THE FUZZY MAPPING AGGREGATION OPERATOR BASED ON RIMER AND ITS APPLICATION

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1 Intenatonal Jounal of Computatonal Intellgence Systems, Vol. 7, No. 2 (Apl 2014), THE FUZZY MAPPING AGGREGATION OPERATOR BASED ON RIMER AND ITS APPLICATION Xaopng Qu, Mng Jan School of Tanspotaton and Logstcs, Southwest Jaotong Unvesty, 111#, Noth 1 st secton of 2 nd Rng Road, Chengdu, Schuan , P.R.Chna Natonal Engneeng Laboatoy fo Compehensve Tanspotaton Intellgence, Key Laboatoy of Compehensve Tanspotaton of Schuan Povnce, Chengdu, Schuan , P.R.Chna Jun Lu School of Computng and Mathematcs, Faculty of Engneeng, Unvesty of Ulste at Jodanstown, Newtownabbey BT37 0QB, Nothen Ieland, UK Y Wang Depatment of Netwo Engneeng, Chengdu Unvesty of Infomaton Technology, Chengdu, Schuan , P.R.Chna Yang Xu Intellgent Contol and Development Cente, Southwest Jaotong Unvesty, 111#, Noth 1 st secton of 2 nd Rng Road, Chengdu, Schuan , P.R.Chna Receved 13 Decembe 2011 Accepted 9 August 2012 Abstact A fuzzy mappng aggegaton opeato based on RIMER and ts applcaton n Chnese wod semantc poofng system fo specal doman ae dscussed deeply n ths pape. Fstly, the fuzzy mappng aggegaton opeato based on RIMER ae ntoduced and followed by the coespondng fuzzy nfeence method. Secondly, the collecton of the senstve wods and the substtutons and the soft nfeence ae dscussed manly based on ou pevous achevements. Then the new flowchat of the semantc analyss and the bases and the modules n the Chnese wod poofng system ae llustated subsequently. The expement shows that t s moe feasble and pactcal method fo semantc analyss. Keywods: Fuzzy Infeence; Mappng Aggegaton Opeato; RIMER; Semantc Analyss. 1. Intoducton Aggegaton opeatos and data fuson methods have eceved a lot of attenton n the ecent yeas. Many new methods wth the sound theoetcal esults have been obtaned. Those achevements descbe the basc popetes and defne a oadmap fo the use n pactcal applcatons. The cuent theoetcal nteest to defne a good oadmap fo aggegaton opeatos s tghtly elated wth an nceasng pactcal nteest on usng them fo buldng applcatons [1]. In eal wold, human bengs ae constantly mang decsons unde a lngustc envonment. Wth the help of the aggegaton opeato, the compute can deal wth some wos automatcally and ntellgently. As we nown, the aggegaton opeato plays an mpotant ole n the decson-mang pocess. Accodng to the eal poblems, not only the specal evaluaton tems but also 264

2 Xaopng Qu, Mng Jan, Jun Lu, Y Wang the ey wods n the common expessons need to be consdeed n the lngustcs aggegaton opeatos [2]. As we nown, fuzzy nfomaton s popula n ou daly lfe [3]. In the pape [4], seveal methods have been summazed fo dealng wth lngustc nfomaton, fo nstance: (1) The extenson pncple based method fo opeatons on fuzzy numbes that suppot the semantcs of the lngustc labels; (2) The symbolc method fo computatons on the ndexes of the lngustc tems; (3) A fuzzy lngustc model based method fo the lngustc nfomaton wth a pa of values called 2-tuple, composed by a lngustc tem and a numbe. (4) The dect computng wth wods method. Both the methods (1) and (2) pocess the esults n the ntal expesson domans, whch poduce the consequent loss of nfomaton and hence the lac of pecson. The 2-tuple model n the method (3) can deal wth the lngustcal nfomaton wthout loss of nfomaton. And n ths pape, we follow the 4th method to aggegate lngustc-valued nfomaton based on RIMER below. The abbevaton of RIMER ndcates the ule-base nfeence methodology usng the evdental easonng appoach, whch s dffeent fom most conventonal ule-base nfeence methods. It s chaactezed wth cetan unque featues [5]. Fst, each nput can be epesented as a dstbuton on efeental values usng a belef stuctue. The