconceptand
itsquantitativevalue(LiuC.Y.etal.2004).
Expectation signed as
x
E
, entropy signed as
n
E
,
and super‐entropy signed as
e
H
are numerical
characteristics of cloud model and performance the
quantitative characteristics of qualitative concept.
Expectation is the central value in the domain of
discourse. Entropy measures ambiguity and
probability of qualitative concept and reflects
uncertaintyofqualitativeconcept.Theentropyvalue
is higher, the range of va lue accepted by concept
is
greater and the concept is fuzzier. Super‐entropy
reflects degree of aggregation of numerical value’s
uncertaintyinthenumberdomain,namelyentropyof
entropy.Thevalueofsuper‐entropyexpressescloud
dispersionandthickness.
Cloudgeneratorisanalgorithmusedto generate
cloud according to numerical characteristics, which
can be
divided into forward cloud including basic
cloud, normal cloud, X condition cloud and Y
conditioncloud, andreversecloud.Normal cloud is
universalcloudmodel, sowewill use normal cloud
model to conversion the evaluation criteria and
factor(Liu C.Y. et al. 2005). One of reverse cloud
models don’t have
certainty degree (Lu H.J. et al.
2003), so we choosethis one to generator numerical
characteristics.
Normalcloudmodelisdescribedasfollows:
Input :
(,, )
x
ne
EEH
, the required number of cloud
droplets
n
.
Output:
(, ),
ii
drop x y
1, 2, 3in
.
1 Generate normal random number
'
n
E whose
expectationis
x
E
andstandarddeviationis
e
H
.
2 Generate normal random number
i
x
whose
expectationis
n
E
andstandarddeviationis
'
n
E
.
i
x
isaclouddropletbelongtodomainspace.
3
2'2
exp[ ( ) / 2( ) ]
iixn
xE E
.
i
is membership
degreeof
i
x
belonging toqualitativeconcept.
4 Repeat steps from (1) to (3) until generating
n
clouddroplets.
Improved reverse cloud model is described as
follows:
Input:
(1,2,3 )
i
x
in
.
Output:
(E ,E ,H
x
)
ne
1
1
1
n
i
i
x
x
n
;
1
1
n
i
i
B
xx
n
;
22
1
1
()
1
n
i
i
Sxx
n
.
2
x
E
x
.
3
2
n
E
B
.
4
22
en
HSE
.
Table1.TheevaluationindexsystemofsmallLNGship’snavigationadaptabilityinSoutheastAsia
__________________________________________________________________________________________________
Factorinbasiclayer
i
U
Factorinelementlayer
ij
U Weight
ij
w Reviewandquantization
(weight
i
w
)Excellent Good Medium Poor Inferior
(100~90] (90~80] (80~70] (70~60] (<60]
__________________________________________________________________________________________________
Adaptabilityofnatural windU11(h/1000nmil)0.20000~10 10~30 30~50 50~70 >70
conditionU
1 seafogU12(h/1000nmil) 0.05210~10 10~20 20~30 30~40 >40
(0.2455)tropicalcycloneU
13 0.21440~5 5~10 10~15 15~20 >20
(h/1000nmil)
currentU
14(m/s)0.0614<0.5 0.5~2.0 2.0~4.0 4.0~6.0 >6.0
stormU
15(m)0.21600~2 2~4 4~6 6~8 >8
surgeU
16(m)0.25610~2 2~4 4~6 6~8 >8
AdaptabilityoftrafficdensityU
210.49340~4 5~9 10~14 15~20 >21
(ship/6nmile2)
navigationcondition trafficstructureU
22(%)0.31080~4 4~10 10~20 20~30 >30
U
2(0.2386)complexityofcourseU23 0.1958None Less General More Much
(intersectionnumberofhabitroute)
Adaptabilityofsafety& pilotageconditionU
31 0.2865ExcellentGood Medium Poor Inferior
securityconditionU
3） NAVAIDguideU320.1703 MuchperfectPerfect General ImperfectNone
(0.2891)trafficmanagement0.3406MuchComplete General IncompleteNone
infrastructureU
33complete
maritimesafety0.2026MuchgoodGood General Bad Muchbad
administrationU
34
Adaptabilityofsocial economicconditionU
41 0.1958MuchgoodGood General Bad Muchbad
conditionU
4（0.2268） socialstabilityU420.5034MuchstableStable General Unstable Unrest
developmentlevelof 0.3008MuchhighHigh General Low Muchlow
shippingindustryU
43
__________________________________________________________________________________________________
333
3 CONSTRUCTIONOFCOMPREHENSIVE
EVALUATIONCLOUDMODEL
3.1 EstablishmentofEvaluationIndexSystem
The establishment of evaluation index system is a
prerequisite for scientific comprehensive evaluation
and its principles are scientificity, maneuverability,
comprehensiveness, comparability and relative
independentability. According to navigation
environment characteristics of SoutheastAsia, we
selectonecomprehensiveevaluation
factor,fourbasic
evaluation factors and sixteen element evaluation
factorstoestablishevaluationindexsystem.
