An Indian Journal FULL PAPER ABSTRACT KEYWORDS. Trade Science Inc. The tennis serve technology based on the AHP evaluation of consistency check

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1 [Type text] [Type text] [Type text] ISSN : Volume 0 Issue 0 BioTechnology 0 An Indin Journl FULL PAPER BTAIJ, 0(0), 0 [-7] The tennis serve technology bsed on the AHP evlution of consistency check Mio Zhng Deprtment of Physicl Eduction, Dongbei University of Finnce nd Economics, Dlin 0, Lioning, (CHINA) ABSTRACT Tennis thlete's technology, this pper crries on the nlysis to extrct the comprehensive evlution of tennis thletes technology under the two big index nd the corresponding index of mesures of smll, use AHP (nlytic hierrchy process) set up clss hierrchy, nd imed t the structure judgment mtrix is constructed by pplying the method of pired compred, on the bsis of the overll consistency check model is introduced. In the use of AHP method in this pper, the sports bility of thletes t the sme time, the design of the weight of the judgment mtrix lgorithm nd the lgorithm of overll consistency check, implement the ctul prmeters of four excellent tennis thletes in the world the AHP nlysis obtined four plyers serve technology dvntges nd disdvntges, nd through the consistency check. KEYWORDS Tennis service technique; Judgment mtrix; Consistency test; AHP lgorithm. Trde Science Inc.

2 The tennis serve technology bsed on the Ahp evlution of consistency check BTAIJ, 0(0) 0 INTRODUCTION Since Li N won the Austrlin Open, Chinese tennis hs further rnked mong the top ntions in world sports. Tennis plyers sports bility is kind of sports tht comprehensive reflected by ge, sports flexibility, plying techniques, psychologicl qulities [-]. Now tennis plyers technicl evlution is indispensible in sports trining, nd evlution wys 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 which 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 when plying the gmes [-]. Lin Chu-Hui nd others estblished fuzzy mthemtics evlution model to mke quntittive evlution on tennis techniques ech indictor, which provided fesible mthemtics methods for plyers selection. Zhou Jie in mster thesis, he used world excellent men s tennis plyers technicl sttistics to mke nlysis, he thought the key to win in the field for tennis plyers is incresing winners nd reduce unforced errors []. The pper nlyzes tennis service techniques reltive sttisticl dt, estblishes reltive indictors construction hierrchicl structure, by clculting ech indictor weight, 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 well s hierrchicl structure, it further mkes pired comprison with every primry nd secondry fctors nd clculte their weights, 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 wekens subjective rndomness, increses subjective evlution rtionlity nd ccurcy. In the following, it sttes AHP nlysis steps, sports bility hierrchicl structure estblishment, sports bility judgment mtrix estblishment nd lgorithm designing s well 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

3 BTAIJ, 0(0) 0 Mio Zhng In Figure, it represents decompose overll system into serious of smll prts, s the pper tennis service technicl bility; Step- represents weight 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 wek. 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, which 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, which divides into two lyers tht re respectively two min indictors Clyer nd its corresponding sub section content C lyer, bottom lyer is mesure lyer tht clls P lyer for short, which re four plyers. As Figure, it shows the hierrchicl structurl grph. Figure : Hierrchicl structure grph Evlution model estblishment nd lgorithm design Definition : The first lyer nd second lyer weight expression is s formul () show: w + w = () In formul (), w represents ttck technique to tennis techniques contribution weight, w represents defense technique to tennis techniques contribution weight. Definition : The second lyer nd the third lyer weight expression re s formul () show: w + w + w + w + w w + w + w + w = = ()

4 The tennis serve technology bsed on the Ahp evlution of consistency check BTAIJ, 0(0) 0 w In formul(),, w, w, w, w 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 weight; w, w, w, w Respectively represents second service scoring rte, second service verge speed per hour, receiving scoring rte nd breking rte to defense technique contribution weight. Judgment mtrix estblishment nd ech lyer weight generting lgorithm design If compre n pieces of fctors to one fctor F influence size, generlly dopt pired fctor ij comprison method to estblish judgment mtrix. Set represents fctor β β i nd j to fctor F influence size rtio, it cn get judgment mtrix R, in the pper, we 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 () showed judgment mtrix R : F R = () In formul(), F represents fctor sports bility,,,, represent body shpe fctor, body ij function fctor, psychologicl qulity fctor nd sport qulity fctor, represents fctor i nd fctor j to fctor F influence size. ij size defining, we generlly dopt ~9 proportionl scle to impct weight, s Figure show. ij Definition TABLE : ~9 scle tble Scle 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 If compre fctor i with fctor j, it gets judgment vlue s Reciprocl 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 i j jk = ik construction process, it will not let seriously to be true, so when clculte weight vector under single criterion, it should lso mke consistency test. Tke mtrix R s n exmple to do lgorithm design, s following show:

5 BTAIJ, 0(0) 0 Mio Zhng r Step-: It solves vector = (,,, ) w = nd vector ( w, w, w, w ); Step-: It solves mtrix R mximum feture vlue λmx, its computtionl method is s formul()show: r λ mx r r = w = ( ) w w w w () Step-: Clculte consistency indictor CI, its computtionl method is s formul ()show: λmx n λ CI = = n mx () In formul(), n represents number of criterion, which is lso the number of fctors, so to R mtrix n = Step-: Clculte consistency rtio CR, its computtionl method is s formul()show: CI CR = RI () In formul(), RI represents Rndom Consistency Index vlue, s TABLE show. TABLE : Consistency test n RI mx CR = λ So formul () cn be revised into 0. 9 Step-: Consistency judgment When CR > 0., judgment result outputs present obvious inconsistence, whencr < 0., judgment result outputs present considerble consistence. COMPREHENSIVE EVALUATION ESTABLISHMENT y = w x i i By bove ech indictor weight clcultion, it cn get evlution model: i= w Among them, i, xi, respectively represent second indictor weight nd second grde indictor. TENNIS TECHNICAL EVALUATION APPLICATION EXAMPLE Judgment mtrix nd consistency test According to experts reserch nd interview, experts nd professors dt, it mkes pired comprison on indictors with ~9 grdes scle method, it gets indictor judgment mtrix s following tble. n

6 The tennis serve technology bsed on the Ahp evlution of consistency check BTAIJ, 0(0) 0 / / R= / /7 / / /8 / / / /7 /8 / / /9 / / / / / / /7 7 / / 7 8 / / / / / /7 / / / / / / λ mx =.0, CI = It cn get by MAtlb computing: Mke consistency test on judgment mtrix, it gets: CR = CI / RI = 0.09/ 0. = 0.0 < 0. 0 It psses consistency test tht shows objective weight judgment cn be done. Weight clcultion nd list wi = ij / n j= Ech indictor weight clcultion cn ccord formul: By clculting, it gets ech indictor weight s following TABLE show. TABLE : Weight tble First grde indictor Weight Second grde indictor Weight Attck technique 0. Defense technique 0.7 n First service success rte 0.98 First service scoring rte 0. First service evlution speed per hour Highest speed per hour 0.0 Net success rte 0.07 Second service scoring rte 0.0 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 following TABLE show: TABLE : Indictor dt tble Indictor Djokovic Federer Murry Ndl First service success rte First service scoring rte First service evlution speed per hour Highest speed per hour Net success rte Second service scoring rte Second service verge speed per hour Receiving scoring rte Breking rte

7 BTAIJ, 0(0) 0 Mio Zhng 7 Evlution result Input four tennis plyers indictor dt into nlytic hierrchy process evlution model, clculte scores s following TABLE : TABLE : Comprehensive evlution result tble Nme Djokovic Federer Murry Ndl Score The pper uses simple nlytic hierrchy process comprehensive evlution model to evlute four world excellent tennis plyers, nd then gets the four rnking re successively s: Federer, Ndl, Djokovic nd Murry. 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 weight problems tht provide esy nd fesible methods for tennis tlents selection. Menwhile, 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. Menwhile, different plyers hs different bilities in tennis techniques ech indictor, compres with indictor weights, it cn provide certin evidence for tennis plyers trining, such s, it should put emphsis on trining tennis plyers lrger weights techniques so tht rpidly improve tennis. REFERENCES [] Alirez Fdei Tehrni, Ali Mohmmd Doosthosseini, Hmid Rez Mobllegh, Peimn Amini, Mohmmd Mehdi DneshPnh; RoboCup, 00-0 (00). [] R.E.Klmn; Trnsction of the ASME - Journl of Bsic Engineering, 8, - (90). [] Crlos F.Mrques, Pedro U.Lim; RoboCup, 9-07 (000). [] S.Thrun, D.Fox, W.Burgrd, nd F.Dellert; Artificil Intelligence Journl, 8, 99- (00). [] Kn Li-ping; Bulletin of Sport Science & Technology, 9(), 9-0 (0). [] Zheng Wei; Sport Science nd Technology,, -, (000). [7] Yng Jilin et l.; Journl of Shndong Physicl Eduction Institute, 8(), - (00). [8] Wng Xin; Journl of Nnjing Institute of Physicl Eduction, (), 9-97 (00). [9] Zhng Ji, xing; Journl of Hubei Sports Science, (), 7-7, 79 (00). [0] Li Ning, Zhou Jindong; Journl of Jilin Institute of Physicl Eduction, 7(), -7 (0). [] B.Zhng; S.Zhng; G.Lu; Journl of Chemicl nd Phrmceuticl Reserch, (9), - (0). [] B.Zhng; Interntionl Journl of Applied Mthemtics nd Sttistics, (), -0 (0). [] B.Zhng; H.Yue; Interntionl Journl of Applied Mthemtics nd Sttistics, 0(0), 9-7 (0). [] B.Zhng; Y.Feng; Interntionl Journl of Applied Mthemtics nd Sttistics, 0(0), - (0). [] Bing Zhng; Journl of Chemicl nd Phrmceuticl Reserch, (), 9-9 (0).