man advantage of dong so s that pecse data, andom numbes, and subjectve judgments wth uncetanty can be consstently modeled unde the unfed famewo. Second, the ER appoach povdes a novel pocedue fo aggegatng ules, whch can peseve the ognal featues of vaous types of nfomaton [6,7]. The advantages of RIMER s sutable fo Chnese wod semantc poofng system [8], n whch the test wods n the poofng text may not the same to the ey wods of those nown specal expessons. Fo example, the test wods can be the synonyms, homonym o othe substtuton of the ey wods. So the new quanttatve method s needed to descbe the dffeence between them. At the same tme, the cetanty of the nown specal should be consdeed n the poofng, because they ae collected o extacted fom the exst mateals elated to the specal doman [9]. Coopeated wth fuzzy theoy, the fuzzy mappng aggegaton opeato based on RIMER s appled to Chnese wod semantc poofng system n ths pape, and some components of the poofng system s updated wth espect to the genealzed RIMER based fuzzy aggegaton opeato. In what follows, the fuzzy modelng of mappng aggegaton opeato based on RIMER s ntoduced n the next secton wth the coespondng fuzzy nfeence method. Then the collecton of the senstve wods and the substtutons and the soft nfeence n the system ae dscussed n Secton 2 ncludng the soft nfeence. In Secton 3, the new flowchat of the semantc analyss and the bases and the modules n the system and the elatons ae pesented wth expement. The fnal secton s ou conclusons. 2. Fuzzy Modelng of Mappng Aggegaton Opeato 2.1. The Mappng Aggegaton Opeato The aggegaton opeato s used to aggegate the multple nfomaton o nowledge nto sngle esult, whch seems the mappng fom the fome to the latte. So the mappng aggegaton opeato s poposed [10]. Suppose x (n) be the nput and Y be the output, then the aggegaton opeato s defned as follows: Y = F(x 1, x 2,..., x n) (1) n whch x s nteval value, lngustc value o symbolc value, denote the combnaton of all values of x as X, Y maybe have the same value to x. F s a mappng fom X to Y. Obvously, Y can extend to epesent a vecto of (y 1, y 2y m). So the equaton (1) s a mult-nput and mult-output expesson. In ths mappng, each element of X coesponds a only value of Y, whch need to be defned befoe aggegaton. Owng to the values of x and y j ae fnte, the mappng can be geneated and stoed n database automatcally unde the condton of aggegaton equements. In the followng eseach, the condton of m=1 n Y s consdeed. Then the aggegaton opeato above s countepont to a smple evaluaton system wth two layes, one uppe tem and seveal lowe tems. Then an evaluaton system has the heachcal fame wth multple layes and many evaluaton tems, whch can be egaded as a combnaton of multple mappng aggegaton opeatos [2]. 265

3 Pape Ttle (4 Wods maxmum) 2.2. The Rule-base Infeence Methodology usng the Evdental Reasonng Fomally, a ule-based model s epesented as R = U, A, D, F (2) whee U = {U ; T} s the set of antecedent attbutes, wth each of them tang values (o popostons) fom an aay of fnte sets A = {A 1, A 2 A T}. A = {A j; j J = A } s a efeental set of values (o popostons) fo an attbute U ( T), and the values o popostons n A (e.g., A j) ae efeed to as efeental values, whch can be taen n dffeent types of value. The aay {U 1, U 2 U T} defnes a lst of fnte condtons, epesentng the elementay states of a poblem doman, whch may be elatonshp. D = {D n; n N}$ s the set of all consequents, whch can ethe be conclusons o actons. F s a logcal functon, eflectng the elatonshp between condtons and the assocated conclusons. In the pape [5], a so-called pacet ule usng a belef stuctue s poposed wth belef degees, attbute weghts, and ule weghts, whee all possble consequents ae assocated wth belef degees. A collecton