A Decision-making Method of Supporting Schemes for Deep Foundation Pits Based on Prospect & Evidence Theory

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1 A Deson-mng Method of Supportng Shemes for Deep Foundton Pts Bsed on Prospet & vdene Theory WI Do-ng LI Hu-mng LI Hu. Shoo of Cv ngneerng X n Unversty of Arhteture nd Tehnoogy X n Chn. Insttute of Arhteture Hube Unversty of rt nd sene Xngyng Chn Abstrt In order to optmze the supportng pn for deep foundton pt when prt of the ndex vue s nu method ombng prospet theory nd evdene theory ws put forwrd. An ndex system omposed of trget yer ftors yer nd ndex yer ws estbshed by ppyng the onept of nyt herrhy proess. Then the owners desred gos of the proet were hosen s the referene ponts nd the prospet deson-mng mtrx ws onstruted. Wth the prospet vue of eh sheme s evdene the beef nd pusbty nterv of eh sheme ws reeved by evdene ombnton. Aordng to tht the best sheme n be seeted. A se study showed tht the nfuene mehnsm of the nompete nformton on deson-mng ws reveed by the method. And therefore the method n provde bss for deson-mer to me deson of brng proets for deep exvton wth nompete nformton espey wth nu vue of evuton ndex. Keywords - deson-mng deep foundton pt evdene theory nompete nformton prospet theory supportng sheme I. INTRODUCTION Bred exvton s often requred n the onstruton of hgh-rse budngs nd nfrstruture n urbn res. As the supportng sheme ffets not ony the exvton ost the onstruton shedue but so the sfety of the whoe exvton nd the proteton of the surroundng envronment so t s vt to hoose the best sheme ordng to the hrtersts of spef proet. However beuse of the mted ste nvestgtons mted so bortory tests s we s the nurte orretons for vrous so prmeters some deson-mng nformton for optmzton of support shemes my be defent or nompete. In ths regrd t s essent to be be to hoose the best support sheme n the se of nompete nformton. Sever prevous studes on optm deson for supportng sheme were performed. Q. G. Feng (00) ntrodued grey fuzzy vrbe deson-mng mode whh put forwrd ombnton weghtng pproh for the weght of evuton ndexes bsed on the mxmum oseness degree nd quntfed the quttve ndexes by set-vued sttsts methods. W. H. Go (00) nd H. Zhou (0) proposed fuzzy nyt herrhy proess (AHP) method to seet supportng shemes for ty foundton pt n soft so. In order to sove the mxed ndex deson mng probem n the optmzton of supportng shemes for foundton pt whh resuts from the dversty of evuton ndexes seres of deson mng modes bsed on both ombnton weghtng nd fuzzy theory were put forwrd [-]. A omprehensve evuton method of nterv supportng shemes for foundton pt bsed on onneton number of set pr nyss ws but by Z. R. Jn 00 nd L. X. L 0. And ddton study ws presented by X. W. Lo 00 whh used mthemt progrmmng mode to d wth the mut-ttrbute desonmng. The ommon hrterst of the bove-mentoned reserhes s tht the ndex vue of the evuton nformton s nowbe nd therefore n be desrbed s urte number nterv number or fuzzy number. However s resut of unertny geotehn ondtons ompex surroundngs nd the of wor experene the ndex vues of some shemes my be unnown.e. there mght exst phenomenon of nu vue [ ]. For exmpe s for new sheme there usuy exsts so few referent experene tht we re not be to determne the onstruton perod urtey. In ths ondton t s more resonbe to te the ndex vue s unnown nformton rther thn gve n estmted vue. So the demnds for deson-mng method of