A NOVEL DATA FUSION APPROACH USING TWO-LAYER CONFLICT SOLVING

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1 A NOVEL DATA FUSION APPROAH USING TWO-LAYER ONFLIT SOLVING Ru L * ad Volker Lohweg, Seor Member, IEEE Ostwestfale-Lppe Uversty of Appled Sceces, Departmet of Electrcal Egeerg ad omputer Scece, Lebgstr 87 D-3657 Lemgo, Germay ABSTRAT A Two-Layer oflct Solvg data fuso approach s proposed ths work, wth a am to provde aother approach to data fuso commuty Sce the evdece of Dempster- Shafer Theory, algorthms for combg peces of evdece have draw a cosderable atteto from data fuso researchers, alog wth may alteratves veted However, oe of these approaches receve a agreemet for beg able to perform very successfully all scearos ad hece ths topc s stll hot dscusso Therefore, the suggested approach ths work wll cotrbute as a ovel method ad preset ts ow merts Idex Terms oflct solvg, data fuso, Dempster- Shafer theory, couter-tutve results INTRODUTION Data fuso has foud more ad more applcatos recetly, ragg from fault dagoss [], [], to mltary defece [3] ad so o Data fuso deals wth data whch s receved from sesors, experts or huma lgustc words, etc Furthermore, much of such kowledge s cogtve ad mprecse (complete some degree To deal wth ucerta kowledge, researchers ofte use Dempster-Shafer theory (DST [4], [5] ad [6], because t s capable of maagg ucertaty due to ts framework DST acts as the poeer data fuso algorthms, whch was proposed by Dempster ad exteded by Shafer subsequetly However, data whch s receved from sesor or from cogtve kowledge ca lead to couter-tutve results f oe of the sesors returs bad measuremets or cogtve kowledge teds to be urelable (Sesors ca also be metoed as experts ad vce versa Ths heret defect poted out by Zadeh [7], [8] brgs crtcsm as well as may other alteratves veted For stace, ampos rule [9] ad Dezert Smaradache theory (DSmT [0], [] are addressed recetly wth ew - *rul@hs-owlde; phoe ; fax ; Ths work was faced by the Germa Federal Mstry of Educato ad Research (BMBF, Grat-No 7N407 sghts to data fuso approaches No matter DST or other ad-hoc rules, oe of them have bee regarded as a superor method to ay other I ths research, a Two-Layer oflct Solvg (TLS data fuso approach s amed at cotrbutg a ew fuso algorthm However, t s ecessary to address DST ad some alteratve rules before troducg TLS Dempster-Shafer Theory Servg as a semal fuso approach, DST strs up may dscussos ad studes data fuso DST s actually a mathematc theory of evdece, whch combes depedet sources of formato [4], [5] ad [6] By the combato of evdece sources obtaed from sesors (experts, more relable ad covcg fuso results are expected afterwards Frst a fte frame of dscermets that forms a set Ω should be defed, Ω { Ψ Ψ, Ψ,, Ψ } A power set Ω, 3 Θ cludes all the possble combatos of propostos (Ψ Propostos are regarded to be mutually exclusve ad exhaustve Ω A fucto m: [0, ], s called a mass fucto, also kow as Basc Probablty Assgmet (BP m ( 0, m ( ( A Θ If there s o elemet the BPA, the the mass s zero O the other had, Θ s a power set composed of all the subsets, so that the sum of all the masses must be oe Furthermore, the focal elemet (mass s larger tha zero s defed as: {(, A Θ, > 0} A ( Belef (Bel ad plausblty fucto (Pl are essetal cocepts DST, whch are used decso-makg Bel ( (3 B A 3

2 Pl ( (4 B A Bel s called lower boud probablty, whle Pl s the upper boud probablty, for the reaso that Bel s the probablty must be ad o the other had Pl s the probablty mght be Therefore, Pl cludes more mass tha Bel, whch s llustrated the followg fgure Accordg to the defto of kc, t calculates the empty tersecto of the propostos of all sesors, hece t s also called coflctg coeffcet Alteratve Rules After the veto of DST, especally the heret defect resdes t [7], [8] may other researchers have proposed ther ow data fuso approaches whch serve as ad-hoc alteratves For example, Murphy s rule [4] s a trade-off rule, whch takes the arthmetc average value of two masses Yager s rule [5] regards that the uversal set Θ should clude the mass from the coflctg parts, so that the uversal set (set wth all propostos s always troduced Yager s rule DSmT s a rather comprehesve theory thus referred to [0], [] Murphy s rule m ( + m( m M ( A (9 Yager s rule FIGURE : Belef ad Plausblty (B, A Eq (3 ad Eq (4 From Fgure, oe ca see that the shaded area (Belef s smaller tha the le oted rectagular area (Plausblty, whch also reveals the fact of Eq (5 Bel( Pl( (5 After obtag the above-metoed cocepts, we are able to use DST to fuse depedet data sources Ad t takes the form: m ( K m ( A, (6 A A A A m ( A aggregates the cosoat opos (o-coflctg parts from sesors ad the multplyg wth K, ( where, K, k c (7 ad k m ( A (8 c A m ( A : meas the mass of propostos from sesor m ( Y A, B Θ, A B m ( m ( B, m Y ( Θ m ( Θ m( Θ + m ( m( ampos s rule m ( A + log( (log: logarthm to the base 0 m ( Θ A, B Θ, A B DST A m ( Θ + A Θ, A m ( A m ( A, (0 ( ampos rule s recetly addressed ad explaed [9], whch DST s dvded by aother coeffcet I addto, the coflctg mass s trasferred to m (Θ TWO-LAYER ONFLIT SOLVING Because of the couter-tutve results of DST [7], [8] ad other alteratves have lmted assstace as remedes, thus a Two-Layer oflct Solvg (TLS data fuso approach s 33

