Query Data With Fuzzy Information In Object- Oriented Databases An Approach The Semantic Neighborhood Of Hedge Algebras

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1 (IJCSIS) Inernonl Journl of Compuer Scence nd Informon Secury, Vol 9, No 5, My 20 Query D Wh Fuzzy Informon In Obec- Orened Dbses An Approch The Semnc Neghborhood Of edge Algebrs Don Vn Thng Kore-VeNm Frendshp Informon Technology College Deprmen of Informon sysems, Fculy of Compuer Scence D Nng Cy, Ve Nm vnhngdn@gmlcom Absrc - In hs pper, we presen n pproch for hndlng rbue vlues of obec clsses wh fuzzy nformon nd uncerny n obec-orened dbse bsed on heory hedge lgebrc In hs pproch, semncs be qunfed by qunve semnc mppng of hedge lgebrc h sll preservng n order semncs my llow mnpulon d on he rel domn of rbue n relon wh he semncs of lngusc And hen, evlung semncs, serchng nformon uncerny, fuzzness nd clsscl d enrely conssen bsed on he ensurng homogeney of d ypes ence, we presen lgorhm h llow he d mchng helpng he requremens of he query d I INTRODUCTION In pproch nervl vlue [2], we consder o rbuve vlues obec clss s nervl vlues nd he nervl vlues re convered no sub nervl n [0, ] respecvely nd hen we perform mchng nervl hs owever, rbuve vlue of he obec n he fuzzy obec-orened dbse s complex: lngusc vlues, reference o obecs (hs obec my be fuzzy), collecons, Thus mchng d lso become more complex ence, query nformon mehod proposed n [2] s no ssfy requremens for he cse of hs d ye In hs pper, we reserch hs expnded for hndlng rbue vlue s lngusc vlue There re mny pproches on hndlng fuzzy nformon wh lngusc semc h reserchers neress [], [3] We bsed on pproch hedge lgebr, where lngusc semnc s obned by consderng he erms s expressed by he pr of order relon In hs pproch lngusc vlue s d whch s no lbel of fuzzy se represenon semc of lngusc vlue Usng qunve semncs mppng of hedge lgebr o rnsfer lngusc vlues no rel vlues h preserve n order semncs my llow mnpulon d on he rel domn of rbue n relon wh he semncs of lngusc The pper s orgnzed s follows: Secon 2 presenng he bsc conceps relevn o hedge lgebrc s he bss for he nex secons; secon 3 proposng SASN (Serch Arbues n he Semnc Neghborhood) nd SMSN (Serch Mehod n he Semnc Neghborhood) lgorhms for serchng d fuzzy condons for boh rbues nd mehods; secon 4 presenng exmples for serchng d wh fuzzy nformon, nd fnlly concluson Don Vn Bn Insue of Informon Technology, Acdemy Scence nd Technology of Ve Nm No Cy, Ve Nm II FUNDAMENTAL CONCEPTS In hs secon, we presen some fundmenl conceps reled o hedge lgebr [5] Le hedge lgebr X = ( X, G,, ), where X = LDom(X), G = {, c -, W, c, 0} s se generor erms, s se of hedge consdered s one-rgumen operons nd relon on erms (fuzzy conceps) s relon order nduced from nurl semncs on X Se X s genered from G by mens of one-rgumen operons n Thus, erm of X represened s x = h n h n- h x, x G Se of erms s genered from he n X erm denoed by (x) Le se hedges =, where = {h,, h p } nd - = {h -,, h -q } re lnerly ordered, wh h < < h p nd h - < < h -q, where p, q >, we hve he followng defnons reled: Defnon 2 An fm : X [0,] s sd o be fuzzness mesure of erms n X f: q p, 0 () fm s clled complee, h s u X, fm( h u) = fm( u) (2) f x s precse, h s (x) = {x} hen fm(x) = 0 ence fm(0)=fm(w)=fm()=0 fm( hx) fm( hy) (3) x,y X, h, =, Ths fm( x) fm( y) proporon s clled he fuzzness mesure of he hedge h nd denoed by µ(h) Defnon 22 (Qunve semncs funcon ν) Le fm s fuzzness mesure of X, qunve semncs funcon v on X s defned s follows: () v(w)= θ = fm(c - ), ν(c ) = θ - αfm(c - ) nd ν(c ) = θ αfm(c ) (2) If p hen: v( h x) = v( x) Sgn( h x) fm( h x) ω( h x) fm( h x) = (3) If -q - hen: v( h x) = v( x) Sgn( h x) fm( h x) ω( h x) fm( h x) = hp://sesgooglecom/se/css ISSN

