Avilble online.jocpr.com Journl of Chemicl nd Phrmceuticl Reserch, 0, ():7-79 Reserch Article ISSN : 097-78 CODEN(USA) : JCPRC AHP-bsed tennis service technicl evlution consistency test Mio Zhng Deprtment of Physicl Eduction, Dongbei University of Finnce nd Economics, Dlin, Lioning, Chin ABSTRACT The pper nlyzes tennis plyers techniques, it extrcts comprehensive evlution plyers tennis techniques to min indictors nd their corresponding indictors eleven smll indictors, pplies AHP to estblish hierrchicl structure, nd for the structure, it pplies pired comprison method to construct judgment mtrix, on this bsis it introduces overll consistency test model. Apply AHP method to stte thlete sports bility, menhile it designs judgment mtrix eight lgorithm nd overll consistency test lgorithm, relizes four orld excellent tennis plyers ctul prmeters AHP nlysis nd gets the four plyers service techniques merits nd psses consistency test. Key ords: Tennis service technique, judgment mtrix, consistency test, AHP lgorithm INTRODUCTION Since Li N on the Austrlin Open, Chinese tennis hs further rnked mong the top ntions in orld sports. Tennis plyers sports bility is kind of sports tht comprehensive reflected by ge, sports flexibility, plying techniques, psychologicl qulities [-]. No tennis plyers technicl evlution is indispensible in sports trining, nd evlution ys for ech kind of techniques lso pply more mthemticl theories, nd bndons subjective uncertinness. Service is crucil to tennis, good service cn mster tennis rhythm so tht let opponent to get cught in pssive situtions [-8]. In service technicl evlution reserch, thousnds of people hve mde lots of reserches, nd got some result, these evlution methods hve been pplied in prctice hich mkes considerble rel description on tennis techniques [9-]. Among them, Wu Qing (009) in reserching US Open Federer tennis techniques, he got tht ordinry times trining should focus on tennis plyers techniques, tctics, psychology nd others comprehensive development, nd should py more ttention to psychologicl qulities trining hen plying the gmes [-]. Lin Chu-Hui nd others estblished fuzzy mthemtics evlution model to mke quntittive evlution on tennis techniques ech indictor, hich provided fesible mthemtics methods for plyers selection. Zhou Jie in mster thesis, he used orld excellent men s tennis plyers technicl sttistics to mke nlysis, he thought the key to in in the field for tennis plyers is incresing inners nd reduce unforced errors []. The pper nlyzes tennis service techniques reltive sttisticl dt, estblishes reltive indictors construction hierrchicl structure, by clculting ech indictor eight, pplying nlytic hierrchy process mthemticl model to estblish tennis service technicl evlution model, it relizes service technicl quntittive evlution. TENNIS SERVICE TECHNICAL EVALUATION AHP MODEL ESTABLISHMENTS A complicted problem is composed of lots of brnch problems, AHP mkes methodize combing on complicted influence fctors, nd mkes cler bout these fctors primry nd secondry s ell s hierrchicl structure, it further mkes pired comprison ith every primry nd secondry fctors nd clculte their eights, finlly nlyzes nd gets ech prt priority. In ddition, AHP method cn dopt subjectivity to construct judgment mtrix nd use objective vlues to mke finl evlution mesuring. Objectively, it requires subjective evlution should conform to ctul test evlution consistency tht ekens subjective rndomness, increses subjective evlution 7
Mio Zhng J. Chem. Phrm. Res., 0, ():7-79 rtionlity nd ccurcy. In the folloing, it sttes AHP nlysis steps, sports bility hierrchicl structure estblishment, sports bility judgment mtrix estblishment nd lgorithm designing s ell s consistency test lgorithm designing principles nd methods. AHP nlysis steps Apply nlytic hierrchy process to solve problems need to estblish indictors logic reltions, AHP nlysis includes four steps, s Figure. Figure : AHP nlysis four steps In Figure, it represents decompose overll system into serious of smll prts, s the pper tennis service technicl bility; Step- represents eight ll smll prts fter system decomposing; Step- represents ech smll prts to thlete plyer sports bility totl contribution bility s evlution; Step- represents obtin judgment result ccording to different plyers ech smll