Multi-Criteria Decision Tree Approach to Classify All-Rounder in Indian Premier League

Transcription

1 Internatonal Journal of Adanced Scence and Technology Mult-Crtera Decson Tree Approach to Classfy All-Rounder n Indan Premer League Pabtra Kumar Dey 1, Dpendra Nath Ghosh 2, Abhoy Chand Mondal 3 1 Assstant Professor, Department of Computer Applcaton, Dr.B.C.Roy Engneerng College, Inda 2 Assocate Professor, Department of Computer Scence& Engneerng Dr.B.C.Roy Engneerng College, Inda 3 Assocate Professor, Department of Computer Scence, Unersty of Burdwan, Inda dey_pabtra@yahoo.co.n, ghoshdpen2003@yahoo.co.n, abhoy_mondal@yahoo.co.n Abstract In ths fast entertanment era Twenty-20 crcket becomes one of the most popular entertanng sports n all aged persons. Mult-crtera analyss plays a tal role to measure the performance of crcketers and Decson tree technque helps us to classfy n ery effcent manner. Ths paper makes use of Technque for Order Preference by Smlarty to Ideal Soluton (TOPSIS) method to produce the oerall performance of the all-rounder of Indan Premer League (IPL) T-20 sesson-iii crcket tournament. The results of TOPSIS method are further used to classfy all-rounder n four dfferent categores by usng Decson tree. Fnally, ths paper proposed a mult-crtera decson tree approach whch prodes accurate & effcent data classfcaton upon the players performance. Keywords: Mult-Crtera Analyss, Decson Tree, Data Classfcaton, Performance Measure, Twenty-20 Crcket 1. Introducton Mult-Crtera Analyss (MCA), a promsng and mportant feld of study was ntroduced n the early 70 s for supportng decson makers who are faced wth makng numerous and conflctng ealuatons for both quanttate and qualtate ealuaton crtera. Seeral MCA technques lke Smple Addte Weghtng Model (SAW), Technque for Order Preference by Smlarty to Ideal Soluton (TOPSIS) [1], Analytcal Herarchy Process (AHP) [2, 3], PROMETHEE, ELECTRE, etc. has been wdely used for data analyss was descrbed by Muraldharan [4]. TOPSIS s one of the most classcal MCA methods, was frst deeloped by Hwang and Yoon [5], and s based on the dea that the chosen alternate should hae the shortest dstance from the poste deal soluton and on the other sde the farthest dstance of the negate deal soluton. A decson tree s a predcte modelng technque from the felds of machne learnng and statstcs that bulds a smple tree-lke structure to classfy the data accordng ther categores [6, 7, 8]. Decson trees are commonly used n operatons research, specfcally n decson analyss, to help dentfy a strategy most lkely to reach a goal. The man adantage of 93