2 (IJCSIS) Inernonl Journl of Compuer Scence nd Informon Secury, Vol 9, No 5, My 20 Where: ω( h x) = Sgn( h x) Sgn( hq h x)( β α) { α, β} 2 Defnon 23 Invoe fm s fuzzness mesure of hedge lgebr X, f: X -> [0, ] x X, denoed by I(x) [0, ] nd I(x) s mesure lengh of I(x) A fmly J = {I(x):x X} clled he pron of [0, ] f: (): {I(c ), I(c - )} s pron of [0, ] so h I(c) = fm(c), where c {c, c - } (2): If I(x) defned nd I(x) = fm(x) hen {I(hx): I = pq}s defned s pron of I(x) so h ssfy condons: I(h x) = fm(h x) nd I(h x) s lner orderng Se {I(h x)} clled he pron ssoced wh he erms x We hve p q = I( h x) = I( x) = fm( x) Defnon 24 Se X = { x X : x } { I x x X } =, consder P = ( ) : s pron of [0, ] Is sd h u equl v level, denoed by u = v, f nd only f I(u) nd I(v) ogeher ncluded n fuzzy nervl level Denoe u, v X, u = v P : I( u) nd I( v) III DATA SEARC METOD Le fuzzy clss C = ({, 2,, n }, {M, M 2,, M m }); o s obec of fuzzy clss C Denoed o s rbue vlue of o on rbue ( n ) nd om s vlue mehod of o ( m ) In [2] we presened he rbue vlues re 4 cses: precse vlue; mprecse vlue (or fuzzy); obec; collecon In hs pper, we only neresed n hndng cse nd 2: precse vlue nd mprecse vlue (fuzzy vlue) nd o see precse vlue s prculr cse of fuzzy vlue Fuzzy vlue s complex nd lngusc lbel s ofen used o represen he vlue of hs ype Domn fuzzy rbue vlue s he unon wo componens: Dom( ) = CDom( ) FDom( ) ( n ) Where: - CDom( ): domn crsp vlues of rbue - FDom( ): domn fuzzy vlues of rbue A Neghborhood level We cn ge fuzzy nervl of erms lengh s he smlry beween erms I mens h he erm h represenve vlue of hem dependng on fuzzy nervl level s smlr level owever, o buld he fuzzy nervl level, represenve vlue of erms x hve lengh less hn s lwys n he end of fuzzy nervl level ence, when deermnng neghborhood level, we expec represenve vlue mus be nner pon of neghborhood level Bsed on fuzzy nervl level nd we consruc pron of he domn [0, ] followng s [8]: () Smlr level : wh =, fuzzy nervl level ncludng I(c ) nd I(c ) fuzzy nervl level 2 on nervl I(c ) s I(h -q c ) I(h -q c ) I(h -2 c ) I(h - c ) υ A (c ) I(h c ) I(h 2 c ) I(h p- c ) I(h p c ) Menwhle, we consruc pron smlr level nclude he equvlence clsses followng: S(0) =I(h p c ); S(c )=I(c ) \ [I(h -q c ) I(h p c )]; S(W) = I(h -q c ) I(h -q c ); S(c ) = I(c ) \ [I(h -q c ) I(h p c )] nd S() = I(h p c ) We see h excep he wo end pons υ A (0) = 0 nd υ A () =, represenve vlues υ A (c ), υ A (W) nd υ A (c ) re nner pon correspondng of clsses smlr level S(c ), S(W) nd S(c ) (2) Smlr level 2: wh = 2, fuzzy nervl level 2 ncludng I(h c ) nd I(h c - ) wh -q p We hve equvlence clsses followng: S(0) = I(h p h p c ); S(h c ) = I(h c ) \ [I(h -q h c ) I(h p h c )]; S(W) = I(h -q h -q c ) I(h -q h -q c ); S(h c ) = I(h c ) \ [I(h -q h c ) I(h p h c )] nd