3 suggested, whch cludes two layers to combe peces of evdece (oflct s solved some degree durg combato, so that t s amed as coflct solvg The frst layer resolves the coflct some extet, the the secod oe cotues to solve t ad hece acheves better results Psychologcally, as clearly stated [] Decso makg has bee tradtoally studed at three levels: dvdual, group ad orgazatoal (Further refer to [3] Ths equals to say that decso s made at three layers, whch coflct s uavodable to be cosdered ad solved: dvdual s the basc elemet that holds coflct; group has a larger rage whch cludes coflct whle orgazato s the largest I such a way, people beleve that coflct ca be optmally solved, although t s mpossble to totally elmate ts egatve mpacts Therefore, a TLS data fuso algorthm s suggested ad studed ths work It could become three layers f several groups of sesors are cosdered a larger system The fgure below depcts the scheme of TLS s used DST, ths dfferece ca be see from the codto of summato Eq (8 ( A A ad Eq ( ( A,, A,L, A A Due to the specfed way of determg coflcts Eq (, ths kd of coflct wll very lkely be larger tha oe, whereas DST the deomator s ( k c, hece the deomator DST should be modfed as well Frst of all, the deomator s modfed as: k A,, A, A A! where,!(! m ( A, (3 (4 Below s the graphc llustrato of DST ad MDST wth respect to dfferece coflct calculato FIGURE : Two-layer coflct solvg system I Fgure, layer s regarded as workg at the dvdual level because oflct Modfed Dempster-Shafer theory (MDST s a approach whch combes every two sesors data so that coflct s sort of cosdered ad solved betwee dvduals After recevg the results from the prevous layer, layer collects sesors orgal kowledge ad fuses them wth combed results from MDST, hece coflct s further resolved at a group level The followg secto troduces the frst layer, e MDST MDST Based o the dea of DST, MDST calculates the coflct a dfferet maer as show the formula (cf Fgure 3: k A, A3, A, A A m ( A ( Wth ths defto, coflcts are calculated betwee every two sesors stead of all the sesors together (whch FIGURE 3: oflct calculato DST ad MDST I Fgure 3, coflct DST assocates three sesors together The same le always coects three sesors DST, whle t coects oly two sesors MDST For example, DST, oe par of coflct s: 34

4 A ( P B( P ( P As for MDST, ths par of coflct s decomposed to two parts as: A ( P B( P + A( P ( P Other pars of coflct ca be determed lkewse It ca be readly see that the total coflct MDST s lkely to be larger tha oe, so that Eq (3 s chose I Eq (3, the reaso for choosg (bomal coeffcet s that there are possble combatos for cal- culatg coflcts ( s the umber of sesors Thus, K (K DST s: K A,, A, A A Fally, MDST s formed as: A A, A, A A, A A A m ( A m ( K m ( A Group oflct Redstrbuto (5 (6 As stated [] ad [3], decso makg s also studed a group level Hece, Group oflct Redstrbuto (GR, layer Fgure acts as group coflct solvg strategy, solvg coflct a larger extet compared to dvdual level (MDST Dstgushg from layer (MDST, GR combes sesors propostos a group maer whch meas all sesors shall partcpate ths procedure m ( A + ( log( k + + log( k + MDST ( (7 A A (: umber of sesors; log: logarthm to the base 0; : absolute value sg I Eq (7, the deomator cludes the umber of sesors ad how may possble combatos ( amog sesors as well as coflct evaluato term log( k I the umerator part, sesors org- al propostos A A m ( A are calculated wth correspodg MDST results whch are obtaed from layer Fally, the sum of fal fused results remas 3 Numercal Examples To show the effect of TLS, a umercal example s gve Suppose there are fve sesors predctg tomorrow s weather TABLE : Fve sesors propostos weather Suy Ray Stormy Sesor A Sesor B Sesor Sesor D Sesor E I Table, oe ca readly observe that Suy s strogly emphaszed by these sesors except sesor B Table presets the combed results usg DST, Murphy, Yager, ampos ad TLS accordgly 3 Results ad Dscussos I Table, DST always shows 0 (couter-tutve results for Suy because sesor B assgs 0 to t I ampos ad Yager s rule, m (Θ (represets ambguty or gorace acheves a large umber, sce there s a hgh coflct amog sesors Murphy s rule prefers Suy whe more sesors are troduced As for TLS, t does ot provde couter-tutve results, eve sesor B assgs 0 to Suy ad presets close to real stuato coclusos It could be ascrbed to the use of two layers to solve coflct, whch sesors dsagreemet wth each other s cosderably resolved 3 ONLUSIONS DST presets udesrable results f oe of the sesors has ll-proposed data Other alteratve rules ether take a tradeoff strategy or trasfer hgh coflct to uversal set (Θ, whch leads the results more ucerta to decso makers The suggested TLS decomposes solvg of coflct two layers, amely two levels (dvdual ad group Each of them plays ts ow role solvg coflct ooperato of these two levels avods couter-tutve results ad presets relable oes Therefore, TLS s proposed as a ovel algorthm data fuso 35

