ARCHITECTURAL PROPOSAL AND HARDWARE REALIZATION OF A TYPE-2 FUZZY INFERENCE SYTEM

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1 ARCHITECTURAL PROPOSAL AND HARDWARE REALIZATION OF A TYPE- FUZZY INFERENCE SYTE gue egaejo,, Antono Gacía, Caos A. Peña-Rees 3. ( Unvesdad Dstta Fancsco José de Cadas, Bogotá DC, Coomba Laboatoo de Automátca, coeectónca e Integenca Computacona. ( Unvesdad de os Andes, Bogota DC, Coomba (3 Swss Fedea Insttute of Technoog at Lausanne, EPFL, Logc Sstems Laboato, Swtzeand mmegaejo@udstta.edu.co, angaca@unandes.edu.co, Caos.Pena@epf.ch SUARY Ths pape pesents an achtectua poposa fo a hadwae-based nteva Tpe- fuzz nfeence sstem. It poposes a computatona mode whch consdes paae nfeence pocessng and nneoute bound sets-based tpe educton. Takng nto account ths mode, we conceved a hadwae achtectue fo a Tpe- fuzz sstem wth sevea ppene stages fo fu paae executon of fuzz nfeences. Dstbuted athmetc s poposed fo effcent computng on hadwae the tpe-educton stage. The achtectua poposa s used fo specfng a tpe- fuzz pocesso wth econfguabe ue base. It was mpemented ove FPGA technoog. Some advantages of ths technoog wee taken nto account n ode to mpove the pefomance of the fna mpementaton. Resuts show that ths pocesso pefoms moe than 30 ons of tpe- fuzz nfeences pe second.

2 ARCHITECTURAL PROPOSAL AND HARDWARE REALIZATION OF A TYPE- FUZZY INFERENCE SYTE gue egaejo, Antono Gacía, Caos A. Peña-Rees. 3 ( Unvesdad Dstta Fancsco José de Cadas, Bogotá DC, Coomba ( Unvesdad de os Andes, Bogotá DC, Coomba. (3 Swss Fedea Insttute of Technoog at Lausanne, EPFL, Logc Sstems Laboato, Swtzeand mmegaejo@udstta.edu.co, angaca@unandes.edu.co, Caos.Pena@epf.ch ABSTRACT Ths pape pesents an achtectua poposa fo a hadwae-based nteva tpe- fuzz nfeence sstem. It poposes a computatona mode whch consdes paae nfeence pocessng and nne-oute bound sets-based tpe educton. Takng nto account ths mode, we conceved a hadwae achtectue fo a Tpe- fuzz sstem wth sevea ppene stages fo fu paae executon of fuzz nfeences. Dstbuted athmetc s poposed fo effcent computng on hadwae the tpeeducton stage. The achtectua poposa s used fo specfng a Tpe- fuzz pocesso wth econfguabe ue base. It was mpemented ove FPGA technoog. Some advantages ths technoog wee taken nto account n ode to mpove the pefomance of the fna mpementaton. Resuts show that ths pocesso pefoms moe than 30 ons of Tpe- fuzz nfeences pe second.. INTRODUCTION Tpe- fuzz ogc s an emegent eseach fed. t has been demonstated that tpe fuzz sstems ae capabe of deang wth uncetant souces such as nos tanng data, nos measuements and mutpe meanngs of ngustc categoes [,,3]. As a matte of fact, Tpe- fuzz ogc s a bette choce than tadtona fuzz ogc fo handng phenomena whch ae both non nea and stochastc [,4]. Sevea appcatons of Tpe- fuzz ogc have been ecent addessed [5,6,7]. Some of them eque, fo eatme opeaton, a ve hgh speed pocessng. In ths sense, t s convenent to mpement on hadwae Tpe- fuzz sstems. To the best of ou knowedge, hadwae eazaton of Tpe- fuzz sstems s an aea bae expoed. The authos have poposed a computatona mode and a hadwae achtectue fo an Inteva Tpe- Fuzz Logc Sstem (ITFLS n [3]. Ths achtectue ncudes the tpca stages of an ITFLS [4]: fuzzfcaton, nfeence engne and tpe educton. Ths atte s based on the computaton of nne and oute bound sets [8,9], the so caed Wu-ende cosed foms. Sevea methodoogca aspects egadng the hadwae mpementaton of dgta Tpe- fuzz