S() = I(h p h p c ), wh -q p By he sme, we cn consruc pron equvlence clsses level ny owever, n fc, 4 nd mens h here s mxmum 4 hedges consecuve con ono prmry erms c nd c Precse nd fuzzy vlues wll be he smlr level f he represenve vlue of her n he sme clss smlr level ence, neghborhood level of fuzzy concep s deermnng followng: Assumng pron he clss smlr level s nervls S(x ), S(x 2 ),, S(x m ) Menwhle, every fuzzy vlue fu s only nd only belong o smlr clss Insnce for S(x ) nd clled neghborhood level of fu nd denoed by FRN ( fu ) B Relon mchng on domn of fuzzy rbue vlue Bsed on he concep neghborhood, we gve he defnon of he relon mchng beween erms n he domn of he fuzzy rbue vlue Defnon 3 Le fuzzy clss C deermne on he se of rbues A nd mehods M, A o, o 2 C We sy h o = o nd equl level f: 2 () If o, o 2 CDom( ) hen o = o2 or exsence FRN ( x ) such h o, o FRN ( x) 2 (2) If o or o 2 FDom( ), nsnce for o hen we hve o o2 FRN ( o ) (3) If o, o 2 FDom( ) hen FRN ( o ) = FRN ( o ) Defnon 32 2 Le fuzzy clss C deermne on he se of rbues A nd mehods M, A o, o 2 C We sy h o o f: 2 () If o, o2 CDom( ) hen o o2 (2) If o nd o 2 FDom( ) hen we hve o 2

3 o FRN ( o ) 2 (3) If o, o 2 FDom( ) hen FRN ( o ) FRN ( o ) 2 C Algorhm serch d pproch o semnc neghborhood In [2] we presened he srucure of fuzzy OQL queres re consdered s: selec <rbues>/<mehods> from <clss> where <fc>, where <fc> re fuzzy condons or combnon of fuzzy condon h llow usng of dsuncon or conuncon operons In hs pper, we use pprochng o semnc neghborhood for deermnng he ruh vlue of he <fc> nd ssoced ruh vlues Exmple, we consder query followng show ll sudens re possbly young ge To nswer hs query, we perform followng: Sep : We consruc nervls smlr level, 4 becuse s mxmum 4 hedges consecuve con ono prmry ermsc nd c Sep 2: Deermne neghborhood level of fuzzy condon In he bove query, fuzzy condon s possbly young should neghborhood level 2 of possbly young s FRN 2 (possbly young), nd deermne neghborhood level 2 of fuzzy rbue vlue s FRNA 2 (r) A ls bsed on defnon 3, we perform d mchng wo neghborhood level 2 of FRNA 2 (r) nd FRN 2 (possbly young) Whou loss of generly, we consder on cses mulple fuzzy condons wh noon follow s: - ϑ s AND or OR operon - fzvlue s fuzzy vlues of he rbue On h bss, we bul he SASN lgorhms SASN lgorhm: serch d n cses mulple fuzzy condons for rbue wh operon ϑ Inpu: A clss C = ({, 2,, n }, {M, M 2,, M m }), C = { o, o 2,, o n } where, = p s rbue, M s mehods Oupu: Se of obecs o C ssfy condon p ϑ (o = = fzvlue ) Mehod // Inlzon () For = o p do (2) Begn (3) Se G = {0, c, W, c, }; = Where ={h, h 2 }, = {h 3,h 4 }, wh h < h 2 nd h 3 > h 4 Selec he fuzzy mesure for he generng erm nd hedge (4) D = [mn,mx ] // mn, mx : mn nd mx vlue of domn (5) FD = ( c ) ( c ) (6) End (IJCSIS) Inernonl Journl of Compuer Scence nd Informon Secury, Vol 9, No 5, My 20 (7) Deermne nervls level of fuzzy condon: Q // Pron D no nervl smlr level (8) = Q; // level pron lrges wh = 4 (9) For = o p do (0) For = o 2 5 (-) do () Consruc nervls smlr level : S ( x ); // Deermne neghborhood level of o (2) For ech o C do (3) For = o p do (4) Begn (5) =0; (6) Repe (7) =; (8) Unl o S ( x ) or > 2 5 ( - ); (9) FRNA ( r ) = FRNA ( r ) S ( x ); (20) End // Deermne neghborhood level