5 TABLE : ombed results by dfferet rules ( S : Suy; R : Ray; St : Stormy; Θ : R S St A, B A, B, A, B,, D A, B,, D, E m ( S 0 m ( S 0 m ( S 0 m ( S 0 DST m ( R m ( R m ( R m ( R m ( St 0 m ( St 0 m ( St 0 m ( St 0 m ( S 0495 m ( S 066 m ( S 067 m ( S 0666 Murphy m ( R 00 m ( R 00 m ( R 0056 m ( R 0096 m ( St 0495 m ( St 033 m ( St 074 m ( St 038 m ( S 0 m ( S 0 m ( S 0 m ( S 0 Yager m ( R 0000 m ( St 0 m ( R m ( St 0 m ( R 0 m ( St 0 m ( R 0 m ( St 0 m ( Θ m ( Θ m ( Θ m ( Θ m ( S 0 m ( S 0 m ( S 0 m ( S 0 ampos m ( R 0 m ( St 0 m ( R 04 m ( St 0 m ( R 03 m ( St 0 m ( R 0 m ( St 0 m ( Θ 08 m ( Θ 086 m ( Θ 087 m ( Θ 088 m ( S 04 m ( S 08 m ( S 085 m ( S 085 TLS m ( R 07 m ( R 0005 m ( R 00 m ( R 004 m ( St 04 m ( St 065 m ( St 03 m ( St 0 4 REFERENES [] XF Fa ad M J Zuo, Fault dagoss of maches based o D-S evdece theory Part : D-S evdece theory ad ts mprovemet, Patter Recogto Letters, Vol 7, Iussue 5, pp , 006 [] XF Fa ad M J Zuo, Fault dagoss of maches based o D-S evdece theory Part : D-S evdece theory ad ts mprovemet, Patter Recogto Letters, Vol 7, Iussue 5, pp , 006 [3] J, Schubert, A formato fuso demostrator for tactcal tellgece processg etwork-based defese, It J Iformato Fuso, Vol 8, Issue, 007 [4] A P Dempster, Upper ad Lower Probabltes duced by a mult-valued mappg, Aals of Mathematcal Statstcs, 38:35-339, 967 [5] A P Dempster, A geeralzato of Bayesa ferece, Joural of the Royal Statstcal Socety, 30:05-47, 968 [6] G Shafer, A Mathematcal Theory of Evdece, Prceto Uversty Press, 976 [7] LA Zadeh, A mathematcal theory of evdece (book revew, AI Magaze, 55(8-83, 984 [8] LA Zadeh, A smple vew of the Dempster-Shafer theory of evdece ad ts mplcato for the rule of combato, AI Magaze, 7:85-90,986 [9] F ampos, Decso Makg Ucerta Stuatos, A Exteso to the mathematcal Theory of Evdece, Boca Rato, Florda USA, 006 [0] F Smaradache ad J Dezert, Advaces ad Applcatos o DSmT for Iformato Fuso, ollected Works, Amerca Research Press, Rehboth, 004, [] F Smaradache ad J Dezert, Advaces ad Applcatos o DSmT for Iformato Fuso, ollected Works, Amerca Research Press, Rehboth, 006, [] R Lpshtz, G Kle ad J Orasau, et al, "Takg Stock of Naturalstc Decso Makg," Joural of Behavoral Decso Makg, 4:33-35, 00 [3] SA Suta, Order effects ad memory for evdece dvdual versus group decso makg audtg, Joural of Behavoral Decso Makg, Vol, Issue, pp 7 88, 999 [4] K Murphy, ombg belef fuctos whe evdece coflcts, Decso Support Systems, Elsever Publsher, Vol 9, pp -9, 000 [5] R R Yager, O the Dempster-Shafer framework ad ew combato rules, Iformato Sceces, Vol 4, Iusse