A New PCR Combination Rule for Dynamic Frame Fusion

2018·0.3 MB·

by  Jin Hongbin

Chinese Journal of Electronics
Vol.27, No.4, July 2018
A New PCR Combination Rule for Dynamic
Frame Fusion∗
JIN Hongbin1, LI Hongfei2,3, LAN Jiangqiao1 and HAN Jun1
(1. Air Force Early Warning Academy, Wuhan 430019, China)
(2. Shanghai Jiao Tong University, Shanghai 200240, China)
(3. No.95174 Unit of PLA, Wuhan 430040, China)
Abstract — Dynamic frame fusion which is based on with time taking in account the non-existential integrity
hybridDSmmodelisanimportantproblemininformation constraints to establish new model of frame[3].
fusion. But the traditional combination rules are mainly
In the classical Dempster-Shafer theory (DS
under fixed discernment frame (Shafer model and free
theory)[4−6], the main research focus on the static fusion
DSm model) responding to static model. A new method
for dynamic proportionalconflict redistributionrules (dy- for nonexistence of non-existential integrity constraints
namicPCRrules)basedonhybridDSmmodelisproposed concept, as computation problem[7], static combination
for the shortness of classical dynamic PCR rules. In the rule[8], combination of unreliable evidence[9−11], eviden-
new dynamicPCR rule, combinationinvolvedwithempty
tial classification method[12,13]. But the dynamic frame
set is defined as one kind to obtain more reasonable re-
sults. For the redistribution weight, the conjunction Basic fusion is more practical than static fusion[14]. The the-
belief assignment (BBA) and conflict redistribution BBA atrical foundation of DSm theory is hybrid DSm model
are both taken into account to raise the fusion precision.
anddynamic constraintcondition.So DSm theory is per-
The effectiveness of revised dynamic PCR rule is studied
fect for the definition, representation and procession of
andsimulatedinbothaspectoffusionaccuracyandcalcu-
lation. dynamic frame fusion problem[2]. Constraint condition
Key words — Dynamic frame fusion, Hybrid DSm changes with time to generate new hybrid DSm model.
model, Dynamic proportionalconflict redistribution rule. As the example[3], lets consider the set of three targets
I. Introduction at a given time k to be Θk = {θ1,θ2,θ3}. And one
receives a new information at time k+1 confirming that
Combination rule is the core part of Dezert- onetarget,saytargetθ3 hasbeendestroyed.Theproblem
Smarandache theory (DSm theory)[1,2]. The effectiveness one need to solve is how to combine efficiently evidence
ofDSmtheoryfusionsystemdependsonthepropertiesof takingintoaccountthisnewnon-existentialintegritycon-
combinationrule.Andthecombinationruleshouldsatisfy straintθ3 ≡Ø in the new model ofthe frame to establish
the applicationrequirementsofusers.In mostofclassical the most threatening and surviving targets belonging to
problem using belief functions, the frame of discernment Θk+1 ={θ1,θ2}.
Θ = {θ1,θ2,...,θn} is considered static. This means the Smarandache and Dezert propose a series of combi-
set of elements in the frame (assumed to be non-empty nation rules to solve the fusion problem under dynamic
and distinct) and the underlying integrity constraints of frame.Thesecombinationrulesaredynamicproportional
theframearefixedandremainthesamewithtime.These conflict redistribution combination rules (dynamic PCR
fusion problems are called static fusion. In some appli- rules)[15] and Dezert-Smarandache hybrid combination
cation however, like in target tracking and battlefield rules (DSmH rules)[2]. The combination rules have three
surveillance for example, the use of such invariant frame steps in evidence processing. Firstly, these combination
is not very appropriate because it can truly change with rules define non-existential sets caused by the modifica-
time depending on the changing process of the events. In tion of discernment frame. Secondly, the Basic belief as-
the dynamic frame fusion, frame of discernment changes signment (BBA) of the non-existential sets is transferred
∗Manuscript Received Mar.9, 2016; Accepted May 21, 2016. This work is supported by the National Natural Science Foundation of
China(No.61102168) andMilitaryinnovationFoundation(No.X11QN106).