of fzvlue (2) For = o p do (22) Begn (23) =0; (24) Repe (25) =; (26) Unl fzvlue S ( x ) or > 2 5 ( - ); (27) FRN ( fzvlue ) = FRN ( fzvlue ) S ( x ); (28) End (29) resul= ; (30) For ech o C do (3) f p ϑ = ( FRNA( r ) = FRNA( fzvlue ) ) hen resul=resul {o}; (32) Reurn resul; Smlr o he mehod we hve SMSN lgorhm followng: SMSN lgorhm: serch d cses sngle fuzzy condons for mehod Serch d n hs cse, he frs we deermne neghborhood level fuzzy condons of mehod s FRNP (fzpvlue) Furher, we deermne neghborhood level of rbues whch mehod hndng: FRNA (r), FRNA (r2),, FRNA (rn) We choose he funcon combnon of hedge lgebrs beng conssen wh mehod h opere Then, neghborhood level of funcon combnon s FRNPA (x) A ls bsed on defnon 3, we perform d mchng wo neghborhood level of FRNP (fzpvlue) nd FRNPA (x) Inpu: A clss C = ({, 2,, n }, {M, M 2,, M m }), C = { o, o 2,, o n } where, = p s rbue, M s mehods Oupu: Se of obecs o C ssfy condon (om = fzpvlue ) Mehod 3

4 // Inlzon () For = o p do (2) Begn (3) Se G = { 0, Where c, W, c, }; = (IJCSIS) Inernonl Journl of Compuer Scence nd Informon Secury, Vol 9, No 5, My 20 hen resul = resul {o}; (40) Reurn resul; = {h, h 2 }, = {h 3, h 4 }, wh h < h 2 nd h 3 > h 4 Selec he fuzzy mesure for he generng erm nd hedge (4) D = [mn,mx ] // mn, mx : mn nd mx vlue of domn (5) FD = ( c ) ( c ) (6) End (7) Deermne nervls level of fuzzy condon: Q //Pron D no nervl smlr level (8) = Q; // level pron lrges wh = 4 (9) For = o p do (0) For = o 2 5 ( ) do () Consruc nervls smlr level : S ( x ); //Deermne neghborhood level of o (2) For ech o C do (3) For = o p do (4) Begn (5) =0; (6) Repe (7) =; (8) Unl o S ( x ) or > 2 5 (-); (9) FRNA ( r ) = FRNA ( r ) S ( x ); (20) End // Deermne neghborhood level of fzpvlue (2) = ; f = 0; (22) Whle (<=p) nd (f = 0) do (23) Begn (24) =0; (25) Whle (<= 2 5 ( ) )nd(f = 0) do (26) Begn (27) =; (28) f fzpvlue S ( x ) hen f = ; (29) End; (30) = ; (3) End (32) FRNP ( fzpvlue ) = S ( x ) ; (33) For ech o C do (34) For = o m do (35) funcon combnon hedge lgebrs: p ϑ = FRNPA ( x ) = ( FRNA ( r )) ; (36) resul= ; //Combnon of hedge lgebrs wh operon ϑ s operon nd (37) For ech o C do (38) For = o m do (39) f FRNPA ( x ) = FRNP ( fzpvlue) Theorem: SASN lgorhm nd SMSN lgorhm lwys sop nd correc Proof: The Sonry: Se of rbues, he mehod of he obec s fne (n, p, m s fne) so lgorhm wll sop when ll obecs compleed he pproved 2 The correcve mnennce: Relly, for ech rbue ( n ) n obec o C, he rbue vlues cn ge clssc vlue (precse vlue) or lngusc vlue (fuzzy vlue) In relon mchng for d, we re dvded no he followng wo cses: Frs cse: For clssc rbue vlues (precse vlue), we use operon = o perform d mchng Second cse: For lngusc vlue, we use operon mchng level =, wh s nervl neghborhood level by hedge lgebr Bsed on qunve semncs, we deermned neghborhood level of erm x s FRN (x) = [, b], he followng cses: ) If y s clssc vlue (precse vlue) h y [, b] hen y = x b) If y s lngusc vlue n nervl [x, x 2 ] ( s clculed hrough qunve semncs) h <= x nd x 2 <= b hen y = x Two lgorhms re mplemened o mchng d n cse d s clsscl or lngusc vlues nd he oupu s correcve Compuonl complexy of SASN lgorhm evluon follows s: sep () - (9) complexy s O(p), sep (20) - (32) s O(n*p) So, he SASN lgorhm cn compuonl complexy