Microsoft Word - cet-01.docx CHEMICAL ENGINEERING TRANSACTIONS VOL. 46, 2015 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Peiyu Ren, Yancang Li, Huiping Song Copyright © 2015, AIDIC Servizi S.r.l., ISBN 978-88-95608-37-2; ISSN 2283-9216 Study of Athletic Ability Evaluation Model for Professional Football Teams Based on the Extension Theory Lei Dang*a, Guang Bub Department of Sports Work, Agricultural University of Hebei, Baoding, Hebei. 15669791@qq.com The athletic ability evaluation on professional football teams is a complicated decision-making process with multi-attribute and at multi-level. Fuzzy decision information during the analysis of athletic ability of professional football teams is studied with the combination of qualitative and quantitative methods and an athletic ability evaluation model is proposed based on the extension theory. Firstly, factors that influence the athletic ability of professional football teams are analysed, according to which the evaluation indictors are confirmed. Secondly, based on the extension theory, the matter-element model is established to analyse the athletic ability of professional football teams. The matter-element models for classic domain and for sector domain are constructed according to the grade of the athletic ability. Next, the extension correlation degree is computed according to the extension distance and the extension correlation coefficient between the object under evaluation and the classic domain or the sector domain of indicators. From the extension correlation degree, the object can be evaluated. Last but not the least, the model is verified through a case study. 1. Introduction Football is such a sport that emphasizes skills, tactics and individual ability. It attracts more and more sports lovers owing to the instinct passion for sport and a unique style of performance. As the development of competitive sports, professional football teams pay more attention to competitive skills and spare no effort to develop themselves. The evaluation of athletic ability has become one of the concerns of professional football teams [Guo (2007), Huang (2013) and wang (2010) reported]. In recent years, studies of athletic ability of professional football teams have taken off. Some researchers comprehended the issue from different perspectives and yielded fruitful results[chen (2012), Deng(2010), Du(2014) ,Yang (2004) and Zhu et al (2012) reported].However, the evaluation of athletic ability of professional football teams is intertwined with various factors, some of which are fuzzy and uncertain. Existing methods and models have some limitations. For example: (1) traditional method of fuzzy mathematical calculation fails to deal with fuzzy information as it defines the indicator value before the analysis of athletic ability, which is not fuzzy analysis virtually; (2) traditional methods fail to treat the relation of position in fuzzy information interval and result in errors; (3) the evaluation system and model of athletic ability is not modelled. Therefore, this paper proposes to study the athletic ability of professional football teams based on extension [CAI Et Al (2013), Ti et al (2014), Y et al (2014) and Zhai et al (2014) reported]. An athletic ability evaluation model is established as an improvement of relevant studies. 2. Indicators of athletic of professional football teams and the matter-element model 2.1 Indicators and the evaluation index system of athletic ability After literature review, questionnaire analysis and consultation with experts in this field, following the scientific principle, the objective principle, the comprehensive principle, the principle of subjectivity and the comparable principle, this paper establishes three criteria layers for athletic ability analysis, namely ability of coaching staff, team building and ability of individual athletes. Indicators under each criteria layer are shown in Table 1. DOI: 10.3303/CET1546077 Please cite this article as: Dang L., Bu G., 2015, Study of athletic ability evaluation model for professional football teams based on the extension theory, Chemical Engineering Transactions, 46, 457-462 DOI:10.3303/CET1546077 457 Table 1: Index system of athletic ability of professional football teams System layer Criteria layer Index layer The index system of athletic ability of professional football teams U Ability of coaching staff 1U Game strategy arrangement 11u Adjustments during games 12u Team training ability 13u Basic qualities 14u Coordination