3.2 DeterminationofEvaluationObject,Evaluation
FactorandEvaluationSet
The small LNG ship’s navigation adaptability in
SoutheastAsiaisthefinalevaluationobjectsignedas
U. Factors in basic layer aresecond levelindicators,
whose factor set is
1234
{, , , }UUUUU
. Factors in
elementlayerarethirdlevel indicators,whosefactor
sets are
1 111213141516
{,,,,,}U UUUUUU
,
2212223
{, , }UUUU
,
331323334
{, , , }UUUUU
,
4414243
{, , }UUUU
.Theevaluation
setofeachevaluationfactor’sattributeisdetermined
by asking experts and collecting their reviews. The
evaluation set in this paper is
Excellent, Good, Medium, Poor, Inferior=V
, and its
corresponding value is
(100,90] (90,80] (80,70] (70,60] (60,0]= ,,,,V
.
3.3 DeterminationofEvaluationFactor’sWeightBased
onCloudModel
Empowermentmethodbasedoncloudmodelutilizes
visualcloudtojudgewhethertheexperts’reviewsare
consistent or not, and it achieves gradual
optimizationand gives an ideal andright weight to
evaluation factor (Han B. et al.2012 & Pang
Y.J. et
al.2001. ). The specific steps to determine weight of
evaluationfactoraredescribedasfollows:
Firstly,Selectnexpertswhoarefamiliarwithand
fullyunderstandthemeaningoftheevaluationfactor
to score. Assumed that an evaluation factor‘s
influence degree is decided by m evaluation factors
and
markedas
12
,,,
ii im
UU U
.
Secondly,assumedthatnexpertsscoreevaluation
factor
(1,2,,)
ij
Uj m anditsscoresetis
12
,,,
n
VV V
.
Then using improves reverse cloud generator to get
the weight numerical characteristics
(,, )
x
ij nij eij
EEH of
ij
U .
Thirdly,basedon
(,, )
x
ij nij eij
EEH , cloudatlasof
ij
U
isobtainedthroughforwardcloudgenerator.
Fourthly,observecondensationofclouddroplets
incloudatlas.Ifthedistributionofclouddropletsis
showed as mist, we could indicate that cohesion of
clouddropletsisbadandtheexpertshasnotunified
evaluationcomments.Soweshouldfeedbackandre‐
consolidate
evaluationcomments.
Fifthly, repeat above operation until achieve
gradual optimization and unify the experts’
evaluation comments to get cohesive cloud atlas
whichisfinalweightcloudofevaluationfactor.
Sixthly,repeatstepsfrom(2)to(5)untilgetweight
cloudofmevaluationfactors.
Seventhly, get the weight of
ij
U according to
equationmarkedas
1
xij
m
ij
x
ij
j
E
w
E
.