supportng sheme wth nompete nformton espey wth the nu vue beome more nd more urgent. vdene theory s deson-mng method used to sove unertn nd rs deson-mng probems []. Currenty the evdene theory s often used for deson mng n mut-ttrbute group nd mtry opertons terntves by mny shors [-] but t hs not been reported s deson-mng method for supportng sheme of deep foundton pts. Furthermore prevous studes often hoose the evuton grde s the referene ponts n probbty ssgnment of the fo eement nd suppose tht the utty vues of eh evuton grde re nown. A of these spets re nonsstent wth the tu DOI 0.0/IJSSST...B.. ISSN: -0x onne -0 prnt

2 stuton of deep foundton pt. In the onstruton engneerng re the owners desred go pys vt roe n deson-mng. The ontrtor hs to onsder not ony ther own nterests but so the owners preferene n the seeton of onstruton sheme. So t s qute neessry to hoose the owners desred gos s the referene ponts rther thn rgd evuton grde. For ths reson the pper puts forwrd nd of new method ombng prospet theory nd evdene theory to hoose the optmum sheme. The pper s orgnzed s foows. In seton n ndex system of deep foundton pt supportng sheme deson s frst estbshed on ths bss deson-mng mode ombng prospet theory nd evdene theory s presented. The fesbty of the method s vdted n seton wth se of subwy deep exvton. Fny onusons nd possbe future reserh re presented n seton. II. MATRIALS AND MTHODOLOGY A. An ndex system of deep foundton pt supportng sheme deson The estbshment of n ndex system s the premse of optmum seeng deson for brng shemes of deep foundton pt. Aordng to the hrtersts of the deep exvton supportng engneerng nd so tng nto ount the expettons of the proet owners n ndex system omposed of trget yer ftors yer nd ndex yer s estbshed by ppyng the onept of nyt herrhy proess s shown n tbe. TABL trget yer the ndex of deep foundton pt supportng sheme INDX SYSTM OF DP FOUNDATION PIT SUPPORTING SCHM DCISION ftors yer sfety ndexes eonom ndexes onstruton ndexes envronment ndexes ndex yer the whoe stbty sfety ftor the possbty of seondry dssters the onstruton perod the proet Cost the bty to dpt to the deformton the onstruton degree of dffuty the mutu nterferene degree the nfuene degree on the envronment the rebty of envronment proteton mesures B. The mode of deep foundton pt supportng sheme deson From the tbe we n see tht there re some quntttve ndexes whh n be expressed by ext or nterv number suh s the proet ost nd the onstruton perod. Other ones suh s the onstruton degree of dffuty the rebty of envronment proteton mesures re quttve. We n ony desrbe them by semnt nguge. Therefore the deep foundton pt supportng sheme deson s mut-ttrbute group deson-mng. In order to desrbe nd synthesze the dfferent types of unertnty ndex vue the nt vue of the ndex hs to be mxed nto unfed form of nterv number s foows. It s supposed tht ndex vue x represents the evuton vue of the deson ndtors sheme represents the owners expeted vue of the deson ndtor. Wthout oss of generty me x 0 0 nd... m where m s the tot number of the shemes... n where n s the tot number of the deson ndtors then: ) If x nd re both the ext number me x x x nd thus x nd w be trnsformed nto nterv number respetvey [ x x ] nd [ ] ) If x nd re both the nterv number the trnsformed nterv number re themseves respetvey x x 0 nd 0 ) If x nd re both ngust vrbes nd the vues of whh te vues n predefned set of ngust vrbes S. Where S { S f 0...