Sesors & Trasducers, Vol 172, Issue 6, Jue 2014, pp 39-44 Sesors & Trasducers 2014 by IFSA Publshg, S L http://wwwsesorsportalcom Combg Gray Relatoal Aalyss wth Cumulatve Prospect Theory for Mult-sesor Target Recogto 1 Q Wag, 2 Hapg Re 1 Zhogsha Isttute, Uversty of Electroc Scece ad Techology of Cha, Zhogsha 528402, Cha 2 School of Software, Jagx Uversty of Scece ad Techology, Nachag 330013, P R Cha Tel: 13590788079 E-mal: wagqrhp@163com Receved: 16 Aprl 2014 /Accepted: 30 May 2014 /Publshed: 30 Jue 2014 Abstract: The am of ths paper s to propose a ew mult-sesor target recogto method for solvg the problem whch the dscrmated obect has multple characterstcs dexes The method combes the cocept of gray relatoal aalyss (GRA method ad cumulatve prospect theory Ths method, the characterstc vector matrx was frstly trasformed to stadardze membershp degree decso makg matrx by usg a mmum ad maxmum membershp fucto model The the postve ad egatve deal pots are defed Further, accordg to the cumulatve prospect theory ad GRA, the prospect value fucto s defed, ad a optmzato model s bult to solve the optmum weght vector Fally, the rule of target recogto s gve The method ca avod the subectvty of the weght of characterstc dexes ad mprove the obectvty ad accuracy of target recogto Fally, umercal smulato llustrates the effectveess ad feasblty of the proposed method Copyrght 2014 IFSA Publshg, S L Keywords: Mult-sesor, Target recogto, Cumulatve prospect theory, Gray relatoal 1 Itroducto Mult-sesor data fuso has bee extesvely studed recet years It s defed as the process of tegratg formato from multple sources to produce the most specfc ad comprehesve ufed data about a etty, actvty or evet [1] It has bee appled may felds, such as patter recogto, fuzzy cotrol, robotcs ad medcal Mult-sesor obect recogto s oe of the mportat techologes of mult-sesor data fuso, ad t has attracted may scholars atteto ad research recet years May target recogto methods are put forward For example, methods based o Dempster-Shafer evdece theory [2-5], Vague method [6, 7], varable fuzzy set method [8]; exteso method [9], ad exteso terval devato degree method [10], VIKOR method [11] These fuso methods are all work well, but methods based o Dempster-Shafer evdece extesvely deped o the selecto of basc probablty assgmet ad the approach eeds to kow the dstrbuto type ad the pror probablty However, the determato of pror probablty s greatly emprcal practcal operato The varable fuzzy sets method ad exteso method are both artfcal determed the weght of characterstcs Thus they are too subectve ad absolute obectvty To mprove target detfcato results, Wa [12] proposed etropy weght method, ad Re ad Yag [11] proposed weght coeffcet of varato method to determe the weght of characterstc dexes http://wwwsesorsportalcom/html/digest/p_2099htm 39
Sesors & Trasducers, Vol 172, Issue 6, Jue 2014, pp 39-44 These methods are obectvely determg weghts, but obectvely weght methods are stll few, therefore ths paper presets a ew method to determe the obectve characterstcs of dex weght, ad the mult-sesor obect recogto ca be treated as a mult-dex decso makg problem [8-12] The prospect theory ca obectvely determe the weght of dex, t s frstly put forward Kahema ad Tversky [13], ad further developed by Kahema ad Tversky [14] I recet years, prospect theory has extesvely studed ad the method s also used to mult-dex decso makg problems [15-17] Thus ths paper wll use the prospect theory to determe weghts of characterstc dexes Ths paper wll propose a ew mult-sesor target recogto method, whch combg GRA wth cumulatve prospect theory The rest of ths paper s orgazed as follows Secto 2 costructs the mult-sesor target recogto model The troducto of prospect theory s gve Secto 3 The ew mult-sesor target recogto