(cid:2)c 2018ChineseInstitute ofElectronics.DOI:10.1049/cje.2018.04.008
822 Chinese Journal of Electronics 2018
toemptysetØ.Lastly,theBBAisredistributedforthere- is determined by both the elements in the discernment
lationshipemptysetØandelementsindiscernmentframe frame and non-existential integrity constraints. The dis-
tocompletethedynamicframefusion.ThedynamicPCR cernmentframechangeswiththenon-existentialintegrity
rulesare moreeffective thandynamic DSmH rulesshown constraints. Hybrid DSm model fits the reality because
in Ref.[15]. But there are two kinds of drawbacks for dy- somesubsetsofΘ cancontainelementsknowntobetruly
namicPCRrules: a)the unreasonableredistribution,the exclusivebutalsotrulynonexistingatallatagiventime.
redistribution of empty set Ø is similar with the redis-
tribution of existential sets; b) insufficiency use of infor-
mation, some useful information is not involved in the
redistributionweight.Thecontributionofthispaperisto
propose a revised method for dynamic PCR rule based
on hybrid DSm model. In the revised method, combina-
tion involved with empty set Ø is defined as one kind Fig.1.The model of fusion problems. (a) Free DSm model;
to obtain more reasonable results. For the redistribution (b)Shafermodel;(c)HybridDSmmodel
weight, the conjunction BBA and conflict redistribution The traditionalcombinationrules areunder fixeddis-
BBAarebothtakinginto accountto raisethe fusionpre- cernment frame (Shafer model and free DSm model) re-
cision.The revisedPCRrule makesbetter use ofexisting sponding to static fusion. But the dynamic frame fusion
information without adding more calculation. The effec- and hybrid DSm model are consistent with the practi-
tiveness of revised PCR rule is shown in the simulation. cal situation. Smarandache and Dezert propose a series
II. Hybrid DSm Model of combination rule to solve the problem under dynamic
frame fusion. These combination rules are dynamic PCR
rules and DSmH rules. Firstly, the dynamic PCRa rule is
DSm theory is motivated by expanding the frame of
analyzed in the paper. Then, a new revised PCR rule is
discernmenttoallowforpresumedsingletonsinDStheory
to actually have a well-defined intersection[3]. The frame proposedtoovercomethe shortnessofPCRarule.Lastly,
thecalculationisdefinedandstudiedtoevaluatethecom-
of discernment changes with time according to the dy-
bination rules.
namic constraint condition, which is the foundation of
1. Revisedmethod of dynamic frame PCR rule
dynamic frame fusion.
Smarandache and Dezert analyze dynamic PCR rules
DSm theory contains Shafer model, free DSm model
andhybridDSmmodel.Dependingontheintrinsicnature and DSmH rules in Ref.[15] to draw a conclusion
oftheelementsofthefusionproblemunderconsideration, that PCRa rule is the most effective rule. PCRa rule:
it can however happen that free DSm model and Shafer mPCRa(Ø)=0 and ∀A∈GΘ\Ø
model do not fit the reality because some subsets of Θ
mPCRa(A)
cancontainelementsknowntobetrulyexclusivebutalso
=m12(A) (cid:3) (cid:4)
twrourlkyinngononexdisytninagmaictfaulslioant aprgoibvelenmtiwmheer(septehceialflryamweheΘn + (cid:2) m1(A)2m2(X) + m2(A)2m1(X)
varieswith time with the revisionofthe knowledge avail- X∈GΘ\Ø m1(A)+m2(X) m2(A)+m1(X)
able). These integrity constraints are then explicitly and X(cid:2)∩A=Ø
formally introduced into the free DSm model Mf(Θ) in + [m1(A)m2(X)+m2(A)m1(X)] (1)
X∈Ø (cid:2)
order to adapt it properly to fit as close as possible with m1(X)m2(Y)
the reality and permit to construct a hybrid DSm model
X,Y∈Ø
M(Θ). The hybrid DSm model M(Θ) can deal with the +m12(A)· (cid:2)
situationofsets whichmightbecome empty attime tk or m12(Z)
Z∈GΘ\Ø
new sets/elements that might arise in the frame at time
tk+1[3]. The model in Fig.1(c) is the hybrid DSm model TheredistributionstrategyforBBAnotinvolvedwith
with θ1∩θ3 = Ø and θ2∩θ3 = Ø. The free DSm model empty set Ø is the same as that of classicalPCR rule[16].
and Shafer model can be considered as two special case And PCRa redistributes the BBA involved with empty
of hybrid DSm model. set Ø to non-empty sets, as two kinds. Firstly, the redis-
tributionstrategyofintersectionbetweennon-empty sets
III. Combination Rule of Dynamic Frame
Fusion and empty set Ø is defined as S1. Secondly, the redistri-
bution strategy of intersection between empty set Ø and
ThediscernmentframesofShafermodelandfreeDSm empty set Ø is defined as S2.