2 Internatonal Journal of Adanced Scence and Technology decson trees [9, 10] oer many other classfcaton technques s that they produce a set of rules that are transparent and easy to understand. Among dfferent forms of crcket played at the nternatonal leel, Twenty-20 crcket [11, 12] s one of the most entertanng and faorte game n all around the world are becomng the most popular after started Indan Premer League (IPL) n Inda n the year 2008 by Board for Control of Crcket n Inda (BCCI) [13, 14]. Intally, IPL started wth 8 franchses or teams but n IPL sesson-v 9 teams took partcpated. The franchse owner formed ther teams by compette bddng from a collecton of Indan and nternatonal players and the best of Indan upcomng talents. In crcket all-rounder means the player who can play n the both role as a batsman and a bowler and n twenty-20 crcket the all-rounder plays a tal role for success of any teams. IPL T-20 crcket tournament dataset [15] of sesson-iii has been consdered to classfy the allrounder. We here select such players who batted at least 11 nnngs and scored mnmum of 20 runs, bowled for at least 21 oer and got mnmum of 3 wckets n IPL sesson-iii. Dfferent crteron such as Battng Innngs(Inns-Bat), Battng Aerage(Ag-Bat), Battng Strke Rate(SR-Bat), Bowlng Economy Rate (Econ-Bow), Aerage (Ag-Bow), Strke Rate (SR-Bow) hae been consdered for ealuatng the all-rounder performances wth the help of TOPSIS and accordng ther performances classfy them nto seeral categores wth the help of decson tree. Ths work proposed a mult-crtera decson tree approach whch prodes accurate and effcent data classfcaton n the feld of MCA on the bass of players performance. Fnally, all-rounder s classfed n four classes such as Performer, Under- Performer, Battng and Bowlng All-rounder. The paper s organzed as follows: Secton 2 dscuss about the Mult-Crtera Analyss usng TOPSIS. Secton 3 focuses about the basc concepts of Decson Tree. Experment and results are carred out on Secton 4. Fnally, Secton 5 concludes the paper. 2. Mult-Crtera Analyss usng TOPSIS Mult-Crtera Analyss (MCA) s a decson-makng tool deeloped for complex problems to handle a large amount of arables and alternates assessed n arous ways and consequently offer aluable assstance to the decson maker n mappng out the problem. The frst complete exposton of MCA was gen n 1976 by Keeney and Raffa [16]. By usng MCA the members don't hae to agree on the relate mportance of the Crtera or the rankngs of the alternates. Each member enters hs or her own judgments, and makes a dstnct, dentfable contrbuton to a jontly reached concluson. Seeral MCA technques lke Smple Addte Weghtng Model (SAW), Technque for Order Preference by Smlarty to Ideal Soluton (TOPSIS), Analytcal Herarchy Process (AHP), PROMETHEE, ELECTRE, etc. has been wdely used for data analyss. TOPSIS was frst deeloped by Hwang and Yoon [5], s based on the dea that the chosen alternate should hae the shortest dstance from the poste deal soluton and on the other sde the farthest dstance of the negate deal soluton. TOPSIS works not only by the poste soluton but also use the negate soluton to fnd the relate closeness of the crtera. Due to ths among seeral MCA technques TOPSIS ges the better result n mult crtera analyss. Abo-snna and Amer [17] extend TOPSIS approach to sole mult-objecte nonlnear programmng problems. Jahanshahloo, et al., [18] extend the concept of TOPSIS to deelop a methodology for solng mult-crtera analyss wth nteral data. The steps of TOPSIS method are as follows: Step 1: TOPSIS begns wth a decson matrx hang n crtera/attrbutes and m alternates. 94

3 Internatonal Journal of Adanced Scence and Technology Step 2: Obtan the normalzed decson matrx by usng any normalzaton technque. Step 3: Construct the weghted normalzed matrx j. Ths s calculated by multplyng each column of the matrx rj by the weght wj, whch s calculated by AHP. Step 4: Obtan the IDEAL (best) and Negate- IDEAL (worst) solutons. The IDEAL (best) and Negate- DEAL (worst) solutons can be expressed as j j max mn j j mn ' j J, j j J 1, 2,..., m 1 2 max ' j J, j j J 1, 2,..., m (1) n... (2), where J= ( j =1, 2,..., n)/j s assocated wth the benefcal attrbutes and J =( j =1, 2,..., n)/j s assocated wth the non-benefcal attrbutes. Step 5: Determne the separaton dstance between the alternates. The separaton of each alternate from the IDEAL soluton s gen by n S n j1 j j 2, 1,2,..., m (3) The separaton from the Negate- IDEAL soluton s denoted by S n j1 j j 2, 1, 2,..., m Step 6: Calculate the relate closeness to the deal soluton, whch can be expressed as C S S S, 1, 2,..., m (4) (5) 3. Decson Tree A decson tree, a predcte modelng technque from the felds of machne learnng and statstcs that bulds a smple tree-lke structure to classfy the data accordng ther categores descrbed n [6, 7, 8]. Decson tree s a tree where the root and each nternal node are labeled wth a queston; the arcs represent each possble answer to the assocated queston and each leaf node represents a predcton of a soluton to the problem. The man adantage of decson trees [9, 10] oer many other classfcaton technques s that they produce a set of rules that are transparent, easy to understand and the graphcal representaton of tree prodes more realstc ew to dfferentate the dfferent categores. In my preous work [19] IPL T-20 players classfcaton was done wth two crtera. 95

