Consistency test of martial arts competition evaluation criteria based on mathematical ahp model

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1 ISSN : Volume 8 Issue 2 BoTechology BoTechology A Ida Joural Cosstecy test of martal arts competto evaluato crtera based o mathematcal ahp model Hu Wag Isttute of Physcal Educato, JagSu Normal Uversty, Xuzhou 226, Jagsu, (CHINA) E-mal: tyux@qq.com BTAIJ, 8(2), 203 [ ] ABSTRACT The gradg crtero of Martal art route competto s fe ad complex, the tme for the referee to judge the game s very short ad lmt, such as boxg etc. optoal route oly 90s, some competto tme of the games s eve less. Therefore, such cases, the referee should gve a more accurate grade accordg to the rules, ad the dffculty s very great. I order to strctly abde by the rules ad reach the smple, fast ad accurate goal, we must select some dcators ad varables that ca accurately reflect the comprehesve ablty of athletes. Ths paper attempts to troduce AHP mathematcal model; the evaluato crtera are dvded to two categores; t uses statstcal software tools SPSS to establsh judgmet matrx ad coduct cosstecy test; the results shows that: the judgmet matrx cosstecy test of walkthrough level, CR = <0.; the judgmet matrx cosstecy test of acto completo s CR = <0.. The above judgmet dcators all ca go through cosstecy test evaluato ad ca be appled the actual game. 203 Trade Scece Ic. - INDIA KEYWORDS AHP; Martal arts competto; Performace evaluato; Cosstecy testg. INTRODUCTION The evaluato crtera durg martal arts compettos s a mportat measure of value for experts ad coaches to make preparatos, s the bass for classfcato. Wthout ths measuremet ad bass, the evaluato actvtes caot be carred through. Ths paper uses AHP method, ad selects some dcators ad varables that ca accurately reflect the comprehesve ablty of athletes. The evaluato crtera are dvded to two categores: walkthrough level ad acto completo, where walkthrough level s dvded to skll level, acto choreography, ad exercse tps; acto completo s dvded to posture, style ad sprt three evaluato crtera. It costructs matrx ad coducts cosstecy test, the judges whether the above dcators ca become the judgmet crtera of the match. THE ESTABLISHMENT OF AHP MODEL AHP method s proposed by the Amerca operatoal research experts T. L. Saaty 970s. After years of developmet t has ow become a more mature approach. The basc prcple s: dvdg the varous elemets of the alteratves of the evaluato system to a umber of levels, ad takg the varous elemets of the

2 BTAIJ, 8(2) 203 Hu Wag 205 same level accordace wth upper layer elemet as a crtero, coducts par-wse comparso ad calculates the weght of each elemet, determe the optmal weghtg scheme accordg to comprehesve weght ad the maxmum weght prcple. It s deduced o the bass of smple addtve weghtg method. It reasoably combes qualtatve ad quattatve strateges, layerg ad quatfes the decso-makg process accordace wth thkg ad metal dscple. Sce the method was troduced to the coutry 982, wth the characterstcs of dsposg varous decso-makg processes combg ts qualtatve ad quattatve factors, as well as t s a smple ad flexble system, t has bee wdely used ad valued our socal ad ecoomc felds, such as eergy systems aalyss, urba plag, ecoomc maagemet, ad scetfc evaluato. Establsh a herarchcal structure model Ths paper takes the martal arts athletes performace evaluato as a target layer of herarchy aalyss, takes the walkthrough level ad acto completo as the termedate layer, takes the skll level, techque, acto choreography, posture, style, rhythm ad ovato capablty as the program layer of AHP, establshes the herarchcal model of performace aalyss for martal arts athletes, as show Fgure. Fgure : The structure of AHP model Costruct judgmet matrx ad seek the largest egevalues ad egevectors Sce herarchcal structure model determes the membershp fucto of the upper ad lower elemets, you ca costruct par-wse judgmet matrx of dfferet levels for the above layer crtera. If the par-wse judgmet matrx s ( aj), the a j > 0 ; aj,. j, 2,3, a j The specfc judgmet matrx costructo method of each level s: uder the target layer of martal arts competto comprehesve evaluato, depedg o the walkthrough level, acto completo ad other factors, coduct par-wse comparso o the mportace, the hgher the class level s, the hgher ts mportace becomes. The cossteces of par-wse comparsos: / 2 4 A 2 7 a2 ( C : C2 ) 2 a 4( C : C ) a 8( C : C ) Allow cosstet, but we eed to determe the allowable rage of cosstet. w w w w w2 w w2 w2 w2 A w w2 w w w w w w2 w Cosstet matrx propertes: () The rak of A s ; the oly o-zero egevalues of A s. (2) Ay colums vector of A s correspodg to the egevectors of. (3) The ormalzed egevector of A ca be used as weght vector. For the cosstet par-wse comparso matrx A, recommed takg the correspodg egevector of maxmum egevalue ë as the weght vector w, amely A. Comparso Scale: Saaty et al put forward BoTechology BoTechology A Ida Joural