( T /) T /( T /)... T} f S f represents the semnt nguge f. Beuse of T s even number there re T eements n S. For exmpe when T S { S0 S S S S S S} orrespondng to the seven sttes n turn: the owest ower ow medum hgh hgher nd the hghest. Moreover S hs the hrterst of orderng nmey: f f g then S f S g whh mens S f superor to S g. Then we n onverted x nd nto the form of nterv number fx f x respetvey [ x x ] [ ] nd T T f f [ ] [ ]. Where f x T T nd f re ser numbers of x nd n set of ngust vrbes S. Furthermore n mut-ttrbute group deson-mng the ndex ttrbute n be dvded nto two types: benefttype nd ost-type represented by CB nd CC respetvey. To the beneft-type ndex the hgher ttrbute vue the better ndex. On the ontrry to the ost-type ndex the ower ttrbute vue the better ndex. Therefore n order to emnte the nfuene of dfferent phys dmensons on the resut of desons x nd w be further stndrdzed fter onverson. U U Me P mx{mx{ x } } nd L L P mn{mn{ x } } the stndrdzed formus re s foows: DOI 0.0/IJSSST...B.. ISSN: -0x onne -0 prnt

3 U L P x P x C C P P P P [ x x ] () L U x P x P C B P P P P U L P P C C P P P P [ ] L U P P C B P P P P () Then the deson mtrx X [ x ] mn nd the vetor desred { n} n be reeved through stndrdzton proess. Aordng to the prospet theory the deson mer w mesure the proft or oss of eh sheme bsed on the referene pont frsty. Then through omprng the evuton ndex vue x wth the orrespondng desred ndex vue the dstne between ndex vues nd referene ponts n be uted. On ths bss the prospeted deson mtrx V [ V( x )] mn w be reeved. A of these proesses re represented by the foowng formus: Me: S( x ) ( x x )/ () S ( ) ( )/ () K( x ) x x () K( ) () Aordng to the reserh of Ishbuh (0) when Sx ( ) S ( ) nd ony f Sx ( ) S ( ) then x Conversey f S( x ) S( ) then x. When S( x ) S( ) nd ony f K( x ) K( ) then x If K( x ) K( ) then x If K( x ) K( ) then x. Then the dstne between the evuton ndex vue x nd the orrespondng desred ndex vue n be Cuted s: L L U U D [( x ) ( x ) ] / () The proft or oss vue F( x ) s determned by the sze of the retonshp between x nd : D x F( x ) () D x m n Where s x F( x ) s the proft of x retve to On the ontrry s x F( x ) mens the oss of x retve to. Gven the ft tht the rs tttude of the deson mers s often dfferent when fed wth proft or oss the prospeted deson mtrx V [ V( x )] mn s estbshed. Of whh V( x ) represents the prospeted ndex vue of the sheme on ndtor the formu s s foow: ( F( x )) x V( x ) () ( F( x )) x m n In the bove formuton the prmeter nd represent the onvex or onve degree of the prospeted ndex vue V( x ). Nmey when fed wth proft t s onve funton nd whh represents the rs verson of the deson mer onversey when fed wth oss t s onvex funton nd represents the rs ppette orrespondngy. The prmeter represents the degree of the oss verson usuy nd the hgher represents the greter degree of rs verson. Addtony the vue of nd re both greter thn zero but ess thn one. Aordng to the reserh of Brnbum (00) nd He Xuedong (0) the most deson mers behvor preferenes n be refeted s 0. nd.. So we w dopt the reommended vue n the subsequent exmpe n seton. In the prospeted deson mtrx the prospeted vue V( x ) refets the effetveness of deson-mer s perepton wth the sheme on ndtor : Tht s V( x ) 0 mens the proft whe V( x ) 0 mens oss. Obvousy we n see tht the hgher V( x ) the greter probbty of the sheme on ndtor w be hosen. Therefore f regrdng the probbty dstrbuton vue of sheme