(cid:2)
modelaredeterminedbythe elementsinthe discernment S1 = [m1(A)m2(X)+m2(A)m1(X)] (2)
frame.WhilethediscernmentframeofhybridDSmmodel
X∈Ø
A New PCR Combination Rulefor DynamicFrame Fusion 823
(cid:2)
m1(X)m2(Y) the non-existentialsets whichare not suitable for mutual
X,Y∈Ø processing. In addition, the BBA of conflict redistribu-
S2 =m12(A)· (cid:2) (3)
m12(Z) tion can express the condition of the support to certain
Z∈GΘ\Ø element.ButtheBBAofconflictredistributionleavesout
ButtherearetwokindsofproblemsfordynamicPCR of consideration of PCRa rule.
rules: a) the unreasonable redistribution, the redistribu- To overcome the shortness of PCRa rule, a revised
tion of empty set Ø is similar with the redistribution of PCR rule is proposed. For the problem a), intersection
existential sets in classical PCR rule[16]; b) insufficiency betweennon-emptysetsandemptysetØS1 andintersec-
use of information, some useful information is not in- tion between empty set Ø and empty set Ø S2 uniformly
volved in the redistribution weight. The PCRa rule re- process. For the problem b), redistribution BBA of con-
distributes the empty sets via using the same method of flict set for non-empty sets is added into redistribution
processing unknown set Θ. The unknown set Θ is the weight(besides conjunctionBBA inPCRa rule).Revised
universal set of elements in discernment frame suitable PCR rule is called PCRd for short: mPCRd(Ø) = 0 and
for mutual processing. But empty sets Ø are defined as ∀A∈GΘ\Ø .
⎡ ⎤
mPCRd(A)=mt(A)+ (cid:2)mt(A) ⎣ (cid:2) [m1(A)m2(X)+m2(A)m1(X)]+(cid:2) m1(X)m2(Y)⎦
mt(X) X∈Ø,A∈GΘ\Ø X,Y∈Ø
X∈GΘ\Ø
(4)
(cid:3) (cid:4)
And
mt(U)=m12(U)+ (cid:2) mm11(U(U))+2mm22(P(P)) + mm22(U(U))+2mm11(P(P)) (5)
U,P∈GΘ\Ø
P∩U=Ø
RevisedPCRruleusesthe informationinintersection TherevisedPCRruleandclassicaldynamicPCRrules
more effective. And the redistribution of empty set Ø is are simulated and analyzed with two examples. The ex-
more reasonable.The fusion resultof revisedPCRrule is ample1isaclassicalcaseinSmarandache’spaper[15].The
better than that of PCRa rule. example 2 is a dynamic frame example with overall pro-
2. Analysis of calculation cess.ThefusionresultandcalculationofrevisedPCRrule
The calculation is taken into account besides the fu- (PCRd) and dynamic PCR rules (PCRa, PCRb, PCRc)
sion result to evaluate the combination rules. It is lack of are analyzed below.
applicabilityforcombinationrulewhichhasperfectfusion 1. Example 1 (classical case in Smarandache’s
result and high calculation.In the areaof BBA combina- paper[15])
tion,evidencecombinationcanbe consideredasthecom- InTable1,therevisedPCRruledistributesmoreBBA
position of multiplication operation (division operation) to single elements than other three methods. The calcu-
which is atom operation. lation of revised PCR rule and PCRa rule is 46, higher
Definition 1 In hybrid DSm model, lets consider than that of PCRb rule and PCRc rule.