4 Internatonal Journal of Adanced Scence and Technology The decson tree algorthm s as follows: T: Input Decson tree, D: Input Database and M: Output Model Predcton For each t ε D do n = root node of T whle n not leaf node do Obtan answer to queston on n appled t; Identfy arc from t whch contans correct answer; n = node at end of ths arc; Make predcton for t based on labelng of n; Fgure 1. The predcton tree for classfyng the all-rounder 4. Experment & Result In Twenty-20 crcket the all-rounder s (who can bat and ball both) performance plays tal role for team s success. As a batsman the battng Strke Rate, battng Aerage and the No. of Innngs played by batsman are the most essental crtera for performance measure of a batsman although seeral other crtera lke Runs Scored by a batsman and No. of Not-Out Innngs of a batsman are there whch s descrbed n my preous work [20]. My preous work [21, 22] dscussed about the bowlng performance n IPL wth multple crtera lke No. of Matches played by a bowler n a partcular tournament, No. of Oer bowled by a bowler and No. of Wcket taken by a bowler, Economy Rate of a bowler, Bowlng Aerage and Bowlng Strke Rate whereas the last three are the most essental crtera. For classfcaton of the all-rounder IPL sesson-iii dataset s consdered and shown n the Table 1. 96

5 Internatonal Journal of Adanced Scence and Technology Table 1. IPL Sesson-III Dataset Methodology for classfcaton of All-Rounder - Step 1: Takng the dataset as decson matrx and normalzed the dataset. Step 2: The weghts of the mportant crtera of the players are calculated wth the help of par-wse comparson method known as AHP [2, 3] and the correspondng weghts of the crtera are descrbed n the Table 2. Table 2. Weghts of the Crtera Crtera Weghts Name Inns-Bat 0.12 Ag-Bat 0.16 SR-Bat 0.22 Econ-Bow 0.20 Ag-Bow 0.17 SR-Bow 0.13 Step 3: TOPSIS method s used separately for ealuaton of batsmen and bowlers performance. Step 4: Calculate the mean of the both battng and bowlng performance of the players. 97

6 Internatonal Journal of Adanced Scence and Technology Step 5: Wth the help of our predcton Decson Tree classfcaton of all-rounder s made nto four dfferent classes named as Battng All-rounder, Bowlng All-rounder, Performer and Under Performer. Step 6: The players n seeral categores are descrbed n the Table 3 and the correspondng graph s shown n the Fgure 2. Table 3. Players wth Seeral Categores Fgure 2. Graph of Seeral Categores of all-rounder 98

7 Internatonal Journal of Adanced Scence and Technology 5. Concluson In IPL twenty-20 crcket tournament the franchsee owners selected ther players through aucton and the nddual performances of the players reflected n team performances. For approprate bddng prce of each players depend on ther nddual performances and the franchsee owners get the actual pcture and they decde ther approprate team wth approprate players and they get much more proft from IPL T-20 tournament. The role of the all-rounder n twenty-20 crcket s much more than other category players for team s better performance. TOPSIS used the relate closeness of poste deal soluton and negate deal soluton to produce the better result among seeral MCA technques and use of decson tree s ery easy to understand. Due to ths reason our proposed methodology Mult-Crtera Decson Tree technques ges the clear pcture of the players seeral category lke Performer, Battng All-rounder, Bowlng All-rounder and Under Performer whch helps the franchsee owners for selectng the all-rounder n aucton and pay them accordng ther performances. The players are also know ther oerall performances and also aware of ther weakness of ther playng where they really need the better performance and uplft themseles as a better player wth ths proposed. Ths proposed methodology helps decson makers to take ther decson ery easly accordng seeral crtera and the graphcal representaton of the classfcaton s easy to understand and error free. References [1] K. De, S. P. Yada and S. Kumar, Extenson of fuzzy TOPSIS method based on ague sets, Internatonal Journal of Cmputaonal Cognton, ol. 7, no. 4, (2009), pp [2] T. L. Saaty, The Analytc Herarchy Process, McGraw-Hll, New York, (1980). [3] T. L. Saaty, "Prorty Settng n Complex Problems", IEEE Transactons on Engneerng Management, ol. 30, no. 3, (1983), pp [4] C. Muraldharan, Applcaton of Analytc Herarchy Process (AHP) n materals and human resource management under group decson makng enronment, Unpublshed Ph.D. Thess, Annamala Unersty, (2000). [5] C. L. Hwang, K. Yoon, Multple Attrbute Decson Makng Methods and Applcatons, Sprnger, Berln Hedelberg, (1981). [6] J. R. Qunlan, Inducton of decson trees, Machne Learnng, ol. 1, (1986), pp [7] J. Gehrke, R. Ramakrshnan and V. Gant, RanForest - a Framework for Fast Decson Tree Constructon of Large Datasets, Proceedngs of the 24th VLDB conference, New York, USA, (1998), pp [8] P. Utgoff and C. Brodley, An Incremental Method for Fndng Multarate Splts for Decson Trees, Machne Learnng: Proceedngs of the 7th Internatonal Conference, (1990), pp. 58. [9] J. R. Qunlan, Programs for Machne Learnng, Morgan Kaufmann, San Mateo, CA, (1993). [10] [11] Wkpeda, [12] Crcnfo, [13] IPL Blog, [14] Wkpeda, [15] IPL, Indan Premer League, [16] R. L. Keeney and H. Raffa, Decsons wth Multple Objectes: Preferences and Value Tradeoffs, John Wley, New York, reprnted, Cambrdge Unersty Press, (1976). [17] M. A. Abo-Snna and A. H. Amer, Extensons of TOPSIS for mult-objecte large-scale nonlnear programmng problems, Appled Mathematcs and Computaton, ol. 162, (2005), pp [18] G. R. Jahanshahloo, F. Hossenzadeh, L. f and M. Izadkhah, An algorthmc method to extend TOPSIS for decson-makng problems wth nteral data, Appled Mathematcs and Computaton, (2005). [19] P. K. Dey, G. Chakraborty and A. C. Mondal, Fuzzy Classfcaton usng Decson Tree Algorthms, Inc. n Proc. of 1st Internatonal Conference on Computng and Systems (ICCS- 2010), Burdwan, Inda, ISBN: , (2010), pp