sstems ae evsed n ode to conceve the two fst sectons of the achtectue. We popose the use of dstbuted athmetc (DA to compute the Wu-ende cosed foms. Due to the nheent paae natue of an ITFLS, we consde ppened paae oganzaton n ode to guaantee the speed pefomance of the fna mpementaton. A Tpe- fuzz pocesso s desgned egadng the poposed achtectue. It s constaned to a maxmum of eght Tpe- fuzz sets pe nput and nne Tpe- sngetons sets at the output. It s mpemented onto a FPGA. Some featues of ecent FPGAs ae expoted n ode to maxmze the pefomance of the sstem. Ths pape s oganzed as foows: secton pesents the consdeed computatona mode. Ou achtectua poposa s expaned n secton 3. Sevea methodoogca aspects egadng the mpementaton of ou achtectue ove FPGA technoog ae pesented n secton 4. Secton 5 exposes some mpementaton and testng esuts fo the Tpe- fuzz pocesso. We daw some concusons n secton 6.. PROPOSED COPUTATIONAL ODEL. A Tpe- fuzz sstem s a ue-based fuzz sstem that uses Tpe- membeshp functons to descbe ts ngustc vaabes. A FLS s nteva Tpe- as ong as an one of ts antecedent o consequent sets s nteva Tpe- [,3,4,0]. Seectng a computatona mode fo pocessng Tpe- fuzz nfeences has a consdeabe mpact on the pefomance that a hadwae mpementaton coud offe. Regadng the bock dagam pesented n Fgue, we consde an nfeence executon mode that pefoms the foowng tasks:. Tpe- fuzzfcaton The fst opeaton n the ogc secton s fuzzfcaton, whch maps a csp vaue nto a Tpe- fuzz set [,4]. An

3 Fgue. Bock dagam of a Tpe- fuzz nfeence sstem. exampe of sngeton fuzzfcaton ove an nteva Tpe- fuzz set s pesented n Fgue. Fo each pont of the unvese of dscouse, two membeshp eves ae computed, one caed uppe membeshp vaue whch s obtaned fom the uppe membeshp functon, and the othe caed owe membeshp vaue whch s obtaned fom the owe membeshp functon. In ths computatona mode, sngeton fuzzfcaton s seected due to t s computatona the smpest method. The acquston of sevea nputs to be fuzzfed, as we as the uppe and owe fuzzfcaton can be pefomed n paae. As ong as the acquston of each nput s ndependent on the othes, the can be acqued and fuzzfed smutaneous.. nfeence engne Ths stage opeates accodng to a set of ues. The ue base does not depend on the natue of fuzz sets. consequent, t s epesented n the same wa as n the Tpe- case [,]. The nfeence engne combnes and computes the ues and gves a mappng fom the Tpe- fuzz antecedents sets to the Tpe- fuzz consequent sets. Thee exsts sevea choces to pefom the antecedent and consequent opeatons equed b the nfeence engne [,]. The nfeence pocess fo one ue s shown n Fgue and t poceeds as foows:. The uppe membeshp vaues ae T-nomed n ode to obtan the uppe fng vaue f.. The owe membeshp vaues ae T-nomed n ode to obtan the owe fng vaue f. 3. The uppe and owe membeshp functons of the consequent fuzz set ae T-nomed wth the pevous computed fng vaues. So as to obtan an output Tpe- fuzz set. In ou computatona mode, the antecedent and consequent opeatons ae computed sepaate fo each ue of the base. Hee agan, a hadwae computaton can expot paaesm. Sevea actve ues can be pocessed smutaneous and the fng ntevas can be cacuated b paae computaton of the T-nom of the uppe and owe membeshp vaues..3 Tpe educton. Tpe educton s obtaned b appng zadeh s extenson pncpe to defuzzfcaton. It epesents a mappng of a Tpe- fuzz set nto a Tpe- fuzz set [,,0]. In ths sense, tpe educton seaches the best Tpe- fuzz set that epesents a Tpe- set. It