3.4 DescriptionoftheConceptCloudModelofReview
andEvaluationFactorinElementIndexLayer
Evaluation factors in evaluation index system and
evaluation reviews in evaluation set are qualitative
variables which can become quantitative va riables
with upper and lower bounds shown as
min max
[, ]CC
after experts score. Then we use the following
equation to calculate cloud parameters of the
quantitativevariables.
xminmax
max min
()/2
()/6
n
e
EC C
EC C
Hk
(1)
Where,
k
isaconstant,whichisadjustedbythe
stability of the va riable. For reviews with unilateral
boundary of value range such as
min
[,]C
and
max
[, ]C
, we can firstly determine the
expectationofitsdefaultboundary,thencomputeits
cloudparametersbyequation(1).
Assumed that there are N experts to judge
evaluationfactorsinelementlayer.Sothatwecanget
N evaluation cloud models marked as
(,, )(1,2,,)
xi ni ei
EEH i N
. Then, a comprehensive cloud
model is obtained by using comprehensive cloud
algorithm to gather N cloud models. The
comprehensivecloudalgorithmisshownasfollows:
x1 1 x2 2 xN
12
12
11 2 2
12
nn nN
x
nn nN
nn nN
n
en e n eNnN
e
nn nN
EEEE E E
E
EE E
EE E
E
N
H
EHE H E
H
EE E
(2)
3.5 JumpOperationofCloudModelofEvaluationFactor
Since a single evaluation factor’s cloud model is a
language indicator, an algorithm should be used to
gather multiple cloud models in same level to be a
moregeneralizedcloudmodeltoletlowerevaluation
factors’ cloud models jump to
higher. According to
the different characteristics of evaluation factor of
each layer, different levels of evaluation factor take
different algorithm. The evaluation factors in lower
layerisindependentandnon‐related,sowechoose
floating cloud algorithm to gather clouds , and
comprehensivecloudalgorithmtothehighestlevel.
Floatingcloud
algorithmisshownasfollows:
334
x1 1 x2 2 xn
12
2
1
1
22 2
12
2
2
2
22 2
12
2
22 2
12
2
1
1
22 2
12
2
2
2
22 2
12
2
22 2
12
n
x
n
nn
n
n
n
n
nn
n
ee
n
e
n
n
en
n
E
wE w E w
E
ww w
w
EE
ww w
w
E
ww w
w
E
ww w
w
HH
ww w
w
H
ww w
w
H
ww w
(3)
Comprehensive cloud algorithm is shown as
follows:
x1 1 1 x2 2 2 xn
11 2 2
11 2 2
111 2 22
11 2 2
nn nnn
x
nn nnn
nn n nnn
en e n ennnn
e
nn nnn
E
Ew EEw EEw
E
Ew E w Ew
EEwEw Ew
H
Ew H E w H Ew
H
Ew Ew Ew
(4)
Where,
(1,2,,)
i
wi n
is weight of evaluation
factor.
E,E,H
xi ni ei
are numerical characteristics of
each evaluation factor.
n
is the number of
evaluationfactors.
4 PROCESSOFSMALLLNGSHIP’SNAVIGATION
ADAPTABILITYCOMPREHENSIVE
EVALUATION
We take the route from Haikou to Malaysia in
Southeast Asia as example to evaluate small LNG
ship’snavigationadaptabilitytoverifythefeasibility
ofthemethodproposedinthispaper,andalsomake
comparative analysis with fuzzy comprehensive
evaluationmethod.
4.1 ComprehensiveEvaluationCloudmodel
4.1.1 DeterminetheWeightofEvaluationFactor
According to the empowerment method
introduced in section 3.3, the weight of each
evaluation factor in evaluation index system can be
ensured. Now, take one evaluation factor named
“wind”asexample.
Firstly,
there are ten experts scoring for “wind”
marked as(5，5，5，7，5，3，7，3，3，5) . We
cangetnumericalcharacteristicsvaluewhichis(4.8，
1.3536，0.5879).Thenwegetthecloudatlasshownin
Fig.1(a)basedonforwardcloudgenerator.Fromthe
Fig.1(a), we can
see that the dispersion of cloud
droplets is relatively large and the cloud atlas is
shownasmist.Soweshouldcollateexperts’scoresto
feedback to experts and prepare next round of
experts’ scoring. Repeat above operation until unify
experts’ cognition. and get final numerical
characteristics signed as (4.6
， 0.8021 ， 0.2602) of
“wind”whosecloudatlasisshowninFig.1(b).Sodo
the remaining five evaluation factors . The final
weight of “wind” is 0.2000 throughnormalizing the
abovesixexpectations.Allweightsoftheevaluation
factorsarerecordedinTable1.