and organization skills 15u Team building 2U Capital investment 21u Echelon building 22u Team management 23u Construction of incentive mechanism 24u Team cohesion 25u Ability of individual athletes 3U Athletic quality 31u Athletic skill 32u Athletic function 33u Psychological quality 34u Cooperation and coordination ability 35u Tactic execution ability 36u Wisdom during games 37u 2.2 Matter-element model of athletic ability According to the concept and model of matter-element in extents, a matter-element model for athletic ability of professional football teams can be established. Corresponding to the layers and the content in Table 1, the matter-element model UR is: ( ) ( ) ( ) 1 1 2 2 3 3 U U U V U U V U U V U    =      R (1) Where ( )1V U , ( )2V U and ( )3V U refer to the value of indicator set 1U , 2U and 3U . The matter-element models of the criteria layer can be expressed by ,1 3 iU i≤ ≤R : ( ) ( ) ( ) 1 1 2 2 i i i i i i U i n i n U u v u u v u u v u      =          R (2) 3. Athletic ability evaluation model for professional football teams based on the extension theory 3.1 Standardization of indicators There are two categories of indicators for athletic ability evaluation, namely quantitative indicator and qualitative indicator. It is necessary to standardize them. For qualitative indicators, a 0-1 ratio scale is used to measure the value of indicator. The value ( )jv u of indicator j is expressed as: ( ) ( ) ( ),a bj j jv u v u v u =   , ( ) ( )0 1 a b j jv u v u≤ ≤ ≤ (3) Where, 0 is the worst state and 1 is the best state. For quantitative indicators, if the original value of indicator j is ( ) ( ) ( ),a bj j jv u v u v u∗ ∗ − ∗ − =   , and when it is a the bigger-the better positive indicator, the standardized value ( )jv u is: 458 ( ) ( ) ( ) ( ) ( ) ( ) ( ), / , /a b a b b bj j j j j j jv u v u v u v u v u v u v u∗ − ∗ − ∗ − ∗ −+ +   = =    (4) Where: ( )b jv u∗−+ is an ideal positive value of indicator j . If the original value of indicator j is ( ) ( ) ( ),a bj j jv u v u v u∗ ∗ − ∗ − =   , and when it is the smaller-the better positive indicator, the standardized value ( )jv u is: ( ) ( ) ( ) ( ) ( ) ( ) ( ), / , /a b b b b aj j j j j j jv u v u v u v u v u v u v u∗ − ∗ − ∗ − ∗ −− −   = =    (5) Where: ( )b jv u∗−+ is an ideal negative value of indicator j . 3.2 Classic domain matter-element and section domain matter-element Suppose there are m grades in the athletic ability evaluation. The classic domain matter-element of different grades for indicators can be established after standardization. The matter-element C iR of Grade ( )1i i m< < is: [ ] 1 1 1 2 2 2 , , , , , a b i i i i a b i i iC i i a b i n i n i n N c v v c v v R N C V c v v       = =            (6) Among them， 1 0ajv = ， 1bmjv = . On the basis of m grades of matter-element for indicator j , the section domain matter-element model C oR of indicator j can be constructed: ( ) 0 0 1 0 1 0 0 1 0 2 0 2 0 2 0 0 0 0 , 1 0 , 1 , , 0 , 1 C o n n n c v c c v c R C V c v c 0 Ν Ν Ν         = = = =                (7) 3.3 Extension distance and extension correlation function Through survey, questionnaire and statistical analysis, the values of indicators of athletic ability of professional football teams are available. So the matter-element model D R for the object under evaluation is: [ ] 1 1 1 2 2 2 , , , , , a b D D D D a b D D D D D a b D n D n D n N c v v c v v R N C V c v v       = =            (8) According to the extension theory, the extension distance ( )D ijρ between matter-element DR and the classic domain C iR of Grade i about the j -th matter element is: ( ) ( ) ( )( ) / 2a bDj Djv vD D Dij ij ijρ ρ ρ= + (9) Among them， ( ) 2 2 a D j a b b a v i j i j i j i ja D D j v v v v i j vρ + − = − − ， ( ) 2 2 b D j a b b a v i j i j i j i jb D D j v v v v i j vρ + − = − − . Similarly, the extension distance ( )o ijρ between matter-element DR and the classic domain C iR of Grade i about the j -th matter element is: ( ) ( ) ( )( ) / 2a bD j D jv vo o oi j i j i jρ ρ ρ= + (10) 459 Among them， ( ) 1 1 2 2 a D jv a o D ji j vρ = − − ， ( ) 1 1 2 2 b D jv b o D ji j vρ = − − Therefore, the extension correlation coefficient ( )k ij between matter-element D R and the classic domain C iR of Grade i about the j -th matter element is: ( ) ( ) ( ) ( ) ( )( ) / , , / , , a b a b D i j D j D j i j i j a b a b D o D D j D j i j i j i j v v v v v k i j i j i j i j v v v v ρ ρ ρ ρ  − ∈=  − ∉ (11) 3.4 Weight allocation based on comprehensive analysis method The influence of indicators on the evaluation of athletic ability of professional football teams can be distinct under different principles. Therefore, weight should be given to indicators to make the evaluation more reliable. This paper adopts the comprehensive analysis method to allocate weight. Assume p experts are invited. 