on ndtor s pee of evdene the beef nd pusbty nterv of eh sheme under the omprehensve ndex system n be reeved by evdene ombnton. As the beef nd pusbty nterv refets the redbty of sheme to be the best senro so ordng to the beef nd pusbty nterv the optmum sheme w be obtned. As the thnng goes we tret the supportng sheme sets s frmewor for dentfton nd gve the foowng defnton: Defnton []: the set funton m : [0] ( s the power set of ) f m( ) 0 nd ma ( ) then m A s ed the bs probbty dstrbuton n frme wor for dentfton. A s ed fo eement nd A ma ( ) s the probbty dstrbuton vue of A. Aordng to the bove defnton we need frsty to stndrdze the prospeted deson mtrx. Gven the mnmum prospeted vue w be onverted to zero usng the mn-mx stndrdzed method thus the mnmum prospeted vue nnot be dstngushed effetvey from the nu vue. So the ogrthms Logst method s used n ths pper for stndrdzng the prospeted deson mtrx: DOI 0.0/IJSSST...B.. ISSN: -0x onne -0 prnt

4 V ( x ) m n V( x ) e (0) Where V [ V ( x )] m n denotes the prospeted deson mtrx fter stndrdzed. Defnton []: If s nd r s r nd so V ( x ) V ( x ) s stsfed of whh... n then s r s nd r re beong to the sme fo eement. It foows from the bove defnton tht the fo eement onsttuted n eh deson ndex n be expressed s A (... n... t t m ). Now set weght for eh deson ndex m ( A ) where the stsfes 0 nd n the bs probbty dstrbuton vue of the fo eement of eh deson ndex s s foows: m( A ) ( A ) () ( A ) V ( x ) V ( x ) () Beuse of the ompexty of the obetve thngs nd the mttons of wreness the sum of the bs probbty dstrbuton vue of fo eement n deson ndex s often ess thn one tht s m ( A ) whh ustrtes tht there exsts degree of unertnty wth over understndng. In order to redue unertnty n deson mng the bs probbty dstrbuton vue of the unertnty wth over understndng s ssgned to the dentfton frmewor n ths pper. From dong ths we n me mxmum use of the exstng nformton. Aordng to the evdene theory f there exsts stuton of mm... mn then we n ombne mutpe probbty dstrbuton vues m ( A ) nto one probbty dstrbuton vue ma ( ) by evdene ombnton the formu s tht: m( A ) n A... A A n A... n A A A ma ( ) ( mm... mn)( A) A K 0 A Of whh () K m ( A ) ndtng the n A... A A n A... n A A degree of mpt between the vrous evdene nd the rger K the greter the degree of mpt. Defnton []: If s frmewor for dentfton A s subset of wrtten s A. Gven tht Be( A) m( B) nd P( A) m( B) re both B A AB stsfed then Be( A ) s ed the beef funton of A ndtng the eve of beef n the se tht A s true P( A ) s ed the pusbty eve of A ndtng degree of dose not deny A. Aordng to the bove defnton we n determne the beef eve Be( ) nd the pusbty eve P( ) of eh nddte sheme (... m): Be( ) m( A ) () A P( ) m( A ) () A The onfdene nterv of the nddte sheme s mde up of Be( ) nd P( ) s: [ Be( ) P( )]. The onfdene nterv ndtes the beef eve of n terntve to be the optmum sheme [-0]. Therefore we n hoose the best supportng sheme by omprng the onfdene nterv. The method s shown beow: If nd s stsfed menwhe the onfdene nterv of nd re respetvey [ Be( ) P( )] nd [ Be( ) P( )] then the probbty of the ft tht s superor to s mx[0 P({ }) Be({ })] mx[0 Be({ }) P({ })] P ( ) [ P({ }) Be({ })] [ P({ }) Be({ })] where P ( ) [0] the rnng rue re s foows: ) If P ( ) 0. then sheme s superor to wrtten s ) If P ( ) 0. then sheme s nferor to wrtten s ) If P ( ) 0. then sheme s s the sme s wrtten s ) Tng ny three of the shemes q ( q... m )f P ( ) 0. nd P ( q) 0. then sheme s superor to q wrtten s q. Aordng to the bove rue we n eventuy rn the supportng shemes (... m). III. CAS STUDY A. The proet profe The frst phse of Chngsh Metro Lne three s twostory underground snd ptform stton. The over dmenson of ths stton s 0. m 0. m. The re of the stton s. squre meters. A method of open exvton s dopted n ths stton nd the exvton depth s.