s possbe to popose an equvaent tpe educe fo each defuzzfcaton method. Tpe educton of genea Tpe- fuzz sets s computatona expensve. two agothmc pocedues fo computng tpe educton have been poposed fo nteva Tpe- fuzz sets: the kanck-mende teatve pocedue [,,4,0] and the Wu-ende cosed foms [8,9]. The fome method povdes an exact computaton of tpe educton but t s computatona cost, so t s not we suted fo hadwae mpementaton. The atte method fnds the nne and oute-bound sets fo the output tpe educed set of an ITFLS [8,9]. Resut of the tpe educton of an nteva Tpe- fuzz set s an nteva Tpe- fuzz set [,], so computng tpe educton conssts on cacuatng an nteva [, ]. Due to uncetant, coud e n the nteva [, ], whe n [, ]. Two nteva Tpe- fuzz sets can be defned: the nne bound set [, ] and the oute bound set [, ]. Appoxmatons of and ma be obtaned as foows: ~ + ( ~ + The defuzzfed pont s cacuated as the aveage of and ~. ( ~

4 Fgue. An exampe of fuzzfcaton and nfeence pocess fo an ITFLS. Regadng the fact that an ITFLS can be vewed as a coecton of embedded Tpe- fuzz sstems [,8], t s possbe to obtan ~ and ~ b computng fou of those sstems, caed bounda Tpe- FLSs. Patcua fo heght-tpe educton these sstems ae computed as foows: (0 ( ( (0 f f f f (3 (4 The nne bound set s obtaned fom (3 (4 as : mn max (0 ( {, } (5 (0 ( {, } (6 Whe the oute bound set s obtaned as foows : ( f f f f ( f f + f f f ( + f ( + f ( f ( f ( f ( f ( f (.... (7 (8 Ou computatona mode appes heght tpe educton as t s computatona, the smpest method. Usua s chosen as the pont wth the hghest pma membeshp vaue n the uppe membeshp functon of the espectve consequent set. If the tems L - and - ae consdeed as the coeffcents of nea combnatons nvoved n expessons (7 and (8, thee s a coeffcent shang between sevea of those nea combnatons. Ths s an mpotant fact that shoud be taken nto account fo educng scon aea n paae-hadwae mpementaton. Even though two dedcated pocessos ae necessa fo computng and, the coud shae hadwae components takng advantage of the smat between the nvoved expessons. 3. HARDWARE ARCHITECTURE. Fgue 3 depcts the hadwae achtectue, conceved fo dgta hadwae mpementaton, of an nteva Tpe- fuzz nfeence sstem. The achtectue s specfed to have two nputs and one output as we as a ue base of maxmum ues. It accepts a maxmum of consequent sngeton sets and S antecedent nteva Tpe- fuzz sets pe nput. Accodng to the computatona mode descbed n pevous secton, t s oganzed as a cascade of thee ppene stages. The fst stage conssts on the fuzzfcaton unts, whch pefom paae sngeton fuzzfcaton fo a antecedent sets. In the second stage, thee s an aa of confguabe ue-computng unts, each one capabe of computng a fng nteva. The ast ppene stage computes heght tpe educton, usng the Wu-ende cosed foms. Foowng we deta the methodoogca aspects that wee taken nto account to conceve each stage. 3. Fuzzfcaton stage. emo based fuzzfcaton s the most used computatona method n Tpe- fuzz pocessos [,4]. It aows to mpement an membeshp functon shape and povdes ow fuzzfcaton-computng tmes, whch ende t appopated fo hgh speed fuzz pocessng. Howeve, the depth of the memoes gowths exponenta wth the desed esouton. An othe we used stateg to pefom fuzzfcaton s athmetc geneatos. The ae stuctua smpe and aso have educed computng tmes, but the ae genea mted to tapezoda membeshp functons [3,7]. Ths featue ma educe the appcaton fed of the fna mpementaton. whee s the numbe of consequent sets.

