Fuzzy Love Selection by Means of Perceptual Computing

Transcription

1 Fuzzy Love Selecto by Meas of Peceptual Computg Mohammad M Koja Sgal & Image Pocessg Isttute Uvesty of Southe Calfoa Los Ageles, CA, , USA koja@uscedu Jey M Medel Sgal & Image Pocessg Isttute Uvesty of Southe Calfoa Los Ageles, CA, , USA medel@spuscedu Abstact The ma cotbuto of ths pape s to develop a Peceptual Compute fo Fuzzy Love Selecto poblem Ths s a poblem of akg all membes (alteatves) a dvdual lst ode of pefeece Ucetaty of the dvdual about ctea scoes ad weghts assged to each alteatve s hadled by meas of Peceptual Compute Ths pape also pesets a compaso of two Peceptual Compute eges: lgustc weghted aveage ad lgustc weghted powe meas Results show the flexblty ad age of logcal feece povded by aggegato opeatos Keywods- computg wth wods; type- fuzzy logc; peceptual computg; aggegato opeatos I INTRODUCTION Medel ad Wu s appoach to Computg wth Wods (CWW) [] s poposed by thee compoets: the ecode, computatoal ege ad decode The ecode of Peceptual Computg (Pe-C) ceates a codebook of put ad output wods ad modeled them as Iteval Type- (IT) fuzzy Membeshp Fuctos (MFs) Method of ecodg fo epesetg mpecse kowledge of membeshp values s based o two pemses that wods mea dffeet thgs to dffeet people, ad wods mea same thgs to dffeet people The Iteval Appoach (IA) s a vey staght fowad method to establsh IT MFs based o these pemses The Computatoal ege aggegates the pe-specfed put wods wth pe-specfed weghts to coespodg output Two achtectues of CWW eges ae f-the ules ad Lgustc Weghted Aveage (LWA) LWA s a specal case of the Novel Weghted Aveage (NWA) whch all puts ad weghts whch ae epeseted by IT MFs ae mapped to a output IT MF Although LWA s a wellkow aggegato CWW, t caot model madatoy equemet that humas uses the decso makg oute The Lgustc Weghted Powe Mea (LWPM) [] opeato s much close to the tuto of the huma beg I fact, LWA s oe membe of the class of LWPM LWPM coves a wde age of opeatos fom logcal cojucto of the puts to logcal dsjucto The output of computatoal ege s IT MFs whch by meas of decode s mapped to a ecommedato The ecommedato s a wod the output codebook; a ak whch s geeally a teval whose mdpot descbes the defuzzfed scala of type-educed IT MFs; o, a class to show a set of puts belogs to whch goups The ma cotbuto of ths pape s to develop a Pe-C fo fuzzy love selecto poblem ad povdes a compaso of two computatoal eges: LWA ad LWPM aggegato opeatos Ths s a poblem of akg all membes (alteatves) a peso lst ode of pefeece; eg, a dvdual wll be able to ak people based o hs/he ctea lke age, heght, body type, beauty, ad come The est of the pape s ogazed as follows: Secto II povdes the statemet of fuzzy love selecto poblem; Secto III befly pesets two CWW eges: LWA ad LWPM; Secto IV shows the compaso of LWPM aggegato opeato vesus the LWA; ad, Secto V povdes coclusos II PROBLEM STATEMENT Selecto of pate s a poblem of akg all membes a peso lst ode of pefeece The Pe-C ca be a pactcal soluto fo ths poblem The goal s to decde whch peso s the best match wth the use s teest The esult s aked pesos based o the dvdual s pefeece We assume that the poblem s to choose the best peso betwee a set of alteatves, A { a :,, m} based o some ctea, C { c :,, } Ctea ae used to judge alteatves We also assume that a set of fomato descbes each