method s proposed Secto 4 Numercal example s gve Secto 5 Fally, a cocluso s gve Secto 6 2 Mult-sesor Target Recogto Model A target recogto database cotas dfferet target recogto category, oted as, { 1, 2,, m }, ad each target has a set of m characterstc dexes o { o1, o2,, o } Set 2 ad are respectvely the characterstc (attrbute value ad varace of category wth respect to the character o The system has a characterstc vector matrx X ( m I the target recogto problem, through the detfed target of each characterstc parameters, ad the observato ad target database kow target characterstc parameters matchg to determe the detfed target category We use dfferet sesors to measure a ukow target obect, thus we ca obtaed m characterstc values That s to say, the frst th sesor to measure the ukow obect ad gets the observed value 0 ( 1,2,, wth respect to the th characterstc dex The task of data fuso s, accordg to the value of state ( 1,2,, 0, to ascerta whch category wll be the ukow obect belogg to As the varato coeffcet weght method easy to use s proposed ths paper, we put the orgal model was trasformed to a mmum ad maxmum membershp fucto model frstly, the feature vector matrx to the dex membershp degree matrx R (, where r m r m{ 0, } (1 max{, } 0 Set R ( r 1, r 2,, r be the th optoal obect Eq (1 shows that r s the relatve membershp degree betwee measured value ad the characterstc values The target recogto task s to fd the closest to the target class ad each sesor measuremets 3 Prospect Theory The prospect theory selected the course of acto based o the prospect value The prospect value V s defed as follows [13] 1 V ( p v( x, (2 where ( p s the probablty weght fucto whch s the mootoe creasg fucto wth respect to p, ad vx ( s the value fucto comg from the subectve feelg of the decso maker The fuctoal formula vx ( s proposed by Kahema ad Tversky [13], ad gve as follows: x, x 0 vx ( ( x, x 0, (3 where x s the gas or the losses of the surface value, ad the gas are the postve values ad the losses are the egatve values; ad are the cocave-covex degree of the rego value power fucto of the gas ad the losses, respectvely, where 0, 1; whe the values of ad are larger, the the decso maker s ted to rsk; shows that the rego value power fucto s more steeper for the losses tha for the gas, ad 1 shows the losses averso Kahema ad Tversky [13] expermetally determed the values of 088, ad 225, whch are cosstet wth emprcal data The characters of the prospect theory's value fucto are gve as follows: The gas ad the losses are relatve terms of decso makg referece pots; People are tedg to rsk averso whe they face the gas, but ted to rsk seekg whe they face the losses; People are more sestve to the losses tha to the gas Kahema ad Tversky [14] cosdered that the probablty weght s the subectve udgmet of the 40
Sesors & Trasducers, Vol 172, Issue 6, Jue 2014, pp 39-44 decso maker based o the probablty p of the evet outcome, ad t s ether the probablty or the lear fucto of the probablty It s the correspodg weght o the probablty The probablty weght fucto s show as follows [14]: p ( p ( p (1 p 1/ (4 4 Target Recogto Method Combg GRA wth Prospect Theory Gray relatoal aalyss (GRA method was orgally developed by Deg [18], ad has bee successfully appled solvg a varety of mult-attrbute decso makg (MADM problems [19-21] I ths secto, we wll gve the calculato steps of the gray relatoal aalyss (GRA method based o prospect theory for the mult-sesor target recogto as follows: Step 1 Characterstc matrx to the membershp matrx dcators R ( r ; m Step 2 Defe the postve ad egatve deal pot, as follows: Suppose the dex membershp degree matrx s R (, we defe r m R ( r1, r2,, r (max{ r },max{ r },, m{ r } s the postve deal pot; 1 2 R ( r1, r2,, r (m{ r },m{ r },,m{ r } 1 2 (5 (6 s the egatve