0-1 ratio scale is used to score on n indicators. The initial judgment matrix A is: ij pxn a =  A (12) The weight j w of indicator j of athletic ability of professional football teams is: 1 1 1 / p pn j s t s t s t s w a a = = = =    (13) 3.5 Extension correlation degree and realization of the algorithm With the acquirement of the extension correlation coefficient ( )k ij between matter-element D R and the classic domain C iR of Grade i about all matter-elements, the extension correlation degree ( )iλ can be calculated: ( ) ( ) 1 1 n j i k i j n λ = =  (14) If the weight j w of indicators is considered, the weighed extension correlation degree between matter- element D R and the classic domain C iR of Grade i about the j -th matter element, the extension correlation degree ( )iλ can be calculated as: ( ) ( )( ) 1 n w j j i w k i jλ = = ∗ (15) Thus, according to the extension correlation degree, the grade of the object can be judged. If it satisfies: ( ) ( )( ) 1w wi m k max iλ λ ≤ ≤ = (16) 4. Case study Performance prediction, development and planning and tactic management for a football team should be based on present athletic ability and state of the team. Consequently, the athletic ability of a team participating in A-class League is studied, in order to verify the model. After consulting with experts and team managers, the athletic ability of a team is divided into four grades, namely excellent (grade 4), good (grade 3), mediocre (grade 2) and poor (grade 1). The classic domain and the section domain of indicators are shown in Table 2. Table 2: Classic domain and section domain of indicators Grades Classic domain Section domain Grade 4 0.9-1.0 0-1.0 Grade 3 0.8-0.9 0-1.0 Grade 2 0.6-0.8 0-1.0 Grade 1 0-0.6 0-1.0 460 On the basis of the survey and statistical analysis, the matter-element models 1U R , 2U R and 3U R of athletic ability of this professional football teams are expressed below: 1 1 1 1 1 2 1 3 1 4 1 5 0 .7 5, 0 .8 5 0 .8 0 , 0 .9 0 0 .8 0 , 0 .9 0 0 .8 0 , 0 .9 0 0 .7 5, 0 .8 5 U U u u u u u        =         R ， 2 2 21 22 23 24 25 0.80, 0.90 0.70, 0.80 0.75, 0.85 0.70, 0.80 0.60, 0.70 U U u u u u u        =         R 3 3 3 1 3 2 3 3 3 4 3 5 3 6 3 7 0 . 7 0 , 0 . 8 0 0 . 7 5 , 0 . 8 5 0 . 8 0 , 0 . 9 0 0 . 6 0 , 0 . 7 0 0 . 8 0 , 0 . 9 0 0 . 7 0 , 0 . 8 0 0 . 7 0 , 0 . 8 0 U U u u u u u u u           =             R According to the formula introduced in this paper, the extension distance (See Table 3) and the extension correlation coefficient (See Table 4) between the matter-element and different grades are computed below. Table 3: Extension distance of athletic ability Criteria layer Index layer Grades Section domain Grade 4 Grade 3 Grade 2 Grade 1 1U 11u 0.10 0 0 0.20 -0.20 12u 0.05 0 0.05 0.25 -0.15 13u 0.05 0 0.05 0.25 -0.15 14u 0.05 0 0.05 0.25 -0.15 15u 0.10 0 0 0.20 -0.20 2U 21u 0.05 0 0.05 0.25 -0.15 22u 0.15 0.05 -0.05 0.15 -0.25 23u 0.10 0 0 0.20 -0.20 24u 0.15 0.05 -0.05 0.15 -0.25 25u 0.25 0.15 -0.05 0.05 -0.35 3U 31u 0.15 0.05 -0.05 0.15 -0.25 32u 0.10 0 0 0.20 -0.20 33u 0.05 0 0.05 0.25 -0.15 34u 0.25 0.15 -0.05 0.05 -0.35 35u 0.05 0 0.05 0.25 -0.15 36u 0.15 0.05 -0.05 0.15 -0.25 37u 0.15 0.05 -0.05 0.15 -0.25 Table 4: Extension correlation coefficient of athletic ability (continue) Criteria layer Index layer Grades Grade 4 Grade 4 Grade 4 Grade 4 1U 11u -0.333 0 0 -0.500 12u -0.250 0 -0.250 -0.625 13u -0.250 0 -0.250 -0.625 14u -0.250 0 -0.250 -0.625 15u -0.333 0 0 -0.500 2U 21u -0.250 0 -0.250 -0.625 22u -0.375 -0.167 0.250 -0.375 23u -0.333 0 0 -0.500 24u -0.375 -0.167 0.250 -0.375 25u -0.417 -0.300 0.250 -0.125 461 Table 4: Extension correlation coefficient of athletic ability 3U 31u -0.375 -0.167 0.250 -0.375 32u -0.333 0 0 -0.500 33u -0.250 0 -0.250 -0.625 34u -0.417 -0.300 0.250 -0.125 35u -0.250 0 -0.250 -0.625 36u -0.375 -0.167 0.250 -0.375 37u -0.375 -0.167 0.250 -0.375 Based on the formula of extension correlation degree, and given the weight of indicators in the criteria layer ( )0.50, 0.20, 0.30w = , the extension correlation degrees between matter-element of athletic ability and different grades can be computed, namely ( )0.319, 0.059, 0.034, 0.496λ = − − − − . 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