5 Fgue 3. Poposed hadwae achtectue. Othe appoaches mpement appoxmatons of Gaussan membeshp functons [8]. Regadng a genea pupose achtectue, t s necessa to combne both tapezoda and Gaussan geneatos. Howeve ths stateg w demand a consdeabe amount of hadwae esouces nto a fu paae fuzz pocesso. We chose a memo based ook up tabe scheme to pefom fuzzfcaton n ou achtectue, due to the fact that most of utmate econfguabe technooges (.e. CPLDs, FPGAs, etc have dedcated memo aas [9,0]. The wdth and depth of the memoes ae seected accodng to an accuac cteon [3,7]. We popose to use one memo to pefom a the fuzzfcaton pocess fo one set. Each Tpe- fuzz set s epesented b means of ts uppe and owe membeshp functons. Suppose the memo wdth s Q bts ( whee Q shoud be a mutpe of two, so the vaues of the owe bound ae stoed n the ess sgnfcant Q/ bts of the memo postons, whe the uppe bound vaues ae stoed n the Q/ most sgnfcant bts. Vaues of the two nputs ae stoed usng two egstes. The wdth W of those egstes depends on the seected memo depth D as W Log ( D. Input one s fuzzfed b addessng the memoes of ts assocated fuzzfcaton unts wth the output of the fst egste. Input two s fuzzfed n the same wa. Note that fuzzfcaton fo both nputs s pefomed n paae ove a the antecedents sets. 3. Rue-computaton unts. Rue computaton unts use mnmum t-nom fo pefomng Tpe- fuzz nfeences. Hadwae mpementaton of mnmum t-nom s the most used stateg n dgta Tpe- fuzz pocessos [,3,7]. Some featues of ths t-nom make t a bette opton than poduct t-nom fo hadwae mpementaton. Fo nstance, It s we known that mnmum opeatos demands ess hadwae esouces than mutpes do. Aso nmum stuctues ntoduce a owe dea n the ctca path of the fna mpementaton, so a bette speed pefomance coud be acheved. A ue-computaton unt s shown n Fgue 4(a. Ths unt computes a fng nteva. It conssts on two dentca stuctues: S fo computng f and S fo f. Both ue stuctues have two mutpexes and one mnmum unt. The mutpexes Q and Q seect the ue antecedent of nput one; Q seects the owe bound and Q the uppe one. Whe the mutpexes Q and Q seect the ue antecedent of nput two. The mnmum unt U computes the mnmum between the outputs of Q and Q, whch coesponds to f, whe the unt U computes f fom the outputs of Q and Q. A tpca hadwae stuctue fo a mnmum unt s pesented n Fgue 4(b.

6 Tabe I. Oganzaton of nea combnaton bocks. LC LC Bock Bock Bock 3 f 3 f ( f L 5 f ( f f 4 ( L 6 ( Fgue 4. (a Rue computaton unt, (b nmum t-nom hadwae mpementaton. 3.3 Rue base confguaton memo. Confguaton vaues of ue computaton unts ae stoed n the ue base confguaton memo. These vaues fx the output of mutpexes Q. utpexes that coespond to the same nput have the same confguaton vaue. Each vaue has a sze of u bts whch depends on the maxmum numbe of sets pe nput S as u Log ( S. So a wod of u bts suffces to confgue one ue. Two addtona bts ae added fo enabng the mutpexes, defnng thus, the actvaton of the ue computaton unt. Accodng to ths appoach, the memo sze equed fo stong the ue base woud be ( u + bts, whee s the maxmum numbe of ues to be hande. Note that the actvaton bts aow to confgue ue bases contanng fom one to ues. The ue base confguaton memo ma be oganzed as a postons- (u+ bt memo. As a speca featue of ths memo, thee must be one output fo each memo poston. 3.4 Tpe educe and bound sets aveagng. Hadwae eazaton of heght tpe educton s the ke pont of ou achtectua poposa. It s dvded n seven ppened stages, as shown n Fgue 5, thus the tota atenc of the poposed achtectue s nne cock cces. The fst stage computes nea combnatons equed b the Wu-ende cosed foms. Ths stage s dvded n fve functona bocks, whch cacuate the nea combnatons wth shaed coeffcent and the sums of the uppe and owe fng vaues. Tabe I esumes how nea combnatons ae aanged. The foowng stages compete computaton of cosed foms. The bounda sstems as we as the ght tems of expessons (6 and (7 ae computed between ppene stages two and fve. Hee, opeatons ae pefomed b usng fxed pont athmetc, and a components have one cce atenc fo fu paae opeaton. Due to ths knd of athmetc s used, ntege scang must be ntoduced n dvsons and mutpcatons[]. Some e-oganzaton of the cosed foms has been ntoduced n ode to save hadwae esouces. Fo exampe, nstead of computng ( f f f f, we popose to cacuate the tems f and f and then subtact them; note that those tems ae aso used fo computng the bounda sstems. Ths consdeaton saves one mutpe and one dvde. The aveage of the bound sets equed fo computng the defuzzfed output s pefomed n stages sx and seven, even though an expct computaton of ( and ( s not mpemented. It s cea n expessons (6 and (7 that and depend espectve on and, so b epacng (6 n ( and (7 n ( and then aveagng and ~, the defuzzfed output can be computed as foows : + out + 4 f ( f ( + f f f ( f ( f ( f ( + f ( f ( ~ (9