deal pot Step 3 Calculatg the dstace measures of alteratve obect wth postve ad egatve deal pot as follows: Set dr (, r rr, dr (, r r r (7 The the dstace set of the alteratve A wth the postve deal pot s D ( d( r, r m dr ( 11, r1 dr ( 12, r2 dr ( 1, r dr ( 21, r1 dr ( 22, r2 dr ( 2, r dr ( m1, r1 dr ( dr ( m, r (8 The dstace set of the alteratve A wth the egatve deal pot s D ( d( r, r m dr ( 11, r1 dr ( 12, r2 dr ( 1, r dr ( 21, r1 dr ( 22, r2 dr ( 2, r dr ( m1, r1 dr ( dr ( m, r (9 Step 4 Determe the gas ad the losses of each alteratve π By Eq (3, the utlty value fucto of π, s gve as follows: To the egatve deal soluto as the referece pot, alteratve s superor to the egatve deal soluto For decso maker, he/she was facg gas By the prospect theory kowledge, decso maker s rsk-averse At ths tme, we choose v ( r ( d( r, r as a postve prospect value, ad brefly ote t as v To the postve deal soluto as the referece pot, alteratve s feror to the deal soluto For decso maker, he/she s facg loss By the prospect theory kowledge, at ths tme the rsk of decso maker s to pursue At ths tme, we choose v ( r ( d( r, r as a egatve prospect value, ad brefly ote t as v Step 5 Calculate the comprehesve prospect value: Assume that the weght fuctos ( w ad ( w are respectvely the weght fucto whch the decso maker faces to the gas ad losses The the comprehesve prospect value of A s the sum of a postve prospect value ad a egatve prospect value, ad gve as follows (Ref [14]: where 1 1, (10 V v ( w v ( w w 1/ w ( w [ w (1 ] w ( w [ w (1 ] 1/ w, (11 (12 Accordg to the Ref [17], ths artcle wll adopt the parameter values fucto utlty value prospects ad prospects weghtg fucto as follows: 088, 225, 061, 069 (13 41
Sesors & Trasducers, Vol 172, Issue 6, Jue 2014, pp 39-44 Step 6 Determe the optmal characterstc dex weghts Assume that the weghts of characterstc dex are satsfy the followg set H, where H {0 a w b 1, 1, 2,, } (14 For each alteratve, ts comprehesve prospect value s always the bg the better, so we ca costruct the optmzato model wth the follow obectve fucto: max (,,, (15 V V1 V2 V m Sce the alteratves are far competto, thus we ca costruct the followg optmzato model: m m m 1 1 1 1 1 max V V v ( w v ( w wh st w 1 1 w 0, 1,2,, (16 The above model ca be solved by Matlab software, e oe ca use the Matlab geetc algorthm toolbox to solve The obtaed optmal soluto w ( w1, w2,, w s the optmal characterstc dex weghts vector Step 7 Calculate the optmal comprehesve prospect value s The optmal comprehesve prospect value of 1 1 V v ( w v ( w A (17 Step 8 Recogto rule From the above aalyss, accordg to the optmal comprehesve prospect value of caddate obects A ( 1,2,, m, we gve the target recogto rule: If k arg max{ V } (18 0 1 m The the ukow obect belogg to the target π k0 5 Example Study To llustrate the effectveess of the ew multsesor target recogto method, a example adopted from the paper [22] s gve I order to realze the automatc recogto ad classfcato for tellget robots, several sesors are fxed the robot system The system by SCARA robot, the robot cotrol ad drve, sesor system, the ma computer, etc, the mult-sesor system equpped wth sx force sleep, ad close to sleep, ad cotact sleep ad sldg sleep, ad array touch, heat sesato for the sesor ad the correspodg sgal processor I the expermet determed the four depedet characterstc dexes to show the work pece, they were shape factor 1, the secto ceter momet 2, surface reflecto ablty 3, surface roughess 4 of the work pece (part The weghts of characterstc dexes are partly kow, ad they satsfy H : 016 w1 020,014 w2 016, 015 w 018,013 w 017 3 4 (19 There are four stadard parts used to test the expermet, ad the characterstc dex value ad varace of the four parts are reported Table 1 Table 1 The characterstc dex value ad stadard