~0. m. Aordng to the reevnt provsons of Code for geotehn engneerng nvestgton of urbn rwy trnst both the eve of mportne nd the sfety ss of ths foundton pt engneerng re frst-ss. In order to ensure the onstruton sfety there re four tenttve supportng sheme optons vbe: 000@00drng o-ont pe + renfored onrete support + three stee ppe 0 support ( ) DOI 0.0/IJSSST...B.. ISSN: -0x onne -0 prnt

5 dred groutng pes + four pre-stressed nhor be support( ) 000@00 dred groutng pes + renfored onrete support + three stee ppe 0 support( ) 00 mm th dphrgm w + renfored onrete support + three stee ppe 0 support( ). B. Proet deson- mng The bove four shemes re frsty evuted ordng to the ndex system of deep foundton pt supportng sheme deson. The evuton resuts re shown n tbe. TABL VALUATING VALUS OF TH DCISION INDX OF FOUR SUPPORTING SCHMS Support sheme deson ndtors * ower [..] [000] hgh ower ow ow hgh. * [.0.] [00] hgher medum owest ower hgh. ower [..] [00] hgher ow ower ower hgher. ow [.0.] [000] hgh ower ow medum * Note: * denotes the nu vue the unt of ndtor s ten thousnd yun per meter unt of s dy By the degree to whh the proet owner tes eh ndex serousy the weght for eh deson ndex nd the expetton vetor of ndex re gven respetvey s: W={ } nd ={. ower [.0.0] [0 0] hgher ower ower ower hgher}. Then usng formu () nd () to stndrdze the nt vue nd the expetton vue of the ndex. After tht the deson mtrx n be estbshed s tbe. TABL TH STANDARDIZD DCISION MATRIX x * [00.] [0.0.] [0.0.] [0.] [0.0.] [0.0.] [0.] [0.] [0.0.] * [0.] [0.] [00.] [00.] [0.] [0.0.] [0.] [00] [00.] [0.0.] [00.] [00.] [0.] [00.] [0.0.] [00.] [] [0.] [00.] [0.0.] [0.] [0.0.] [0.0.] [00.] * The stndrdzed expeted vetor {[0.0.] [00.] [0.] [0.] [00.] [0.0.] [00.] [0.0.] [0.]}. The prospeted deson mtrx re onstruted by formu () ~ () nd shown n tbe. TABL PROSPCTD DCISION MATRIX V( x ) * * * Aordng to defnton the sme prospeted vues n ndex re merged nto one fo eement. And then the bs probbty dstrbuton vue of the fo eement re uted by usng formu (0) ~ (). The uted resut s shown n tbe. TABL TH FOCAL LMNT AND TH BASIC PROBABILITY DISTRIBUTION VALU OF ACH INDX ndex the fo eement nd the bs probbty dstrbuton vue m ({ }) =0.0 m ({ }) =0.0 m ({ }) =0.0 m ({ }) =0. m ({ }) =0.0 m ({ }) =0.0 m ({ }) =0. m ({ }) =0.0 m ({ }) =0.0 m ({ }) =0.0 m ({ }) =0.0 m ({ }) =0. DOI 0.0/IJSSST...B.. ISSN: -0x onne -0 prnt

6 ({ }) m ({ }) =0.0 m ({ }) =0.0 m ({ }) =0.0 m ({ }) =0. m ({ }) =0.0 m ({ }) =0.0 m ({ }) =0. m ({ }) =0.0 m ({ }) =0.00 m ({ }) =0.0 m ({ }) =0. m ({ }) =0.0 m ({ }) =0.0 m ({ }) =0.00 m ({ }) =0. m =0.0 m ({ }) =0.0 m ({ }) =0.0 m ({ }) =0. m ({ }) =0.0 m ({ }) =0.0 m ({ }) =0. Fny by the formus () ~ () the onfdene ntervs of the four shemes re uted respetvey s: [0.0 0.] [0.0 0.] [0. 0.] [0. 0.]