3 206 Cosstecy test of martal arts competto evaluato crtera based BTAIJ, 8(2) 203 ~ 9 scale,.e. the value of a j s, 2,3 9 ad ts re- cprocal,,,, so as to facltate the coverso from qualtatve to quattatve. Proporto Scale TABLE : Relatve mportace scale BoTechology A Ida Joural Meag Represets the mportace of the two elemets are the same Represets a factor s slghtly mportat tha aother elemet Represets a factor s sgfcatly mportat tha aother elemet Represets a factor s hghly mportat tha aother elemet Represets a factor s extremely mportat tha aother elemet 2,4,6,8 The meda value of the above adjacet judgmet,,, 2 9 Is the recprocal of the above scale Psychologsts beleve that factors of par-wse comparsos should be o more tha e. Calculate the maxmum egevalues ad egevectors of judgmet matrx by geometrc mea approxmato method (root method) o. The calculato steps are: ()Calculate the product of matrx elemets each row: m aj,,2,3 () (2)Calculate the -th order root m (2) (3)Normalze the vector (, 2, ) T : j j j, 2,3 (3) The obtaed (, 2, ) T s the egevector approxmato, amely the weght of each factor. (4)Calculate the maxmum egevalue max of the matrx; Amog them, ( A ) s the -th elemet of the vector max ( A ) (4) A. Calculate the cosstecy dex of judgmet matrx ad test ts cosstecy I order to test the cosstecy of the matrx, defe TABLE 3 : The judgmet matrx cosstecy test of walkthrough level X X2 X3 X4 M O cubc W Aw AW/W CI=((ë-)/(-)) CR=CI/RI X2 /3 4 / X3 3 / X4 /4 / Maxmum egevalue =2.3 TABLE 4 : The judgmet matrx cosstecy test of acto completo Acto completo Posture Style Sprt Multpled by le O cubc W Aw AW/W CI=(ë-)/(-) CR=CI/RI Posture / Style Sprt /5 / TABLE 2 : Average radom cosstecy dex Order RI X: Walkthrough level; X: Skll level; X3: Acto choreography; X4: Exercse tps; M: Multpled by le Maxmum egevalue =2.06

4 BTAIJ, 8(2) 203 Hu Wag 207 CI = max. Whe t s fully cosstet, the we have CI 0. The larger s CI, the worse the cosstecy of the matrx s. For the~ 9 order matrx, the average radom cosstecy dex RI s show TABLE. Whe the order 2, the matrx has always complete cosstecy; whe the order> 2, CR RI s called radom cosstecy of the matrx. aci CI CR 0. Whe RI, the overall level sort re- a CI sults have a satsfactory cosstecy. As ca be see from the TABLE CR , that the three dcators walkthrough level, acto choreographed ad exercse tps have goe through cosstecy test. As ca be see from the TABLE CR , that the three dcators: posture, style ad sprt have goe through cosstecy test. CONCLUSIONS CI Ths paper troduces the AHP Comprehesve Evaluato dcators ad gves judgg mathematcal model of martal arts competto. Ths model just eeds geeral PC to ru ad operate, whch s coducve to computerzato. Evaluato crtera s dvded to walkthrough level ad acto completo two dcators, where walkthrough level s dvded to skll level, acto choreography, ad exercse tps; Acto completo s dvded to posture, style ad sprt three evaluato crtera; establsh judgmet matrx ad carry out cosstecy test through well-kow statstcal tools EXCLE, the results show: the judgmet matrx cosstecy test of walkthrough level,, dcates that three dcators skll level, acto choreography, ad exercse tps have goe through cosstecy test; the judgmet matrx cosstecy test of acto completo,, dcates that three dcators posture, style ad sprt have goe through cosstecy test. The above judgmet dcators all have passed the assessmet, ad ca be appled the actual game. REFERENCES [] Bg Zhag, Ya Feg; The Specal Qualty Evaluato of the Trple Jump ad the Dfferetal Equato Model of Log Jump Mechacs Based o Gray Correlato Aalyss. Iteratoal Joural of Appled Mathematcs ad Statstcs, 40(0), (203). [2] Bg Zhag; Dyamcs Mathematcal Model ad Predcto of Log Jump Athletes Olympcs. Iteratoal Joural of Appled Mathematcs ad Statstcs, 44(4), (203). [3] Ca Cu; Applcato of Mathematcal Model for Smulato of 00-Meter Race. Iteratoal Joural of Appled Mathematcs ad Statstcs, 42(2), (203). [4] Hab Wag, Shuye Yag; A Aalyss of Hurdle Performace Predcto Based O Mechacal Aalyss ad Gray Predcto Model. Iteratoal Joural of Appled Mathematcs ad Statstcs, 39(9), (203). [5] Hogwe Yag; Evaluato Model of Physcal Ftess of Youg Tes Athletes Based O AHP- TOPSIS Comprehesve Evaluato. Iteratoal Joural of Appled Mathematcs ad Statstcs, 39(9), (203). [6] L Bg, The equvalece aalyss of shp rudder based o aalytc herarchy process. Chese Joural of Scetfc Istrumet, 34(2), (203). [7] L We-guo; Research o qualtatve method of power trasformato codto assessmet usg aalytc herarchy process. Joural of Hua Uversty (Natural Sceces), 0, (20). [8] Luo Zheg-qg, Comparatve study o several scales AHP. Systems Egeerg-theory & Practce, 24(9), 5-56 (2004). [9] She Ju-y; A research o the comprehesve evaluato of physcal educato teachg ad sports trag wth fuzzy theory. Cha Sport Scece Ad Techology,36, (2000). [0] Wag Xao-ju; Applcato of the aalytcal herarchy process to determg evaluato dex weghts for the predcto of reservor damage. Acta Petrole Sca, 6, (20). [] Y Lu; The Establshmet of Herarchcal Model for Basketball Defesve Qualty. Iteratoal Joural of Appled Mathematcs ad Statstcs, 44(4), BoTechology A Ida Joural

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