n focal elements Θ = {θ1,θ2,...,θn} in the k evidence, Table 1. Fusion result and calculationof
the set of(cid:9)foca(cid:9)l elements is GΘ, the number of focal ele- Smarandache’s classical case
ments is (cid:9)GΘ(cid:9)(cid:9), fo(cid:9)r the evidence mj(Ajl), j = 1,2,...,k, θ1 θ2 θ3≡Ø θ1∪θ2 Calculation
l = 1,2,...,(cid:9)GΘ(cid:9), Ajl ⊆ Θ, The weighted sum of mul- Prior:m1(.) 0.2 0.4 0.3 0.1 –
tiplication operation times (division operation) for cer- Prior:m2(.) 0.3 0.1 0.4 0.2 –
mPCRa(.) 0.420 0.452 0 0.128 46
taincombinationruleistheBBAcombinationcalculation
mPCRb(.) 0.404 0.436 0 0.160 30
which is expressed as O(f(n,k)). mPCRc(.) 0.364 0.396 0 0.240 26
Theredistributioncontentandredistributionweightis mPCRd(.) 0.417 0.457 0 0.126 46
adjusted in the revised PCR rule. The conjunction BBA
2. Example 2 (dynamic frame example with
andredistributionBBA ofconflict set for non-empty sets
overall process)
which have been obtained in the pre-processing are used
Lets assume a fusion system which runs on hybrid
in revised PCR rule. So the calculation of revised PCR
DSm model. The system starts at time t = 1, the dis-
rule is same as that of PCRa rule. The revised PCR rule
cernment frame Θ = {θ1,θ2,θ3,θ2∩θ3}. There is new
has better fusion result without more calculation. So the
information to confirm θ2∩θ3 ≡Ø in t=3, the discern-
revised PCR rule is more effective in the aspect of calcu-
ment frame update as Θ = {θ1,θ2,θ3} (m3(θ2∩θ3) also
lation analysis.
appearsinoriginalBBA).Thereisnewinformationadded
IV. Simulation and Analysis toconfirmθ3 ≡Øint=9,thediscernmentframeupdate
824 Chinese Journal of Electronics 2018
as Θ = {θ1,θ2} .We assume that the target is 1 in the
simulation. The sensor obtain the incorrect identification
result (BBA) caused by interference in time t = 4 and
t = 8.The BBA and non-existential integrity constraints
at different moments are shown in Table 2.
Table 2. BBA and non-existential integrity
constraintsat different moments
Time θ1 θ2 θ3 θ2∩θ3 Constraints
mt=1(.) 0.5 0.2 0.2 0.1 –
mt=2(.) 0.6 0.1 0.2 0.1 –
mt=3(.) 0.7 0.1 0.1 0.1 θ2∩θ3≡Ø
mt=4(.) 0.2 0.7 0.1 0 θ2∩θ3≡Ø
mmtt==56((..)) 00..76 00..11 00..11 00..12 θθ22∩∩θθ33≡≡ØØ Fig.2.ThetendencyoffusionresultBBAforθ1
mt=7(.) 0.6 0.2 0.1 0.1 θ2∩θ3≡Ø The calculationoffourcombinationrulesis simulated
mt=8(.) 0.3 0.4 0.2 0.1 θ2∩θ3≡Ø
and analyzed in Table 4.
mt=9(.) 0.6 0.1 0.2 0.1 θ2∩θ3≡θ3≡Ø
mt=10(.) 0.8 0.1 0.1 0 θ2∩θ3≡θ3≡Ø
Table 4. The calculationof four combination rules
The BBA is fused by three PCR rules and revised 1 2 3 4 5 6 7 8 9 Total
PCRrule.The dynamicfusionresultsareshowninTable mPCRa 50 54 54 54 54 54 54 24 24 422
3. The tendency of fusion result BBA for θ1 displays in mPCRb 50 51 51 51 51 51 51 22 22 400
Fig.2. The figure shows four key points of BBA for θ1. mPCRc 50 46 50 50 50 50 50 26 26 398
mPCRd 50 54 54 54 54 54 54 24 24 422
Table 3. Dynamic fusion result
Numberof 3. Analysis of simulation
θ θ θ θ ∩θ θ ∪θ ∪θ
1 2 3 2 3 1 2 3
fusion
Example 1 is classical case in Ref.[15]. The character
mPCRa(.)0.6862 0.0583 0.0986 0.1569 0
1 mPCRb(.) 0.6862 0.0583 0.0986 0.1569 0 of single element focusing is shown in example 1. A com-
mPCRc(.) 0.6862 0.0583 0.0986 0.1569 0 plete simulation with dynamic non-existential integrity
mPCRd(.) 0.6862 0.0583 0.0986 0.1569 0 constraints is given in example 2. The original BBA is
mPCRa(.)0.8919 0.0465 0.0616 0 0 responding to the time BBA obtained (Time). In Table
2 mPCRb(.) 0.8820 0.0516 0.0664 0 0 2, we define the time of combination as number of fusion
mPCRc(.) 0.8767 0.0463 0.0613 0 0.0157
mPCRd(.) 0.9203 0.0327 0.0470 0 0 (Number). Number 1 means the first time of fusion, and
mPCRa(.)0.6254 0.3499 0.0247 0 0 so on. The fusion begins in Time 1, the BBA of Time 1
3 mPCRb(.) 0.6180 0.3556 0.0264 0 0 and that of Time 2 are fused to obtain fusion result of
mPCRc(.) 0.6153 0.3585 0.0262 0 0 Number 1. The constraints of θ2 ∩θ3 ≡ Ø and θ3 ≡ Ø
mPCRd(.) 0.6462 0.3338 0.0200 0 0
areaddedinTime3andTime9.The dataofTime4and
mPCRa(.)0.7881 0.1895 0.0224 0 0
mPCRb(.) 0.7836 0.1935 0.0229 0 0 Time 8 are conflicting evidence. From Table 2 and Fig.1,
4
mPCRc(.) 0.7817 0.1954 0.0229 0 0 revised PCR rule is better than other three combination
mPCRd(.) 0.8179 0.1609 0.0212 0 0 rule in the overall process. There are not constraints in
mPCRa(.)0.8697 0.1073 0.0230 0 0 Number 1. So the fusion results of four rule are same.