. Aordng to the rnng rue: sheme w be hosen s the optm supportng sheme. C. The mpt of the nompete nformton on the sheme deson In order to further nyze the nfuenes of nompete nformton on the sheme deson n ndex vue hosen rbtrry from the tbe s hnged nto nu vue. Subsequenty we w nyze the vrton of the onfdene nterv used by the hnge nformton. Due to mted spe ths pper ony nyzes the ndex bout the bty to dptve deformton of the sheme nmey the ndex x. Assumng x s pee of unnown nformton to the deson mer other thngs equ we re be to reute the onfdene nterv of eh sheme by usng the method proposed the resuts re respetvey: sheme [0.00.] sheme [0.0.] sheme [0.0.] sheme [0.0.]. Aordng to the rnng rue the rnng of the terntves n be rrved s:. It s not hrd to see tht the onfdene of sheme nd re redued exept sheme. Addtony the resut so presents ft tht the desent of onfdene n sheme s the bggest. Whh n be nterpreted s tht the onsttuton of the fo eement nd the probbty dstrbuton vue of ndtor re re-dstrbuted s m ({ }) =0.0 m ({ }) =0.0 nd m ({ }) =0. when the ndex vue x hngng from nown nformton to unnown. Obvousy sheme beme seprte fo eement to prtpte n bs probbty dstrbuton fter nformton hnge whh eds the probbty dstrbuton vue of sheme nresng from 0.0 to 0.0. Tht s mor reson why the onfdene of sheme nresed. Beuse of m ({ }) s redued from 0. to 0. the deresng degree s greter thn the nresng degree of m ({ }) nd the sheme s no onger prtpte n the probbty dstrbuton fter nformton hnge. So the onfdene of nd dereses nd moreover the desent of onfdene n sheme s the bggest. Fny from the bsoute vue of the hnge n onfdene ntervs the vue of sheme s so the bggest whh ndtes tht there mybe ertn degree of nfuene on the onfdene of shemes s the ndex evuton nformton of ny one sheme hnged but the sheme tsef w be nfuened the most serous. IV. CONCLUSION The exeuton of bred exvton often ndues ground movement whh my potenty dmge budngs dent to the exvton. Therefore t s vt to optmze the souton for bred exvton n the deformton onstrned envronment. However beuse of the mted nformton espey the nu vue nformton t s most mpossbe to me deson usng the onventon methods. In ths regrd nd of new method ombng prospet theory nd evdene theory ws put forwrd n ths pper. Une the onventon methods the new method hoose the owners desred gos of the proet s the referene ponts nd onstruted the prospet desonmng mtrx. After tht wth the prospet vue of eh sheme s evdene the beef nd pusbty nterv of eh sheme ws reeved by evdene ombnton. By sortng the beef nd pusbty nterv the best sheme n be seeted. Through the ppton of the method n metro foundton pt some onusons n be rrved s foow: () The prospet theory wh onsderng the owners desred gos of the proet used n deson-mng of supportng shemes for deep foundton pts s onsstent wth the tu exvton stuton. Compre wth the prevous sheme t s more resonbe to hoose the owners desred gos of the proet s the referene ponts. Furthermore the ppton exmpe ndtes tht t s fesbe to ombng prospet theory nd evdene theory n seetng the best supportng sheme. () The hnges of the ndex evuton nformton brng redstrbuton of the fo eement nd the probbty dstrbuton whh hve n effet upon the deson-mng of supportng shemes for deep foundton pts. A the onfdene nterv of the nddte shemes w be nfuened to ertn extent fter n evuton vue hnges from nown to unnown. However the onfdene nterv of the ndex vue tsef w be nfuened the most serous. Therefore redue the number of unnown nformton through vrous oetng s n mportnt wy to mprove the onfdene of the sheme. In despte of the method presented n ths pper n be used n mng deson for bred exvton n the deformton onstrned envronment when there s mted DOI 0.0/IJSSST...B.. ISSN: -0x onne -0 prnt