of pacet ules consttute a ule base wth a belef stuctue (called a belef ule base) as R : If ( 1 ),(D 2, 2 N A 1 A 2 A T ) then {(D 1, D N, N )} (3) 1 ( 1 weghts 1, 2, a ule weght and attbute, { 1,..., L} T whee A ( T ) s the efeental value of the th antecedent attbute n the th ule, T the numbe of antecedent attbutes used n the th ule, and ( N}) s the belef degee to whch D s beleved to be the consequent n the th pacet ule, the nput satsfes the pacet antecedents A = { A 1, A 2 N A }. If T 1 1, the th pacet ule s sad to be complete; othewse, t s ncomplete. The condton N 1 0 denotes total gnoance about the output, gven the nput n the th pacet ule. s the elatve weght of the th ule, and 1, 2 ae the T elatve weghts of the T antecedent attbutes used n the th ule. L s the numbe of all pacet ules n the ule base. Rema 1 [5] : Antecedent attbutes o the numbe of attbutes s not equed to be the same fom one ule to anothe, even though they shae a common consequent set D = {D n; n N}. In ou pevous wo [8], a nonlnea multple nput sngle output elatonshp s expessed by Mamdan-type fuzzy model. R(): If (x 1 s A 1 ) and (x 2 s A 2 x n s then Y s B wth cetanty facto (4) A n ) Assume the popostons of A (T ) n ule x s A Rema 2: Rule (4) s the specal case of ule (3), wth { 1, 2 N } and { 1, 2 T }beng gven specal values. In fact, f = B, j =0 (j N) ae appled, and = 1( = T ) ae used n ule (3), then ule (4) can be establshed wth =, = and T = n. So the ncomplete pacet ule (3) has the chance to suppot the Chnese wod semantc poofng wth T ). A belef ule base gven n the fom shown n ule (3) epesents functonal mappngs between antecedents and consequents wth uncetanty. It povdes a moe nfomatve and ealstc scheme fo uncetan nowledge epesentaton. Note that the degees of belef could be assgned dectly by expets, o moe geneally, they may be taned and updated usng dedcated leanng algothms o up-todate nfomaton egadng the nputs and outputs of a ule-based system s avalable. Once such a belef ule base s establshed, the nowledge contaned n the belef ule base can be used to pefom nfeence fo gven nputs. The nfeence pocedue s nvestgated n the followng subsectons The Constucton of Fuzzy Mappng Aggegaton Fo each ule the antecedent defnes a fuzzy egon of the nput space, U 1 U2 Un, such that f the nput les n ths egon the consequent holds. Taen as a collecton, the antecedents of all ules fom a fuzzy patton n the nput space, and the consequents of all ules fom a fuzzy patton of the output space. The pocess of fndng the output of a fuzzy model fo a 266

4 Xaopng Qu, Mng Jan, Jun Lu, Y Wang gven value of nput s called the The choce of the tem nfeence as opposed to solvng s a esult of the logcal stuctue n whch the fuzzy nfeence system s ooted. In ode to constuct the new ule base fo Chnese wod poofng, the followng leanng pocess needs to be poceeded. 1) Based on ou pevous ule base, the database stuctue s modfed unde the gudelne of ule (3) wth 1( = 1, T ) and N=1; 2) Collect the elatve mateals, obtaned each (, )(=1, J ) of each attbutes n antecedent and of the th ule by judgng the weght by expets; 3) Use the smple weghted multplcatve aggegaton functon to calculate : T ( ) (5) whee 1 max }{ } (6) { 1,..., T 4) Owng to the mpotance of T n the Chnese wod poofng, so we calculate : T (7) 5) In the nfeence pocess, the only can be obtaned based on the gven : T J (, ) 1 j1 j (8) T (, ) 1 whee (, ) 1 when U s used n defne R (=1, T ), othewse (, ) 0. s the degee to whch the j * nput A belongs to the efeental value A j wth 0 J and j 1 j 1 ( T) and { j ; J }. Hee T s the total numbe of dffeent antecedent attbutes nvolved n all the ules n a ule base. See the detal n the pape [5]. In the nfeence pocess, the ule wth the hghest wll be actvated and ts s used to