O(n*p) Compuonl complexy of SMSN lgorhm evluon follows s: sep () - (23) complexy s O(p), sep (24) - (32) s O(n*p), sep (33) - (36) s O(m*n*p), sep (37) - (40) s O(m*n) So, he SMSN lgorhm cn compuonl complexy O(n*p*m) IV EXAMPLE We consder dbse wh sx recngulr obecs s follows: Recngulr D nme lengh of edges wdh of edges re() D hcn 62 Lle shor D2 hcn D3 hcn3 very very shor 70 D4 hcn4 58 very long D5 hcn5 lle long 45 D6 hcn6 55 Lle shor Query : Ls of recngles hve lengh Lle long or wdh Lle shor Usng lgorhms SASN he followng: Sep () - (6): Le consder lner hedge lgebr of lengh, X lengh = ( X lengh, G lengh, lengh, ), where G lengh = {shor, long}, lengh = {More, Very}, - lengh = {Possbly, 4

5 Lle}, where P, L, M nd V snd for Possbly, Lle, More nd Very, wh Very > More nd Lle > Possbly Suppose h W lengh = 06, fm(shor) = 06, fm(long) = 04, fm(v) = 035, fm(m) = 025, fm(p) = 02, fm(l) = 02 Dom(DODAI) = [0, 00] Resul= ; LD = ( shor) ( long) lengh lengh lengh Sep (7) - (20): so lle long nd lle shor = 2 so we only need o buld nervl smlr level 2 We perform pron he nervl [0, 00] no nervl smlr level 2: fm(vvshor) = 035 * 035 * 06 * 00 = 735, so S(0) = [0, 735]; fm(mvshor) fm(pvshor) = (025 * 035 * * 035 * 06) * 00 = 945, so S(Vshor) = (735, 68]; fm(lvshor) fm(vmshor) = (02 * 035 * * 025 * 06) * 00 = 945; fm(mmshor) fm(pmshor) = (025 * 025 * * 025 * 06) * 00 = 675, so S(Mshor) = (2625, 33]; fm(lmshor) fm(vpshor) = (02 * 025 * * 02 * 06) * 00 = 72; fm(mpshor) fm(ppshor) = (025 * 02 * * 02 * 06) * 00 = 54, so S(Pshor) = (402, 456]; fm(lpshor) fm(vlshor) = (02 * 02 * * 02 * 06) * 00 = 66; fm(mlshor) fm(plshor) = (025 * 02 * * 02 * 06) * 00 = 54, so S(Lshor) = (522, 576]; wh smlr clculons, we hve S(W) = (576, 66]; S(Llong) = (66, 652]; S(Plong) = (696, 732]; S(Mlong) = (78, 825]; S(Vlong) = (888, 95]; S() = (95, 00]; Sep (2) - (28): Deermne he neghborhood level 2 of Lle Long nd Lle Shor We hve Lle Long S(Lle Long) so neghborhood level 2 of Lle Long s FRN 2 (Lle Long) = S(Lle Long) = (66, 652], nd neghborhood level 2 of Lle Shor s FRN 2 (Lle Shor) = S(Lle Shor) = (522, 576] Sep (29) - (32): Accordng o condons: - The lengh Lle Long so we hve wo obecs ssfed s D, D5 - The wdh Lle Shor so we hve hree obecs ssfed s D, D2, D6 So resul = {D, D2, D5, D6} ssfed query wh he operon or Query 2: Ls of recngles hve re s less smll Usng lgorhms SMSN he followng: Sep () - (6): Le consder lner hedge lgebr of lengh, X lengh = ( X lengh, G lengh, lengh, ), where G lengh = {Shor, Long}, lengh = {More, Very}, - lengh = {Possbly, Lle}, where P, L, M nd V snd for Possbly, (IJCSIS) Inernonl Journl of Compuer Scence nd Informon Secury, Vol 9, No 5, My 20 Lle, More nd Very, wh Very > More nd Lle > Possbly Suppose h W lengh = 06, fm(shor) = 06, fm(long) = 04, fm(v) = 035, fm(m) = 025, fm(p) = 02, fm(l) = 02 Dom(DODAI) = [0, 00] Resul= ; LD = ( shor) ( long) lengh lengh lengh Sep (7) - (20): so less smll we see corresponds o Lle Shor, h Lle Shor = 2 so we only need o buld nervl smlr level 2 We perform pron he nervl [0, 00] no nervl smlr level 2: (smlr clculon n query ) S(0) = [0, 735]; S(VShor) = (735, 68]; S(MShor) = (2625, 33]; S(PShor) = (402, 456]; S(LShor) = (522, 576]; S(W) = (576, 66]; S(LLong) = (66, 652]; S(PLong) = (696, 