prts to tennis techniques contribution bility strong nd ek. Sports bility hierrchicl structure estblishment When AHP method reserches on problems, it should divide problems into severl lyers ccording to the problems ech fctor cusl reltionship, hich is clled hierrchy. Reltive simple problems usully cn be divided into three lyers: trget lyer (tennis techniques), criterion lyer (ttck technique, defense technique) nd mesure lyer (four thletes). The pper reserched problems re reltive complex tht totlly divides into four lyers, top lyer is trget lyer nd clled O lyer for short tht is tennis technique; medium lyer is criterion lyer tht clls C lyer for short, hich divides into to lyers tht re respectively to min indictors Clyer nd its corresponding sub section content C lyer, bottom lyer is mesure lyer tht clls P lyer for short, hich re four plyers. As Figure, it shos the hierrchicl structurl grph. Figure : Hierrchicl structure grph Evlution model estblishment nd lgorithm design Definition : The first lyer nd second lyer eight expression is s formul () sho: 7
Mio Zhng J. Chem. Phrm. Res., 0, ():7-79 + In formul (), represents ttck technique to tennis techniques contribution eight, technique to tennis techniques contribution eight. () represents defense Definition : The second lyer nd the third lyer eight expression re s formul () sho: + + + + + + + (),,,, In formul(), respectively represent first service success rte, first service scoring rte, first service evlution speed per hour, highest speed per hour nd net success rte to ttck bility contribution,,, eight; Respectively represents second service scoring rte, second service verge speed per hour, receiving scoring rte nd breking rte to defense technique contribution eight. Judgment mtrix estblishment nd ech lyer eight generting lgorithm design If compre n pieces of fctors to one fctor F influence size, generlly dopt pired fctor comprison method ij β β to estblish judgment mtrix. Set represents fctor i nd j to fctor F influence size rtio, it cn get judgment mtrix R, in the pper, e set the second lyer nd the first lyer judgment mtrix to be R, element to be ij, fctors to be i, j, fctor to be F, nd then it hs s formul () shoed judgment mtrix R : F R,,, In formul(), F represents fctor sports bility, represent body shpe fctor, body function ij fctor, psychologicl qulity fctor nd sport qulity fctor, represents fctor i nd fctor j to fctor F influence size. ij size defining, e generlly dopt ~9 proportionl scle to impct eight, s Figure sho. Scle ij Tble : ~9 scle tble Definition fctor i nd fctor j hve equl importnce fctor i is slightly more importnt thn fctor j fctor i is reltive more importnt thn fctor j 7 fctor i is extremely more importnt thn fctor j 9 fctor i is bsolute more importnt thn fctor j,,, 8 Indictes middle stte corresponding scle vlue of bove judgments Reciprocl If compre fctor i ith fctor j, it gets judgment vlue s () ji / ij, ii At first, solve judgment mtrix, ccording to bove principle, reference -9 scle setting, nd ccording to experts experiences nd refer to lots of documents, it gets pired comprison mtrix. Consistency test lgorithm design Due to objective things complex nd people recognition diversity decision, in judgment mtrix construction process, it ill not let i j jk ik seriously to be true, so hen clculte eight vector under single criterion, it should 7
Mio Zhng J. Chem. Phrm. Res., 0, ():7-79 lso mke consistency test. Tke mtrix R r ( ) Step-: It solves vector,,, ( ) nd vector,,, s n exmple to do lgorithm design, s folloing sho: Step-: It solves mtrix R λ mximum feture vlue mx, its computtionl method is s formul()sho: r ; λ mx r r ( ) () Step-: Clculte consistency indictor CI, its computtionl method is s formul ()sho: λmx n λ CI n mx () In formul(), n represents number of criterion, hich is lso the number of fctors, so to R mtrix n Step-: Clculte consistency rtio CR, its computtionl method is s formul()sho: CI CR RI () In formul(), RI represents Rndom Consistency Index vlue, s Tble sho. mx CR λ So formul () cn be revised into 0. 9 Step-: Consistency judgment When outputs present considerble consistence. Tble : Consistency test n 7 8 9 0 RI 0 0 0.8 0.90......9. CR > 0., judgment result outputs present obvious inconsistence, hen CR < 0. COMPREHENSIVE EVALUATION ESTABLISHMENT By bove ech indictor eight clcultion, it cn get evlution model: y n i i x i, judgment result Among them,, x i i, respectively represent second indictor eight nd second grde indictor. TENNIS TECHNICAL EVALUATION APPLICATION EXAMPLE Judgment mtrix nd consistency test According to experts reserch nd intervie, experts nd professors dt, it mkes pired comprison on indictors ith ~9 grdes scle method, it gets indictor judgment mtrix s folloing tble. 77