pompt the degee of non-tuth. 3. The Pepaaton fo Fuzzy Mappng Aggegaton Opeato In ou pevous eseach, the collecton of senstve wods s mentoned and the gd nfeence, the soft nfeence wth the concepton matchng, the ole j No matchng and the quotaton matchng ae nvestgated fom the fuzzy mappng aggegaton ules' pont of vew. Based on those achevements, the mpovng eseach focuses on the soft nfeence. The mappng aggegaton opeato based on RIMER s adopted to bette the Chnese wod poofng effect n semantc analyss. In ode to smplfy the contbutons hee, the compasons wth the pevous achevements ae mentoned as follows The Collecton of Senstve Wods and the Substtutons As to the specal doman, some wods ae senstve n the sentence expesson, whch can be collected by nvestgaton of the coespondng expets o some egulatons. So the fst step s the collecton of senstve wods. Futhemoe, the synonym of the senstve wods s consdeed wth the smlaty between them. All those nfomaton ae saved n Table 1, whch lsts the man felds n database table. Table 1. The senstve wods and the substtuton Senstve Wods Substt uton Smla ty Ceate Tme 1 X1 S X1 S X2 S3 0.9 Modfy Tme unque the synonym o the homonyms of the coespondng senstve wod. The same senstve wod may have ndependent smlaty, whch s dentfed by dffeent ecod (lne). The value of the s detemned by the mateal analyss and expets' evaluaton n the coespondng doman The Soft Infeence The soft nfeence s an mpotant pat of the Chnese wod poofng system, whch s ealzed based on a bacgound nowledge named scenazed nowledge [11,12], whch ncludes the thesauus, classfed elaton. In ou eseach wo, the followng aggegaton ule wth one output D s consdeed to descbe the fuzzy 267

5 Pape Ttle (4 Wods maxmum) mappng elatons among the components n expesson. D - R : If ( A 1 A 2 A T ) then D wth a belef degee, a ule weght and attbute weghts 1, 2,, (9) T So A T ) whch means the efeental value of the th antecedent attbute n the th ule s coespondng X s A pevous ule. Hee, the fome ule sequence numbe s equal to the latte footnote numbe. The value of A s the esult of the membeshp functon A (x ), whch s llustated n Fgue 1. In Fgue 1, U s be the synonymous o smla wod set of x ncludng tself, whch can have the postve matchng, U a be the antonyms set of x whch can have the negatve matchng, then U = U s U a. Othewse, A (x )=0. The eal lne A-B do not means the membeshp functon A s lnea but the elements n U have the membeshp degee n [-1,1]. The fuzzy mappng aggegaton ules saved n dffeent databases ae come fom the pactcal equements and need to be used n nfeence pocedue. In the database, the synonym and the antonyms of the concepton o the ole below ae saved n the tables le Table1, n whch the Smlaty feld s n [-1,1] coespondngly. Fgue 1 The new membeshp functon fo the soft nfeence On the bass of the new membeshp functon above, the scenazed nowledge epesentaton s poposed and the matchng needs to dscuss n the followng two types [8] Concepton Matchng Ths method s used to match the nowledge whch sn't scenazed, such as name descpton, man-class descpton, substtute descpton and elatve descpton. Based on the semantc elatons, ncludng synonymous elaton, smla elaton, contay elaton, genec elaton and espectve elaton, the matchng ules fo the name descptons ae lst as followng. Postve Matchng: synonymous, smla o genec elaton Negatve Matchng: contay elaton Not Matchng: espectve elaton. As to the othes descptons, the classfcaton nowledge ae used to match gnoance of the chaactestc of the nowledge objects Role Matchng Ths method s used to match the scenazed nowledge, n whch the oles ae the basc components n nowledge epesentaton. Based on the exstng syntax scenazed templates, whethe the two scenazed nowledge match each othe can be ganed fom the followng