alteatve, la ( ) { X j, j,, } Ths fomato s the fom of lgustc tems Addtoally, each cteo s ot cosdeed to be equally mpotat So, a set of lgustc weghts; W { W j :,, } s assged to them Gvg ths statemet of poblem, we also cosde a set of pefeed lgustc tems, P { p :,, } To help llustate the selecto pocedue, cosde the example of choosg betwee fou alteatves a Ava, a Bella, a Chalotte, ad a Dae ( m ) based o the fve ctea c age, c heght, c body type, c beauty, ad 5 come c ( ) I ode to descbe fomato about alteatves, vocabulaes of wods s ceated to cove the ete scale of each cteo The vocabulaes costuct the codebook The codebook cotas -wod vocabulay fo age, 8-wod vocabulay fo heght, 7-wod vocabulay fo body type, 7- wod vocabulay fo beauty, ad 8-wod vocabulay fo come The followg wods wee chose fo vocabulaes 5

2 Age: Chld, Pubety, Moe o less youg, Modeately youg, Youg, Moe o less adult, Modeately adult, Adult, Mddle age, Moe o less old, Old Heght: Vey shot, Shot, Faly shot, Below aveage, Aveage, Above aveage, Tall, Extemely tall Body type: Th, Slede, About aveage, Athletc, Stocky, Exta poud, Heavy set Beauty: Hdeous, Ugly, Homely, Nomal, Good Lookg, Petty, Gogeous Icome: Noe to vey lttle, Vey low, Low, Moe o less low, Fom fa to moe o less Hgh, Moe o Less hgh, hgh, Extemely hgh Codebook of lgustc weghts cotas fou wods amely Umpotat, Moe o less umpotat, Moe o less mpotat, ad Vey mpotat (FOUs of fou lgustc weghts ae extacted fom [], Table 75) Ifomato descbed alteatves s show Table I The weghts chose by the dvdual ae gve the last ow of Table I; e, age ad beauty of the pate s vey mpotat fo the dvdual whle heght s moe o less umpotat, body type s moe o less mpotat, ad come s umpotat A example of alteatves s Ava who s a youg good lookg peso wth above aveage heght, athletc body, ad low come Next step CWW s sytheszg FOUs fo wods Medel ad Wu beleve that fuzzy set models of wods must be deved fom data that ae collected fom a goup of subjects [] They povde the IA to sythesze IT MFs based o the ucetaty of a peso about the wod (taucetaty) ad ucetaty of a goup of people about the wod (te-ucetaty) Howeve, the dvdual sometmes expects that fomato used thoughout the pocess of establshg fuzzy set models fully acheves based o oly hs kowledge It becomes cleae whe a dvdual would lke to cosde oly hs kowledge decso makg poblems athe tha cludg othes ucetates Fo example, the love matchg poblem, a peso would lke to oly use hs/he kowledge to select a pate ad does ot cae about othes beleve about beauty of a alteatve It s obvous that beauty s eyes of beholds (a good lookg peso may be ugly someoe else s eyes) Theefoe, oly ta-ucetaty s used to fom wod FOUs (Pesoal FOUs) Medel suggests the followg pocess to costuct Pesoal FOUs ) Establsh a teval cotag the possble left ed pots of the wod, ad aothe teval cotag the possble ght ed-pots ) Assume that tevals ae ufomly dstbuted, ad compute the mea ad vaace fo both of them ) Assg the mea ad vaace of the left teval fom Step to a ufom dstbuto ad geeate 50 adom umbes (labeled L, L,, L50) Do the same to geeate 50 adom umbes fo the ght teval (labeled R, R,, R50) Fom 50 ed-pot pas fom these adom umbes {(L, R), (L, R),, (L50, R50)} ) Assume each pa of ed-pots s data collected fom a subject 5) Usg the IA to obta a FOU fo the wod Applyg the above pocedue leads us to pesoal FOUs III CWW ENGINE