5 mmPPCCRRbc((..)) 00..88666597 00..11019181 00..00223332 00 00 The Number 6 and Number 9 are the fusion result of
mPCRd(.) 0.9061 0.0714 0.0225 0 0 low conflicting condition shown in Fig.3(b) and Fig.3(d)
mPCRa(.)0.8961 0.0841 0.0197 0 0 respectively. The fusion result of θ1 mPCRa(θ1) reaches
6 mPCRb(.) 0.8946 0.0857 0.0197 0 0 0.9167and0.9767inNumber6andNumber9better2.3%
mPCRc(.) 0.8939 0.0862 0.0199 0 0 and1.7% than PCRa rule (the best in the three dynamic
mPCRd(.) 0.9167 0.0651 0.0182 0 0
mPCRa(.)0.7781 0.1707 0.0512 0 0 PCR rules). The Number 2 and Number 7 are the fusion
7 mPCRb(.) 0.7769 0.1717 0.0514 0 0 result of high conflicting condition shownin Fig.3(a) and
mPCRc(.) 0.7763 0.1722 0.0515 0 0 Fig.3(c) respectively. The fusion result of θ1 mPCRa(θ1)
mPCRd(.) 0.7800 0.1679 0.0521 0 0 reach0.6462and 0.7780in Number 2 and Number 7 bet-
mPCRa(.)0.8945 0.1055 0 0 0
ter3.3%and0.25%thanPCRarule(thebestinthethree
mPCRb(.) 0.8867 0.1133 0 0 0
8 mPCRc(.) 0.8786 0.1059 0 0 0.0155 dynamic PCR rules). Revised PCR rule has best fusion
mPCRd(.) 0.9282 0.0718 0 0 0 resultinprocessinglowconflictingevidenceandhighcon-
mPCRa(.)0.9601 0.0399 0 0 0 flicting evidence.
mPCRb(.) 0.9571 0.0429 0 0 0
9 The calculation of four combination rules is shown in
mPCRc(.) 0.9568 0.0417 0 0 0.0015
mPCRd(.) 0.9767 0.0233 0 0 0 Table4.ThePCRcrulehasthelowestcalculationas398.
A New PCR Combination Rulefor DynamicFrame Fusion 825
Fig.3.Key points of BBA for θ1 in fusion process. (a) Fusion results of fusion Number 2; (b) Fusion results of fusion
Number6;(c)FusionresultsoffusionNumber7;(d)FusionresultsoffusionNumber9
The calculation of PCRb rule is lager as 400. The PCRa The two kinds of combination rules can be mixed, which
rule has the largest calculation as 422 in three classical is the further researchemphasis for our team.
rules. Revised PCR rule is based on the calculated BBA
ofPCRa rule to obtainthe same calculationas PCRa.In
References
9 times fusion, calculation of revised PCR rule is larger
5.5% and 6% than PCRb rule and PCRc rule, which is [1] J.Dezert,“Foundationsforanewtheoryofplausibleandpara-
acceptable. doxical reasoning”, Information and Security Journal, Vol.12,
No.1,pp.26–30, 2002.
In conclusion, revised PCR rule improves the way of
[2] J. Dezert, “An introduction to DSmT for information fu-
distribution based on the using the information of PCRa sion”,NewmathematicsandNaturalComputation,Vol.8,No.3,
rule effectively. The fusion result of revised PCR rule is pp.343–359, 2012.
better than PCR rules in both high conflicting condition [3] F. Smarandache, and J. Dezert, Advances and Applications
of DSmT For Information Fusion Vol.3, American Research
andlowconflictingcondition.Thecalculationremainsthe
Press,Rehoboth, USA,2009.
same as PCRa rule without extra calculation. The accu- [4] G.Shafer,AMathematicalTheoryofEvidence,PrincetonUni-
racyoffusionresultandcontrollabilityofcalculationshow versityPress,Princeton,USA,1976.
the effectiveness of revised PCR rule. [5] F.Voorbraak, “Onthejustification ofDempster’sruleof com-
bination. Artificial Intelligence”, Artificial Intelligence, Vol.48,
No.2,pp.171–197, 1991.