varace of the four stadard parts Part 1 2 3 4 1 130 186 307 275 (012 (010 (011 (025 2 243 371 228 234 (037 (017 (037 (007 3 218 193 137 152 (015 (011 (013 (012 4 185 252 297 193 (019 (023 (025 (019 The sesor sgal through the data collect ad put to the computer ad through the formato aalyss ad characterstc level data fuso for some ukow characterstc dexes values are reported Table 2 Table 2 The sesor measuremet value ad stadard varace Sesor 1 2 3 4 Measuremet Value 215 130 215 212 Stadard Varace (130 (032 (017 (021 Ths paper presets the use of the proposed method to recogze the ukow work pece Step 1 Table 1, 2 of the data ad (1, (2 type get feature matrx ad cofdece dstace matrx s as 130 243 X 218 185 186 371 193 252 307 228 137 297 275 234 152 193 (20 42
Sesors & Trasducers, Vol 172, Issue 6, Jue 2014, pp 39-44 06047 08087 09121 07709 08848 06199 08143 09060 R (21 09862 08391 04893 07170 08605 09127 09428 09107 Step 2 Determe the deal pot ad egatve deal vectors respectvely are: dexes weght vector by usg the Matlab software, ad gve as follows: w (05, 02, 01, 02 (28 Step 6 Calculate the optmal comprehesve prospect value of each part A R ( r, r, r, r 1 2 3 4 (09862, 09127, 09428, 09107 R ( r, r, r, r 1 2 3 4 (06047, 06199, 04983, 07170 (22 (23 V 03934, V 00980, V 00376, V 00818 (29 1 2 3 4 Step 7 Due to the maxmum V4 00818, so the tme to check the ukow work pece as the fourth kd of work pece The recogto results are cosstet wth [22] Step 3 Calculatg the dstace measures of alteratve obect wth postve ad egatve deal pot as follows: The the dstace set of the alteratve A wth the postve deal pot s D ( d( r, r m dr ( 11, r1 dr ( 12, r2 dr ( 1, r dr ( 21, r1 dr ( 22, r2 dr ( 2, r dr ( m1, r1 dr ( dr ( m, r (24 The dstace set of the alteratve A wth the egatve deal pot s D ( d( r, r m dr ( 11, r1 dr ( 12, r2 dr ( 1, r dr ( 21, r1 dr ( 22, r2 dr ( 2, r dr ( m1, r1 dr ( dr ( m, r (25 Step 4 Calculate v ( r ( d( r, r ad v ( r ( d( r, r, where α= β = 0 8,θ = 2 5 The the postve prospect matrx s: 03815 01040 00307 01398 01040 02928 01285 00047 V ( v m 0 00736 04335 01397 01257 0 0 0 The egatve prospect matrx s: 0 01888 04228 00539 02801 0 03250 01890 V ( v m 03815 02192 0 0 02558 02928 04535 01937 (26 (27 Step 5 Set 061, 069, accordg to the equatos, we ca get the optmal characterstc 6 Coclusos To fully cosder the characterstcs of multsesor dcators of the degree of mportace for target recogto, we use the prospect theory to determe the weghts of characterstc dexes It ot oly reflects the obectve realty, but also ca avod the subectve arbtraress, reducg the terferece of artfcal subectve factors The proposed method, whch combg the GRA wth prospect theory, ca work well wth the multsesor target recogto Ths algorthm provdes a ew target recogto approach, whch s smpler ad easy to use Matlab ad other software to solve The method ca also be appled other mult-attrbute decso makg problems Ackowledgemets Ths work s partally supported by Natural Scece Foudato of Jagx Provce of Cha (No 20132BAB211015, ad Natural Scece Foudato of Jxust (No NSFJ2014-G38 Refereces [1] G Gra, J R Raol, Ra A R, et al, Trackg flter ad mult-sesor data fuso, Sādhaā, Vol 25, Issue 2, 2000, pp 159-168 [2] P L Begler, Shafer-Dempster reasog wth applcato to mult-sesor target detfcato system, IEEE Trasactos o System, Ma ad Cyberetcs, Vol 1, Issue 6, 1987, pp 156-178 [3] Y J Pag, Z F Du, A ew method of the basc probablty assgmet, Joural of Fushu Petroleum Isttute, Vol 14, 1994, pp 52-54 [4] X Yu, C Z Ha, Q Pa, et al, Method based o evdece theory for mult-source target recogto, Systems Egeerg ad Electrocs, Vol 29, Issue 5, 2007, pp 788-790 [5] K J Cao, Z G Zhao, H Jag, Target detfcato based o D-S theory ad rule of codtog, 43
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