732]; S(MLong) = (78, 825]; S(VLong) = (888, 95]; S() = (95, 00]; Sep (2) - (32): Deermne he neghborhood level 2 of less smll So less smll = Lle Shor S(Lle Shor) so neghborhood level 2 of less smll s FRNP 2 (Lle Shor) = S(Lle Shor) = (522, 576] Sep (33) - (40): Accordng o condons: - The lengh Lle Shor so we hve wo obecs ssfed s D2, D6 - The wdh Lle Shor so we hve hree obecs ssfed s D, D2, D6 The funcon combned hedge lgebr s produc of hedge lgebr wh he operon nd, so resul = {D2, D6} ssfed he condons of query 2 V CONCLUSION In hs pper, we propose new mehod for lngusc d proccessng n obec-orened dbse h s nformon s fuzzy nd uncerny pproch o he semc neghborhood bsed on hedge lgebrs Ths pproch mes esy o process d nd homogeneous d Bsed on qunve semncs, we deermned neghborhood level of lngusc vlues nd perform d mchng by neghborhood level hs Ths pper hs proposed mehod combnon of hedge lgebrs n cse he rbue vlue s he lngusc vlue From d mchng bsed semc neghborhood of hedge lgebrs, hs pper hs proposed wo lgorhms SASN nd SMSN for serchng d wh fuzzy condons bsed semc neghborhood of hedge lgebrs REFERENCES [] Berzl, F, Mrn N, Pons O, Vl MA A frmewor o buld fuzzy obec-orened cpbles over n exsng dbse sysem In M, Z (Ed): Advnces n Fuzzy Obec-Orened Dbse: Modelng nd Applcon Ide Group Publshng, 2005,7-205 [2] DVThng, DVBn Query d wh fuzzy nformon n obec-orened dbses n pproch 5

6 (IJCSIS) Inernonl Journl of Compuer Scence nd Informon Secury, Vol 9, No 5, My 20 nervl vlues Inernonl Journl of Compuer pproch o srucure of ses of lngusc domns of Scence nd Informon Secury (IJCSIS), lnguc ruh vrble, Fuzzy Se nd Sysem, 35 Vol9No2, 20, pp -6 (990), pp [3] Le Ten Vuong, o Thun, A relonl dbse exended by pplcon of fuzzy se hoery nd lngusc vrbles Compuer nd Arfcl Inellgence 8(2) (989), pp [4] o Thun, o Cm, An pproch o exendng he relonl dbse model for hndng ncomplee nformon nd d dependences Journl of Compuer Scence & Cybernec (3) (200), pp 4-47 [5] NC o, Fuzzy se heory nd sof compung echnology Fuzzy sysem, neurl newor nd pplcon, Publshng scence nd echnology 200, p [6] NC o, Qunfyng edge Algebrs nd Inerpolon Mehods n Approxme Resonng, Proc of he 5h Iner Conf on Fuzzy Informon Processng, Beng, Mrch -4 (2003), p05-2 [7] N C o, WWechler, edge Algebrs: n lgebrc [8] NCo, NCo, A mehod of processng queres n fuzzy dbse pproch o he semnc neghborhood of edge Algebrs Journl of Compuer Scence & Cybernec, T24, S4 (2008), pp [9] PMTm, TTSon, A fuzzy dbse nd pplcons n crmnl mngemen Journl of Compuer Scence & Cybernec, T22, S (2006), pp AUTORS PROFILE Nme: Don Vn Thng Brh de: 976 Grduon ue Unversy of Scences ue Unversy, yer 2000 Receved mser s degree n 2005 ue Unversy of Scences ue Unversy Currenly PhD suden Insue of Informon Technology, Acdemy Scence nd Technology of Ve Nm Reserch: Obec-orened dbse, fuzzy Obec-orened dbse edge Algebrs Eml:vnhngdn@gmlcom 6

Supporting information How to concatenate the local attractors of subnetworks in the HPFP

Supporting information How to concatenate the local attractors of subnetworks in the HPFP n Effcen lgorh for Idenfyng Prry Phenoype rcors of Lrge-Scle Boolen Newor Sng-Mo Choo nd Kwng-Hyun Cho Depren of Mhecs Unversy of Ulsn Ulsn 446 Republc of Kore Depren of Bo nd Brn Engneerng Kore dvnced