ules. 1) Postve Matchng: the two scenazed nowledges use the same template and the amount of the negatve matchng oles s oven; 2) Negatve Matchng: the two scenazed nowledges use the same template and the amount of the negatve matchng oles s odd; 3) Not Matchng: the two scenazed nowledges use the dffeent templates o the same template but moe than one oles msmatchng. Fom the fuzzy mappng aggegaton ules above, the soft nfeence s moe poweful to descbe the elatve nowledge n the specal doman. Fo example, the postve matchng and the negatve matchng of the scenazed nowledges can be easly obtaned fom the poduct of the wth ts symbol. It s valuable fo ou poofng system wth seveal advantages, such as hghe nfeence effcency, bette nowledge coveage, moe opeaton pactcablty fo the edto. Rema 3: The smlaty s coespond to j o needs to use n equaton (5)-(8) Leanng and Update Methods of Rules Indspensably, the leanng functon s desgned n ou ntellgent wod semantc poofng system fo the uses' equements. If the use fnds out a new ule n the same doman, he can nput t nto the ule base wth the apponted fomat and opeaton. When the fuzzy mappng aggegaton ules ae needed to be updated, the thee types of update opeaton ae consdeed usually. 268

6 Xaopng Qu, Mng Jan, Jun Lu, Y Wang The addton opeaton s used to ench the nowledge bases whch save the fuzzy mappng aggegaton ules. The necessay wo needs to be fnshed s to judge the paadox among the ules, whch can be solved by dffeent poty values. Cetanly, the modfcaton opeaton needs to judge the paadox, too. And the cetanty facto o belef degee maybe updated wth modfcaton afte new statstcs and the expets' evaluaton. And the deleton opeaton s smple fo ules. But fo the senstve wods, each ule elated to them wll be checed caefully. 4. Expements Based on ou pevous wo [8] and fuzzy mappng aggegaton opeato, the coespondng expement s caed out fo valdaton le befoe. doman and fndng the elatve sentences n an atcle. Then the standad sentence analyss s caed out fo the sentences esulted fom the semantc analyss ncludng followng soft nfeence step The Bases and Modules n the System As an ntegated system, the syntax analyss s consdeed as a basc wo. The bases and models and the elaton among them n the system ae shown n Fgue 3. Specal Doman Rule Base Rgd Specal Doman Analyss Module Quotaton Unde Inteface Module 4.1. The New Flowchat of the Semantc Analyss Based on the standad sentence analyss pocedue, the new flowchat of ou system (see Fgue 2) s poposed fo a specal doman because most steps of the standad sentence analyss pocedue has low effcency, especally fo Chnese. Semantc Analyss Module Bacgound Tansfomaton Syntax Analyss Module Wod Dctonay TCT Fgue 3 The bases and modules n the system Fgue 2 The new flowchat of the semantc analyss In ths flowchat, the senstve wods and the substtutons ae found fstly and the gd nfeence s adopted fo judgng the coelaton wth the specal In Fgue 3, the thn lne ndcates the elaton between the model and the bases and the thc lne wth aow ndcate the efeence elaton among the models. Those components wth thc fame ae updated coespondng to the fuzzy mappng aggegaton opeato based on RIMER. [10] ae the necessay bases fo the syntax analyss module and the fome Bas soft nfeence ules based on RIMER. The synonymous stngs, the smla stngs and the othes ae also saved nfomaton, the elatve tansfomaton ules n the the ule bases and the modules, lean new ules and save them n the coespondng bases wth espect to the new 269