LWA s a NWA whch all puts ad weghts ae epeseted by IT MFs It s a exteso of Fuzzy Weghted Aveage (FWA) whch s geealzato of the tadtoal weghted aveage LWA Y LWA s a aggegato opeato mappg IT sub-ctea X { X,, X } ad assocated weghts W { W,, W } to a IT output Y LWA Y LWA XW W The IT Y LWA s chaactezed by ts uppe membeshp fucto (UMF) ad lowe membeshp fucto (LMF) Kak-Medel (KM) algothm [] s a teatve pocess fo computg UMF( Y LWA) ad LMF( Y LWA) Ehaced KM (EKM) algothm [] s ehaced pefomace veso of KM algothm whch educed moe tha 9% of computatoal tme Although LWA s a well-kow ege CWW, t caot model madatoy equemet that humas uses the decso makg oute The Lgustc Weghted Powe TABLE I ALTERNATIVES/CRITERIA ARRAY a AND LINGUISTIC WEIGHTS CORRESPONDING TO CRITERIA Ctea Alteatves C C C C C 5 Age Heght Body type Beauty Icome a : Ava Youg Above aveage Athletc Good lookg Low a : Bella Adult Above aveage Athletc Good lookg Low a : Chalotte Modeately youg Aveage About aveage Gogeous Noe to vey lttle a : Dae Mddle age Above aveage About aveage Good lookg Extemely hgh weghts Vey mpotat Moe o less Moe o less umpotat mpotat Vey mpotat Umpotat a fomato may be acheved fom alteatves themselves lke age, heght, body type, o come; o a dvdual flls ths table about beauty by asweg the followg questo: To me, peso a seems to be? ()

3 Mea opeato s much close to the tuto of the huma beg [] q / q X W Y LWPM ( X, W) lm () q W It coves a wde age of opeatos fom logcal cojucto ( ) of the puts to logcal dsjucto ( ) I fact X X Y X X () LWPM UMF ad LMF fo fte ca be wtte as Y LWPM, Y LWPM m{ X }, m{ X }, () w : > 0 w : > 0 Y LWPM, Y LWPM max{ X },max{ X }, (5) w : > 0 w : > 0 LWPM fo a fte powe ca be wtte as Y X W h ( X ) W h h y X W whee / z 0 h ( z) exp( z) 0 ( ) LWPM (, ) (, ) W y h ( X ) W W Y ca be expessed as a uo of smple T FSs h ( ) ( ) X W h X W [ Y, Y ] m h,max h (9) W W whee m ad max ae take ove { X, X, W, W X X, X, W W, W,,, } Rckad et al [5] have geealzed Ehaced Kak- Medel (EKM) algothm to compute the output of LWPM whch s deoted by Weghted Powe Mea Ehaced Kak- Medel (WPMEKM) The WPMEKM algothm s summazed [6] The LMF ad UMF of () ca be computed by the WPMEKM algothm fo ay abtay value of Note that Y LWPM s a cotuous ad ceasg fucto of Theefoe, Y LWPM s patal cojucto whe < < ad patal dsjucto whe < < LWPM s equal to LWA whe LWPM ca also be used aggegato by meas of Cojuctve Patal Absopto (CPA) [7] Usg the CPA opeato xδ( x x), we ca affect the esult of aggegato by madatoy put x ad desed put x Ths s a expaso (6) (7) (8) of tadtoal absopto theoem x ( x x ) x whch s a model of full absopto of x CPA s obtaed f ad s eplaced by patal cojucto ad o s eplaced by patal dsjucto I CPA, f the madatoy put s zeo, the output of CPA s zeo, egadless of the value of the desed put Howeve, f the madatoy put s patally satsfed, the thee ae two possbltes If x < x the the output value s x decemeted by a adjustable pealty If x < x the the output of CPA s x cemeted by a adjustable ewad The CPA opeato s toduced Fg CPA s costucted fom weghted powe meas [6] s s (,, ) LWPM ((, LWPM (, )), ) CPA X W W Y x Y X W W (0) wth 0, s ad W s a -dmesoal weght vecto whch wll be specfed by ewad ad pealty values Obseved that ode to costuct CPA aggegato, X ad W s eeded Aggegato opeatos o X ae IT FSs elated to the lgustc atg of the dvdual Medel ad Wu [] state that X j may have postve o egatve cootatos Postve cootato meas wods ae ght odeg wheeas egatve cootato meas dvdual teested ves odeg of wods vocabulay Ths s because of atual odeg of wods Howeve, Love selecto poblem, the dvdual may be teested adult pate stead of lookg fo oldest o yougest peso Ths may also happe whe the dvdual s teested the aveage heght pesos I ode to coectly aage all wods the aggegato opeatos, pefeed tems should cotbute moe aggegato ad should have lage FOU, whle othe wods should cotbute less ad should have smalle FOUs Cosequetly, thee should ot be ay wods geate tha pefeed wod; eg, the aveage heght FOU should have the lagest FOU the vocabulay Theefoe, addto to selectg weghts fo ctea, the dvdual should select the pefeed wods fo ctea A example of pefeed lgustc tems s p youg, p tall, p athletc, p gogeous, ad p 5 extemely hgh Medel ad Wu [] used the dea of atoym ode to aage wods vocabulay The dea of a atoym s toduced [8] ad [9] The most basc defto of atoym IT FSs s () μ ( x) μ (0 x), x 0 A A () whee 0 A s the atoym of the IT FS A Madatoy Desed Desed CPA Desed Fg Madatoy/desed CPA aggegato

4 Cosde α cete atoym μ ( x) μ ( α x), x A A () α whee A α s the atoym of the IT FS A aoud the cete α Ths s a eflecto map that tasfoms x to ts mo wth espect to α Notce that f α 5 the μ ( x ) α A μ 0 ( x ) I ode to aage tems based o the A pefeed wod, α 5 plays a mpotat ole Wods wth postve cootatos have FOUs ceasg ode I ths case, the cetod of the pefeed wod s geate tha 5 f the dvdual geeally thks postvely about wod If wods have egatve cootatos atoym of FOUs ae used [] I ths case, the cetod of the pefeed wod s less tha 5 f the dvdual geeally thks egatvely about the wod The α cete atoym should apply oly o wods wth cetod geate tha the pefeed wod To aage wods based o the pefeed wod, followg two ules ae appled to X j ) If wods has egatve cootato the atoym of FOUs ae used ) All FOUs wth geate cetod tha the pefeed wod ae eplaced by α cete atoym of them Applyg above ules cause the pefeed wod has had the lagest cetod The pseudo code fo computg α cete atoym based o the pefeed wod s: Compute cetod of A X j α cetod (p ) If cetod( A ) > α μ ( x) μ ( α x), x α A A Ed To llustate how α cete atoym ca be used fo ou pupose, cosde the FOU fo the -wod vocabulay of Age Fg If the dvdual s teested modeately adult, ts FOU should have the hghest cetod ad all othe wods should be aaged based o the dstace fom the cetod of modeately adult Theefoe, α cete atoym should apply o wods wth lage FOUs tha modeately adult age (adult, mddle age, moe o less old, old ad vey old) Fg shows the ew aaged set of FOUs Note that modeately adult has the lagest FOUs amog all tems Fg FOUs fo the - wod vocabulay of Age Fg FOUs fo the - wod vocabulay of Age wth modeately adult pefeed wod Note that modeately adult has the lagest FOUs ad adult, mddle age, moe o less old, old ad vey old ae elocated Fg Results of love selecto poblem; LWA (th les) ad LWPM (bold les) wth + IV COMPARISON OF AGGREGATION OPERATORS To llustate the age of behavos of the LWPM compae to the LWA, fgues of the output IT FOU fo exteme cases of the powe expoetal ( ± ) ae show Fg shows pue dsjucto + ad Fg 5 shows pue cojucto Bold les show the output IT FOUs of LWPM wheeas th les ae fo the LWA Fg 5 Results fo love selecto poblem; LWA (th les) ad LWPM (bold les) wth