7 Fgue 5. Hadwae achtectue of the heght tpe educe. Regadng the equatons (-( and (7-(8, an expct hadwae mpementaton fo computng the defuzzfed output woud demand fve addes and two mutpes. The e-oganzaton we popose uses one mutpe and thee addes fo the same pupose. Aso note that, the speed pefomance coud be nceased due to sevea ntemedate components ae emnated. 4. FPGA IPLEENTATION ATTERS. Ths secton povdes some methodoogca aspects fo effcent FPGA mpementaton of the poposed hadwae achtectue. 4. Dstbuted athmetc fo computng nea combnatons wth shaed coeffcents. Dstbute Athmetc (DA has been wde used fo FPGA based sgna pocessng [6,]. It povdes an effcent wa fo computng nea combnatons n tems of both speed pefomance and hadwae esouces due to t does not ncude mutpes. Hadwae mpementaton of heght defuzzfcaton usng DA has been ecent addessed n [5]. Foowng we povde a shot evson of paae DA an we popose how to extend t fo computng two nea combnatons wth shaed coeffcents. Consde computng a nea combnaton ke (9 : k A k B k (9 Suppose x k ae scaed bna numbes wth twocompement epesentaton, so the can be expessed as foows : B N k bk 0 + bkj j j (0 whee b k 0 s the bt that ndcates the sgn of x k and b k N- s the ess sgnfcant bt. B epacng (9 n (8 and e-oganzng the sums : [ b0 A + b0 A b 0 A ] [ b A + b A b A ]. (N [ b (N A + b (N A b(n A ]. (N [ b A + b A b A ]. (N (N (N ( Note that each paenthess n (3 ma be computed b means of a ook up tabe scheme (DALUT wth memo postons, as shown n Fgue 6. If dua pot memoes ae used fo stong DALUTs, t s possbe to compute smutaneous ( fo two nea combnatons that shae coeffcents wth on one memo aa. Ths poposed appoach s depcted n Fgue 7, whee 9 ( maxmum numbe of consequent sets and N8 ( 8-bt esouton fo uppe and owe fng vaues. Lookng at fgues 6 and 7, a DA scheme wth fxed aows to compute an nea combnaton wth ength ess o equa to. The wod ength d of DALUTs s fxed

8 mpemented b means of a ook up tabe. The wod wdth dw used hee fo epesentng the ecpoca functon depends on the desed accuac. The man advantage of ths appoach s ts speed pefomance. Howeve, the dsadvantage s that the ook up tabe s depth dd gowths exponenta wth each bt of accuac. Hee agan, dua pot memoes can be used to shae the ook up tabe of the ecpoca functon, as shown n Fgue 8. Ths appoach s used fo two ecpoca geneatos n the second ppene stage of the tpe educe and aso fo othe two n the thd stage, as t s maked wth two dashed boxes n Fgue 5. Fgue 6. Dstbuted athmetc Look Up Tabe. befoe mpementaton, so the coeffcents A k must be scaed adequate n ode to be coheent wth ths ength. Note that the avaabe esouton x fo epesentng each coeffcent w depend on d and the ue base s sze: x Log d P P ( whee P s the sze of the defned ue base. In hegh tpe educton the tems, L - and - ae the coeffcents A k, so postons of the output sngetons ae epesented n the pata sums stoed nto DALUTs. 4. Dvson. Accodng to equaton (8, thee ae fou mpct dvsons n heght-tpe educton. Exact computng of dvson s tme o aea cost n hadwae mpementatons. Howeve, thee ae sevea methods that appoxmate ths opeaton and speed up ts computaton [3]. One of the most used s the aangement mutpe-ecpoca uncton.geneato, whee the ecpoca functon s 4.3 emo esouces. As a concudng emak of ths secton, we can sa that dua pot RAs ae ke eements n ou achtectue. Fo nstance, the ae poposed fo handng data shang nto DA schemes and dvdes of the tpe-educe. Aso, the coud be consdeed to factate on ne modfcaton of fuzz sets and ue base. Utmate FPGA technooges ae we povded of dedcated memo bocks [9,0]. Patcua, Xnx VIRTEXII FPGAs ncopoate age amounts of 8Kbt dua pot RAs. Those bocks can be used to mpement a wde ange of memoes wth dffeent wdths and depths. In ths sense, ou achtectua poposa s we suted fo beng mpemented n ths patfom technoog. emo estmaton fo ou achtectua poposa coud be cacuated as foows : R R t + fuzz + R eng + R [ S D Q] + [ ( u + ] [ 3 ( N d + ( dw dd ] (4 tp Fgue 7. Extended DA scheme.