(a)theweightcloudin (b)thefinalweightcloud
firsttime
Figure1.WeightofevaluationcloudbasedonDelphi
4.1.2 DetermineConceptCloudModelofReviewand
EvaluationFactorinElementIndexLayer
1 Thecloudmodelsofreviewsinevaluationsetare
shownas follows:excellentis(100,10/3,0.5);good
is (85,5/3,0.5); medium is (75,5/3,0.5); poor is
(65,5/3,0.5);inferioris(0,20,0.5).
2 Cloudmodelsofeachevaluationfactorinelement
layer are got according to seven experts’ scores,
recordedinTable2.
Table2.Cloudmodelofevaluationfactorinelementindex
layer
_______________________________________________
Factorinelementlayer cloudmodel
x
,, )
ne
EEH（
_______________________________________________
wind(85,11.6667,0.5)
seafog(85,11.6667,0.5)
tropicalcyclone(85,11.6667,0.5)
current(85,11.6667,0.5)
storm(85,11.6667,0.5)
surge(85,11.6667,0.5)
trafficdensity (91.6667,15,0.5)
trafficstructure (100,23.3333,0.5)
complexityofcourse (100,23.3333,0.5)
pilotagecondition (85,11.6667,0.5)
NAVAIDguide (98.8462,21.6667,0.5)
trafficmanagementinfrastructure (100,23.3333,0.5)
maritimesafetyadministration (100,23.3333,0.5)
economiccondition(85,11.6667,0.5)
socialstability (85,11.6667,0.5)
developmentlevelofshipping
industry (85,11.6667,0.5)
_______________________________________________
4.1.3 ImplementJumpOperationofEvaluationFactor’s
CloudModel
1 Cloud models of each evaluation factor in basic
layeraregotbyfloatingcloudalgorithm,recorded
inTable3.
335
Table 3. cloud model of evaluation factor in basic index
layer
_______________________________________________
Factorinbasiclayer cloudmodel
x
,,
ne
EEH
_______________________________________________
Adaptabilityofnaturalcondition (85,2.3885,0.5)
Adaptabilityofnavigationcondition (95.8883,6.8001,0.5)
Adaptabilityofsafety&securitycondition
(95.5060,5.2506,0.5)
Adaptabilityofsocialcondition (85,4.4594,0.5)
_______________________________________________
2 The numerical characteristics of comprehensive
evaluation cloud model is
92.0942,4.7382,0.5
andthecloudatlasisshowninFig.2.
Figure2.Cloudmodel’snumericalcharacteristicsgraphof
comprehensive evaluation of small LNG ship’s navigation
adaptabilityinSoutheastAsia
InFig.2,fiveredcloudsarereviewclouds;theblue
cloudiscomprehensiveevaluationcloud.Wecansee
the distribution of final comprehensive evaluation
resultintheoriginalreviewsclouds,andexpectation
of small LNG ship’s navigation adaptability is
92.0942,coveringbetween“good”and“excellent”but
mainlybiasinginfavorof
“good”.
4.2 FuzzyComprehensiveEvaluationMethod
The process of fuzzy comprehensive evaluation
method used to small LNG ship’s navigation
adaptability is described as follows: firstly, the
evaluation criteria should be described by the
membershipfunction,sothatthemembershipmatrix
of evaluation factor can be built; secondly,
comprehensive evaluation matrix
is computed by
composite operation between weight matrix of
evaluation factors and membership degree of
evaluation factors. In this paper, tri angular
membershipfunctionisusedtoconfirmmembership
degreeofeachevaluationfactor.Theweightsofeach
evaluationfactorarethesamerecordedinTable1.