7 nformton espey nu vue nformton. The omputton od of the method s hgh however whh my hnder the ppton of the proposed method n prt engneerng. So omputer progrm omped ordng to the proedure s mpertve whh w be regrded s the foow-up reserh n the future. ACKNOWLDGMNTS The uthor wsh to thn Ms. Lhu of the th engneerng bureu of Chn rwy onstruton for her ontrbuton to the metro onstruton dt. The ssstne provded by Dr. H. M. L of X n Unversty of Arhteture nd Tehnoogy s so nowedged. The resuts nd opnons expressed n ths pper re those of the wrter nd do not neessry represent the vew of the ndvdus nowedged heren. RFRNCS [] Brnbum M H. Three new tests of ndependene tht dfferentte modes of rsy deson mng. Mngement Sene vo. no. pp [] C. Y. Lng. Q. Zhng X. W. Q. A method of mut-ttrbute group deson mng wth nompete hybrd ssessment nformton. Chnese Journ of Mngement Sene vo. no. pp [] Fortes I Mores R. Indutve ernng modes wth mssng vues. Mthemt nd Computer Modeng vo. no. pp [] H. Q. Zhng Q. C. Deep foundton pt supportng sheme bsed on ANP. Journ of Henn Unversty (Ntur Sene) vo. no. pp [] H. Zhou P. Co. A fuzzy AHP pproh to seet supportng shemes for ty foundton pt n soft so. Journ of Centr South Unversty (Sene nd Tehnoogy) vo. no. pp [] Ishbuh H Tn H. Mut-obetve progrmmng n optmzton of the nterv obetve funton. uropen Journ of Operton Reserh vo. no. pp [] J. J. Zhu H. Y Hu S. F. Lu. An pproh to deson-mng wth unertn nformton bsed on DS theory. Opertons Reserh nd Mngement Sene vo. no. pp [] Kryszewz M. Rues n nompete nformton systems. Informton Senes vo. no. pp. -. [] L. X. L Y. G. Feng. A omprehensve evuton method of nterv supportng shemes for foundton pt bsed on onneton number of set pr nyss nd ts ppton. Mthemts n Prte nd Theory vo. no. pp [0] Q. G. Feng C. B. Zhou Z. F. Fu. Grey fuzzy vrbe desonmng mode of supportng shemes for foundton pt. Ro nd So Mehns vo. no. pp [] S. Yo Y. J. Guo W. Q. Hung. An pproh of mut-ttrbute group deson mng wth nompete ngust ssessment nformton. Journ of Systems ngneerng vo. no. pp [] S. Y. Zheng S. Q. L. Improved TOPSIS deson method for Optmzng mxed ndexes supportng shemes for foundton pt. Chn Sfety Sene Journ vo. no. pp [] W. G. Co Y. J. Zhng M. H. Zho. Study on nterv retve fuzzy optmzton method to determne support shemes for foundton pts. Chnese Journ of Geotehn ngneerng vo. 0 no. pp [] W. H. Go Z. M. Zhng J. Q. Zhu. Optmzton of supportng pn of deep exvton bsed on fuzzy b propgton neur networ. Chn Sfety Sene Journ vo. no. pp [] X. D. He X. Y. Zhou. Portfoo hoe under umutve prospet theory: An nyt tretment. Mngement Sene vo. no. pp [] X. Tn W. Wng M. J. Zhng. Behvor deson method of CGF wth nompete nformton bsed on evdene theory. Systems ngneerng-theory & Prte vo. no. pp [] X. W. Lo P.Y. Lv. Mut-ttrbute deson-mng nyss on seetng retnng sheme of deep foundton pt. Chnese Journ of Ro Mehns nd ngneerng vo. no. pp [] X. Y. Chen M. S. Gong Y. W. Jng. Seeton of operton shemes wth nompete nformton bsed on D-S evdene theory. Journ of Northestern Unversty (Ntur Sene) vo. no. pp [] Y. Lo Y. X. Wng Z. M. Hu. Mut-eve fuzzy synthess evuton of foundton pt support sheme bsed on mproved nyt herrhy proess. Chnese Journ of Underground Spe nd ngneerng vo. no. pp [0] Z. R. Jn J. S. He. Optmzton of supportng pn for deep foundton pt bsed on dstne dsrmnnt nyss method. Ro nd So Mehns vo. 0 no. pp DOI 0.0/IJSSST...B.. ISSN: -0x onne -0 prnt