5 Obseve that thee s a damatc age of dffeeces betwee LWPM ad LWA ove dffeet alteatves LWPM ofte esults shoulde IT MFs whle LWA always esults teo IT MFs LWA aveages betwee puts wth coespodg weght may cosde as cosesus whle LWPM llustates geate aggegato vesatlty ove the LWA Recall that LWPM output s a cotuous ad ceasg fucto of ; theefoe, by chagg the value of, LWPM shows a wde age of esults fom optmstc vew (complete dsjucto) to pessmstc vew (complete cojucto) wth a cotuous age betwee these two extemes Table I shows the lgustc tems ad lgustc weghts of fou alteatves ad fve ctea The dvdual dcates that age s vey mpotat, heght s moe o less umpotat, body type s moe o less mpotat, beauty s vey mpotat, ad come s umpotat Fg 6 shows IT FOUs output of LWA fo alteatves They ae aked based o the aveage cetods of alteatves The aveage cetod of Ava s 55, Bella s 5, Chalotte s 506, ad Dae s 8 Ava s the best alteatve fo the dvdual based o the LWA aggegato Usg LWPM ad CPA eable us to clude a madatoy put Suppose the dvdual places a madatoy equemet o beauty (ctea c Table I) It s coespodg to x (9) wth x s costucted fom emag ctea wth s Equal weghts ae cosdeed to aggegate x wth x ( W (05,05) ) Fg 7 shows fou LWPM FOUs of dffeet alteatves They ae aked based o the aveage cetods of alteatves The aveage cetod of Chalotte s 6, Ava s 585, Bella s 568, ad Dae s 55 Ituto suggests that the most beautful alteatve should aked fst LWPM aggegato whe beauty s madatoy Chalotte s the best alteatve fo the dvdual based o the LWPM aggegato LWPM FOUs have lage cetods ad aowe akg bads tha LWA FOUs Fg 6 Fou LWA FOUs fo the love selecto poblem; aked deceasg ode of aveage cetods Fg 7 Fou LWPM FOUs fo the love selecto poblem; aked deceasg ode of aveage cetods V CONCLUSION I ths pape, a Pe-C s used fo Fuzzy Love Selecto poblem Ths s a poblem of fdg the best match betwee alteatves based o a dvdual s pefeece LWA ad LWPM ae two aggegato opeatos of Pe-C ege whch ae used to ak all alteatves The compaso of two Pe-C eges shows the wde age of LWPM aggegato opeato It s also show that how LWPM ca be used to poduce CPA The esults show the flexblty ad age of logcal feece povded by LWPM aggegato opeato Also, a ew atoym s toduced ode to coectly aage all wods the vocabulay based o the pefeed dvdual tems REFERENCES [] JM Medel ad D Wu, Peceptual Computg, Hoboko, NJ: Joh Wley & Sos, Ic, 00 [] WS Hog, SJ Che, LH Wag, ad S Che, A ew appoach fo fuzzy fomato eteval based o weghted powe-mea aveagg opeatos, Computes & Mathematcs wth Applcatos, vol 5, pp800-89, Jue 007 [] N Kak ad J M Medel, Cetod of a type- fuzzy set, Ifomato Sceces, vol, pp 95 0, 00 [] D Wu ad J M Medel, Ehaced Kak-Medel algothms, IEEE Tas o Fuzzy Systems, vol 7, o, pp 9 9, August 009 [5] JT Rckad, J Asbett, RR Yage, ad G Gbbo, Fuzzy weghted powe meas evaluato decsos, Wold Cof o Soft Computg, Sa Facsco, CA, 0 [6] [6] JT Rckad, J Asbett, RR Yage, ad G Gbbo, Lgustc weghted powe meas compaso wth the lgustc weghted aveage, IEEE Cof o Fuzzy Systems, Tape, Tawa, 0 [7] J J Dujmovc, Cotuous pefeece logc fo system evaluato, IEEE Tasactos o fuzzy systems, VOL 5, NO 6, 007 [8] [8] C S Km, D S Km, ad J S Pak, A ew fuzzy esoluto pcple based o the atoym, Fuzzy Sets ad Systems, vol, pp 99 07, 000 [9] V Novaka, Atoyms ad lgustc quatfes fuzzy logc, Fuzzy Sets ad Systems, vol, pp 5 5, 00