Mio Zhng J. Chem. Phrm. Res., 0, ():7-79 / / R / /7 / / /8 / / / /7 /8 / / /9 / / / / / / /7 7 / / 7 8 / / / / / /7 / / / / / /8 8 9 7 8 It cn get by MAtlb computing: λ.0 mx, CI 0. 09 Mke consistency test on judgment mtrix, it gets: CR CI / RI 0.09/ 0. 0.0 < 0. 0 It psses consistency test tht shos objective eight judgment cn be done. Weight clcultion nd list Ech indictor eight clcultion cn ccord formul: i n j ij / n By clculting, it gets ech indictor eight s folloing Tble sho. Tble : Weight tble First grde indictor Weight Second grde indictor Weight First service success rte 0.98 First service scoring rte 0. Attck technique 0. First service evlution speed per hour 0.080 Highest speed per hour 0.0 Net success rte 0.07 Second service scoring rte 0.0 Defense technique 0.7 Second service verge speed per hour 0.9 Receiving scoring rte 0.70 Breking rte 0. Men s four min tennis competitions chmpions nd opponents fighting in 0, ech indictor reltive dt sttistics is s folloing Tble sho: Tble : Indictor dt tble Indictor Djokovic Federer Murry Ndl First service success rte 0.7.7 0.7.8 First service scoring rte 7.7 79. 7.7 77. First service evlution speed per hour 88.9 8.8 78. 8.9 Highest speed per hour 0. 0.7.8 0. Net success rte 70.8 7.7 70.9 7.7 Second service scoring rte 9. 9..7 Second service verge speed per hour 0.8 7.7.. Receiving scoring rte..8.8 0.9 Breking rte 7.7.8. Evlution result Input four tennis plyers indictor dt into nlytic hierrchy process evlution model, clculte scores s folloing Tble : Tble : Comprehensive evlution result tble Nme Djokovic Federer Murry Ndl Score 0.0 0. 00. 0.9 The pper uses simple nlytic hierrchy process comprehensive evlution model to evlute four orld excellent tennis plyers, nd then gets the four rnking re successively s: Federer, Ndl, Djokovic nd Murry. 78
Mio Zhng J. Chem. Phrm. Res., 0, ():7-79 CONCLUSION The pper pplies nlytic hierrchy process method into tennis technicl evlution, nd then it estblishes subjective evlution nd objective technicl indictors combtive mthemticl model, scientific nd resonble solves tennis techniques ech indictor eight problems tht provide esy nd fesible methods for tennis tlents selection. Menhile, it provides objective methods for objective nd resonble evluting tennis plyer technique, nd gets rid of single relying on scores to evlute plyers or referees provided subjective evlution. Menhile, different plyers hs different bilities in tennis techniques ech indictor, compres ith indictor eights, it cn provide certin evidence for tennis plyers trining, such s, it should put emphsis on trining tennis plyers lrger eights techniques so tht rpidly improve tennis. REFERENCES []Alirez Fdei Tehrni, Ali Mohmmd Doosthosseini, Hmid Rez Mobllegh, Peimn Amini, Mohmmd Mehdi DneshPnh. RoboCup, 00, 00-0. [] R.E.Klmn. Trnsction of the ASME - Journl of Bsic Engineering, 90, (8), -. [] Crlos F. Mrques, Pedro U. Lim. RoboCup, 000, 9-07. [] S.Thrun, D.Fox, W.Burgrd, nd F.Dellert. Artificil Intelligence Journl, 00, (8), 99-. [] KAN Li-ping. Bulletin of Sport Science & Technology, 0, 9(), 9-0. [] Zheng Wei. Sport Science nd Technology, 000, (), -,. [7] Yng Jilin et l. Journl of Shndong Physicl Eduction Institute, 00, 8(), -. [8] WANG Xin. Journl of Nnjing Institute of Physicl Eduction, 00, (), 9-97. [9] ZHANG Ji, xing. Journl of Hubei Sports Science, 00, (), 7-7, 79. [0] Li Ning, Zhou Jindong. Journl of Jilin Institute of Physicl Eduction, 0, 7(), -7 [] Zhng B.; Zhng S.; Lu G.. Journl of Chemicl nd Phrmceuticl Reserch, 0, (9), -. [] Zhng B.; Interntionl Journl of Applied Mthemtics nd Sttistics, 0, (), -0. [] Zhng B.; Yue H.. Interntionl Journl of Applied Mthemtics nd Sttistics, 0, 0(0), 9-7. [] Zhng B.; Feng Y.. Interntionl Journl of Applied Mthemtics nd Sttistics, 0, 0(0), -. [] Bing Zhng. Journl of Chemicl nd Phrmceuticl Reserch, 0, (), 9-9. 79