8 Internatonal Journal of Adanced Scence and Technology [20] P. K. Dey, D. N. Ghosh and A. C. Mondal, Statstcal Based Mult-Crtera Decson Makng Analyss for Performance Measurement of Batsmen n Indan Premer League, n Internatonal Journal of Adanced Research n Computer Scence (IJARCS), ISSN , ol. 3, no. 4, (2012) July- August, [21] P. K. Dey, D. N. Ghosh and A. C. Mondal, A MCDM Approach for Ealuatng Bowlers Performance n IPL, n Journal of Emergng Trends n Computng and Informaton Scences, ISSN , ol. 2, no. 11, (2011) Noember, pp , [22] P. K. Dey and D. N. Ghosh, Mult Crtera Fuzzy Classfcaton of IPL3, n Internatonal Journal of Informaton and Computng Scence (IJICS), ISSN , ol. 14, no. 1, (2012), pp Authors Mr. Pabtra Kumar Dey s workng as an Asst. Prof. n the Dept. of Computer Applcaton, Dr. B.C.Roy Engneerng College, Durgapur, Inda. He was born on 10/12/1978. He obtaned B.Sc. (Math Hons.) n 2000, M.C.A. n 2004 & M.Tech.(CST) n He regstered hmself as a research scholar n the Dept. of Computer Scence, Burdwan Unersty. He has about more than of 8 years of Teachng Experence and 4 years of Research Experence. He has more than 15 research papers n reputed journals and conference proceedngs. The broad area of hs research nterest s n Soft Computng, Mult Crtera Analyss, Decson Theory, etc. Dr. Dpendra Nath Ghosh s currently Assocate Professor n the department of Computer Scence & Engneerng, Dr. B.C.Roy Engneerng College, Durgapur , W.B., Inda. He obtaned M.Sc. n Mathematcs & M.C.A. from Unersty of Burdwan and Ph.D. n Computer Scence from that Unersty n He has oer 10 years of teachng experence and 07 years of research experence. He s gudng M.Tech. & Ph.D. students and has 20 research papers to hs credt. Dr. Abhoy Chand Mondal s currently Assocate Professor of Department of Computer Scence, Burdwan Unersty, W.B, Inda. He receed hs B.Sc. (Mathematcs Hons.) from The Unersty of Burdwan n 1987, M.Sc. (Math) and M.C.A. from Jadapur Unersty, n 1989, 1992 respectely. He receed hs Ph.D. from Burdw an Unersty n He has 1 year ndustry experence and 19 years of teachng and research experence. No. of journal paper s more than