9 Tabe II. Featues of the mpemented tpe- fuzz pocesso. Fuzzfcaton stage Infeence engne Tpe educe Inputs Sets pe nput (S Rues ( # of DALUTs # of dvde LUTs Output wdth bts Depth Wdth (N Q D u+ d (^ dw dd R t 8 Bts bts 8 bts bts 5 4 bts bts Whee Fgue 8. Dvde wth shaed ecpoca. R s the tota amount of memo esouces, t R the amount of memo demanded b the fuzz fuzzfcaton stage, R the amount demanded b the eng b the tpe- ue confguaton memo and educe. Rtp 5. A FPGA BASED TYPE- FUZZY PROCESSOR. In ths secton, the FPGA mpementaton of a Tpe- pocesso based n ou achtectua poposa s pesented. The man featues of ths pocesso, accodng to the paametes defned n pevous sectons, ae esumed n tabe II. 5. mpementaton toos and mateas. The pocesso was specfed usng the hadwae descpton anguage VHDL. t was espectve sntheszed, smuated and mpemented b means of mento gaphcs eonado spectum, modesm and xnx se 5. desgns envonments. mutpes as we as dua pot am bocks wee obtaned fom the xnx coe geneato too. 5. mpementaton esuts. Some featues pefomance fgues of the fna mpementaton ae povded n Tabe III. The ae efeed to the xcv3000ff5 FPGA. obseve the foowng fom ths tabe:. Due to the paae oganzaton consdeed n the achtectua poposa, speed pocessng measued n mons of Tpe- fuzz nfeences pe second concdes wth the acheved opeaton fequenc.. Ths sstem ma be mpemented nto a smae taget FPGA, even t povdes enough memo esouces. Routng congeston fo the fna mpementaton s pesented n fgue 9. Red zones ndcate the paces wth hghe denst of actve outng channes. As a vadaton exampe, a Tpe- fuzz sstem wth two antecedents sets, fou ues and fou consequents sets s seected. A deta of the nfeence pocess fo ths sstem s depcted n fgue CONCLUSIONS Ths papes deas wth an achtectua poposa fo a Tpe- fuzz nfeence sstem. Some methodoogca aspects egadng the FPGA mpementaton of ths poposa has been pesented. The anass of a nteva Tpe- fuzz sstem has ed to the defnton of an nfeence executon mode, whose man featues ae: Dvson of the nfeence pocess n sevea phases that can be executed concuent. Adopton of Wu-ende cosed foms fo tpe educton, whch can be cost-effectve mpemented n hadwae. The achtectua poposa has been conceved takng nto account the poposed executon mode, t has sevea ppene stages n whch nfeence pocessng phases ae Tabe III. Impementaton esuts XCV3000ff5-4 FPGA Paamete Vaue Opeaton Fequenc Hz Sces 065 (4% 8Kb RA BLOCKs 56 (58% utpes (8x8 56 (58% IOBs 44 (6% Dnamc powe 593 mw consumpton