Eachmembershipfunctionisexpressedas
follows:
1
ij ij
1,
() (65 )10,
0
V
UU
ij
ij
ij
55
55 65
65
U
U
U
2
ij
ij ij
(55)10,
() (75 )10,
0
V
U
UU
ij
ij
ij ij
55 65
65 75
55 75
U
U
UorU
3
ij
ij ij
(65)10,
() (85 )10,
0
V
U
UU
ij
ij
ij ij
65 75
75 85
65 5
U
U
UorU
8
4
ij
ij ij
(75)10,
() (95 )10,
0
V
U
UU
ij
ij
ij ij
75 85
85 95
75 5
U
U
UorU
9
5
ij ij
0,
() ( 85)10,
1
V
UU
ij
ij
ij
85
85 95
95
U
U
U
Themembershipdegreeofeachevaluation factor
iscalculatedandrecordedintable4:
Table4.Membershipdegreeofeachevaluationfactor
__________________________________________________________________________________________________
FactorinbasiclayerFactorinelementlayerScore Inferior Poor Medium GoodExcellent
__________________________________________________________________________________________________
AdaptabilityofnaturalwindU1183 0.20.8
conditionU
1seafogU1284 0.10.9
tropicalcycloneU
1385.5 0.95 0.05
currentU
1486.5 0.85 0.15
stormU
1583.5 0.15 0.85
surgeU
1685.5 0.95 0.05
AdaptabilityofnavigationtrafficdensityU
2189.5 0.55 0.45
conditionU
2trafficstructureU2291.5 0.35 0.65
complexityofcourseU
2390.5 0.45 0.55
Adaptabilityofsafety& pilotageconditionU
3188.5 0.65 0.35
securityconditionU
3 NAVAIDguideU3290 0.50.5
trafficmanagementinfrastructureU
33 92.5 0.25 0.75
maritimesafetyadministrationU
34 91.5 0.35 0.65
Adaptabilityofsocial economicconditionU
4182.5 0.25 0.75
conditionU
4 socialstabilityU4285.5 0.95 0.05
developmentlevelofshipping82.5 0.25 0.75
industryU
43
__________________________________________________________________________________________________
336
The membership degree of small LNG ship’s
navigation adaptability is
0 0 0.0472 0.6466 0.3062U
. The final
evaluation result is “good” in accordance with the
principleofmaximummembership.
4.3 ContrastiveAnalysis
Comparing the evaluation processes and results
betweenfuzzycomprehensiveevaluationmethodand
the comprehensive evaluationcloud model , we can
drawthefollowingconclusions:
1 Intheevaluationprocessoffuzzycomprehensive
evaluation
method, the membership degree of
eachevaluationfactorissubjectivevaluesgivenby
experts, which makes the result unreliable and
non‐objective. However, the comprehensive
evaluation cloud model reduces the subjective
factors of experts during identification of
evaluation criteria and evaluation of evaluation
factor, and fully reflects the fuzziness and
randomnessintheevaluationprocess.
2 For the evaluation results, the fuzzy
comprehensive evaluation method only gives a
concrete membership degree. But the
comprehensive evaluation cloud model can not
onlyprovidesaspecificcomprehensiveevaluation
result, but also be intuitive to show the
distribution of the comprehensive evaluation
resultinoriginal
figure.
5 CONCLUSION
In this paper, cloud model is used to process
evaluationfactorandreview,sothattherandomness
andfuzzinessofqualitativeintheevaluationprocess
are fully reflected. The empower method of
evaluation factor based on cloud model and Delphi
takesfullconsiderationoffuzzinessandrandomness
ofreal‐worldawarenessandovercomesthelimitation
of traditional subjective factor and awareness ,
therefore,theweightsarereasonable.
The comprehensive evaluation cloud modelfor
small LNG ship’s navigation adaptability is a new
methodfor quantitative evaluatingship’snavigation
adaptability. But with the development of water
transport and ship
design industry, we should
constantly improve the evaluation system and
evaluationset.
ACKNOWLEDGMENTS
This paper was supported by the Construction
ScienceandTechnologyProjectsforWestTraffic,the
ScienceandTechnologyPlanningProjectforZhejiang
Transportation Hall, and the Fundamental Research
FundsfortheCentralUniversities.
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