V. Conclusions
[6] E. Lef`evreand Z. Elouedi, “How to preservethe conflict as an
alarminthecombinationofbelieffunctions?”,DecisionSupport
Dynamic frame fusion satisfies the requirement of Systems,Vol.56,No.1,pp.326–333, 2013.
[7] T.L.Wickramarathne, K.Premaratne, andM.N.Murthi,“To-
practical application. The dynamic frame fusion combi-
wardefficient computation of the Dempster-Shafer belief theo-
nation rule based on hybrid DSm model is studied in the reticconditionals”,IEEE Transactions on Cybernetics,Vol.43,
paper. A new dynamic frames PCR combination rule is No.2,pp.712-724, 2013.
presented to overcome the shortness in processing empty [8] J.B. Yang and D.L. Xu, “Evidential reasoning rule for ev-
idence combination. Artificial Intelligence”, Artificial Intelli-
setØandredistributionweightofclassicaldynamicPCR
gence,Vol.205,pp.1–29, 2013.
rule.The effectiveness of revisedPCRrule is studied and
[9] Y.Yang,D.Q.HanandC.Z.Han,“Discountedcombinationof
simulatedinthebothaspectoffusionaccuracyandcalcu- unreliableevidenceusingdegreeofdisagreement”,International
lation. The fusion weight for different evidence is an im- JournalofApproximateReasoning,Vol.54,pp.1197–1216,2013.
[10] D.Q. Han, Y. Deng and C.Z. Han, “Sequential weighted com-
portantresearchdirectionbesidesdynamicframe.Thedy-
bination for unreliable evidence based on evidence variance”,
namic weight combination rule and dynamic frame com-
Decision Support Systems,Vol.56,pp.387–393, 2013.
binationrulearespecifictothedifferentpartsofevidence. [11] M. Khodabandeh, and A. Mohammad-Shahri, “Uncertainty
826 Chinese Journal of Electronics 2018
evaluation for an ultrasonic data fusion based target differen- LI Hongfei is a postdoctoral re-
tiation problem usinggeneralized aggregated uncertainty mea- searcherinShanghaiJiaoTongUniversity.
sure”,Measurement, Vol.59,No.1,pp.139–144, 2015. His research interests include information
[12] L. M. Jiao, Q. Pan and X. X. Feng, “An evidential k-nearest fusion,Uncertaintyreasoningandevidence
neighborclassificationmethodwithweightedattributes”,Proc. theory.
of the 16th international conference on Information fusion,Is-
tanbul,Turkey,pp.145–150, 2013.
[13] Z.G.Liu,J.DezertandQ.Pan,“Combinationofsourcesofevi-
dencewithdifferentdiscountingfactorsbasedonanewdissimi-
laritymeasure”,DecisionSupportSystems,Vol.52,pp.133–141,
2011.
[14] Z.G. Liu, J. Dezert and G. Mercier, “Dynamic evidential rea-
LANJiangqiao isaprofessorofAir
soning for change detection in remote sensing images”, IEEE
Force Early Warning Academy. His recent
TransactionsonGeoscienceandRemoteSensing,Vol.50,No.5,
research interests include military intelli-
pp.1955–1967, 2012.
genceandinformationfusion.
[15] F. Smarandache and J. Dezert, “Extended PCR rules for dy-
namic frames”, Proc. of the 15th International Conference on
Information Fusion,Singapore,pp.263–270, 2012.
[16] F. Smarandache and J. Dezert, Advances and Applications of
DSmTforInformationFusionVol.2,AmericanResearchPress,
Rehoboth, USA,2006.
JIN Hongbin is currently an asso-
HAN Jun (corresponding au-
ciate professor in Air Force Early Warn-
thor) is a lecturer of Air Force Early
ing Academy. His research interests in-
Warning Academy. His recent research
cludeinformationfusion, target identifica-
interests include radar signal process-
tion, and efficiency evaluation for C4ISR
ing and combat application of radar.
system.(Email: [email protected])
(Email: [email protected])