10 Fgue 9. Routng congeston of fna mpementaton Fgue 0. A deta of an nfeence pocess.

11 pefomed n paae. Dstbuted athmetc was poposed fo mpementng tpe educton n hadwae. Dua pot memoes pa a ke oe n the defnton of ou achtectua poposa. A Tpe- fuzz co-pocesso was successfu sntheszed and tested ove a FPGA taget technoog. Its pocessng speed eaches 30 ons of Tpe- fuzz nfeences pe second. Ths pocesso s a good canddate fo pefomng eatme tpe- fuzz adaptve fteng [6]. Ths context has been chosen fo vadatng ou achtectua poposa. Expementa esuts w be epoted n a futhe atce. REFERENCES [] N. N. Kanck, J.. ende, An ntoducton to tpe- Fuzz Logc Sstems, epot, Sgna & mage pocessng nsttute Unvest Southen Cafona, Los Angees CA, 998. [] J.. ende, Uncetan Rue-Based Fuzz Logc Sstems, ntoducton and new dectons, Pentce Ha PTR, Uppe Sadde Rve, NJ, 00. [3]J.. ende, The peceptua compute : an achtectue fo computng wth wods, 00 IEEE Intenatona Confeence on Fuzz Sstems, 00,pp [4] Q. Lang and J. ende, Inteva tpe- fuzz ogc sstems: theo and desgn, IEEE Tans. On Fuzz Sstems, Vo 8. pp , Oct [5] Q. Lang, N. Kank, J.. ende, Conecton admsson conto n AT netwoks usng suve based tpe- fuzz ogc sstems, IEEE Tans. Sst., an., Cben., Vo 30,pp , Aug [6] Q. Lang, N. Kank, J.. ende Equazaton of nonnea tme-vang channes usng tpe- fuzz adaptve ftes, IEEE. Tans. On Fuzz Sstems, Vo. 8, No. 5, pp , Oct 000. [7] Q. Lang, N. Kank, J.. ende, PEG VBR vdeo taffc modeng and cassfcaton usng fuzz technques, IEEE tans. On Fuzz sstems, Vo 9, no, pp , Feb. 00. [8] H. Wu, J.. ende, Intoducton to Uncetant bounds and the use n the desgn of nteva tpe- fuzz ogc sstems, 00 IEEE Intenatona Confeence on Fuzz Sstems, 00, pp [9] H. Wu, J. ende, Uncetant Bounds and the use n the desgn of nteva tpe fuzz ogc sstems, IEEE tansactons on Fuzz sstems, Octobe 00, pp [0] R. I. Bob, J.. ende, Tpe- Fuzz sets made smpe, IEEE Tans. On Fuzz Sstems, Vo. 0, NO., Ap, 00. [] L. X. Wang, A couse on Fuzz Sstems and Conto, New Jese, Pentce Ha, 997. [] ] A. Cabea, et a, Hadwae / softwae codesgn methodoog fo fuzz contoe mpementaton, poceedngs of the IEEE 00 Wod Congess on computatona Integence, Honouu, a 00. [3] I. Batuone et a., coeectonc desgn of fuzz ogc based sstems, CRC Pess, ach, 000. [4] G Asca, V. Catana and. Russo, VLSI Hadwae Achtectue fo Compex Fuzz Sstems, IEEE Tansactons on Fuzz Sstems, Octobe 999, pp [5]. egaejo, D. Oea, A. Gaona, Dstbuted Athmetc n the Desgn of Hgh Speed Hadwae Fuzz Infeence Sstems, nd Intenatona Confeence of the Noth Amecan Fuzz Infomaton Pocessng Socet NAFIPS, Chcago, Inos USA, Ju 4-6, 003. [6] S. A. Whte, Appcatons of Dstbuted Athmetc to Dgta Sgna Pocessng: A tutoa Revew, IEEE ASSP agazne, Vo. 6 No 3, 989. [7] Djuo G., Jame and Bo, Hadwae mpementatons of fuzz membeshp functons, opeatons, and nfeence Computes & Eectca Engneeng, Voume 6, Issue, 7 Janua 000, pp [8] J. J. Bake, L. P. ague, T.. cgnnt, B. Roche and L. J. cdad, The mpementaton of fuzz sstems, neua netwoks and fuzz neua netwoks usng FPGAs, Infomaton Scences, Voume, Issues -4, Decembe 998, pp [9] K. Coffman, Rea Wod FPGA Desgn wth Veog, Petnce Ha PTR, New Jese, 000. [0] Xnx, Vtex-E.8V Fed Pogammabe Gate Aas, Xnx poduct specfcaton V.3,Ju 00. [] Kut Baundendste, An mpoved method of scang fo ea-tme sgna pocessng appcatons, IEEE tansactons on educaton, vo. 3, No. 3, August 994. [] We Wang,.N.S Swam,.O Ahmad, Low powe FIR fte FPGA mpementaton based on dstbuted athmetc and esdue numbe sstem, Poceedngs of the 44th IEEE 00 dwest Smposum on Ccuts and Sstems, 00. WSCAS 00, Voume:, 4-7 Aug. 00,Page(s: 0-05 vo. [3] S.F Obemann,.J Fnn, Dvson agothms and mpementatons, IEEE Tansactons on Computes, Vo. 46, Issue: 8, Aug. 997, pp [4]. egaejo, A. Gacía, C. A. Peña-Rees Computatona mode and achtectua poposa fo a hadwae tpe- fuzz sstem, nd IASTED confeence on Neua Netwok and Computatona Integence(NCI 004, Gndewad, Swtzeand, Febua 004.