7 Pape Ttle (4 Wods maxmum) fnshes the basc wos n syntax analyss, such as syncopatng the sentences and wods, labelng the wods' can tansfe the syntax fame nto scenazed nowledge fame and fnsh the soft nfeence. All the modules ae updated because of the change of the elatve base. ule Wod's embeddng module and a specal softwae fo use convenence. Those two pogams opeate the same ule base fo the same poofng esults. Obvously, the common functons fo the wod pocessng ae ncluded n the sepaate softwae, such as fle functons, clpboad functons and wod fomat functons, whch ae unnecessay to tae nto account n Mcosoft Wod. The compason between ths method and the exstng method s consdeed. Owng to the unfom nfeence pocedue wth fuzzy theoy, the computatonal complexty s deceased wth bette effcency. The belef degee maes the use chec hs pape wth the dffeent cetanty le befoe. Some syntax poofng le the homophone o the homogaph esulted fom the dffeent Chnese nput method can be checed n new system. Fom the descpton above, the fame of ths system s unvesal and the specal doman can be easy changed when a dffeent doman ule base s used. The collecton ules n specal doman s ou fst test data and the expement esults show that ths s a moe feasble and effectve method fo semantc analyss, especally fo Chnese. 5. Conclusons In ths pape, a fuzzy mappng aggegaton opeato based on RIMER and ts applcaton n Chnese wod semantc poofng system fo specal doman ae dscussed deeply. Based on the fuzzy mappng aggegaton opeato and ts nfeence method, the collecton of the senstve wods and the substtutons and the soft nfeence ae updated n detal. Then the new flowchat of semantc analyss and the bases and the modules n the system ae ntoduced subsequently. The expemental esults show that the ntellgent system s moe effectve and the compute can wo well wth the computatonal ntellgence [13]. Ou futue eseach wll focus on the moe applcatons of natual language pocessng [14]. Acnowledgements Ths wo has been suppoted by the Reseach Fund fo the Doctoal Pogam of Hghe Educaton of Chna (Gant No ), Natonal Natue Scence Foundaton of Chna (Gant No , & ), Natonal Socal Scence Fund of Chna (Gant No. 10CGL013), Chna Postdoctoal Scence Foundaton (Gant No ), Schuan Key Technology Reseach and Development Pogam (Gant No. 2013GZX0167 & 2011FZ0051) and the Tanng Fund of Academc and Techncal Leade of Schuan Povnce. Refeences 1. Vcenc Toa. Aggegaton opeatos and models[j]. Fuzzy Sets and Systems, 2005, 156: Xaopng Qu, Xaobng L, Kajun Xu, Hongwe Ma. A new aggegaton opeato based on mappng and ts evaluaton applcaton[c]. Poc. 3d Intenatonal Confeence on Intellgent System and Knowledge Engneeng, Xamen, Xaopng Qu, Yang Xu, Mng Jan, Hamng L. The heachcal fuzzy evaluaton system and ts applcaton [J]. Lectue Notes on Atfcal Intellgent, 2006, 3930: Xaobng L, Da Ruan, Jun Lu, Yang Xu, A Lngustcvalued weghted aggegaton opeato to multple attbute goup decson mang wth quanttatve and qualtatve nfomaton, Intenatonal Jounal of Computatonal Intellgence System[J], Aug. 2008, 1(3): Janbo Yang, Jun Lu, Jn Wang, etc. A belef ule-base nfeence methodology usng the evdental easonng appoach - RIMER, IEEE Tansactons on Systems, Man, and Cybenetcs, Pat A[J], 2006, 36(2): (add) 6. Zhje Zhou, Changhua Hu, Janbo Yang, etc., Onlne updatng belef-ule-base usng the RIMER appoach, IEEE Tansactons on Systems, Man, and Cybenetcs, Pat A[J], Nov. 2011, 41(6): Calzada A., Jun Lu, Hu Wang, etc., Uncetanty and ncompleteness analyss usng the RIMER appoach fo uban egeneaton pocesses: the case of the Geate Belfast Regon, Poc Intenatonal Confeence on Machne Leanng and Cybenetcs[C], Jul. 2012, 3: Xaopng Qu, Gangqao Sh, Y Wang, etc., Chnese wod semantc poofng fo specal doman usng fuzzy mappng aggegaton ules, Jounal of Mult.-Valued Logc & Soft Computng[J], 2012, 18: P Apaa, L Fscaell, G La Commaa, C Petone. A model-dven doman-specfc scptng language fo measuement-system famewos[j]. IEEE Tansactons on Instumentaton and Measuement[J], 2011, 60(12):

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