{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T10:44:10Z","timestamp":1768992250401,"version":"3.49.0"},"reference-count":104,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,8]],"date-time":"2020-12-08T00:00:00Z","timestamp":1607385600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Decision support systems often involve taking into account many factors that influence the choice of existing options. Besides, given the expert\u2019s uncertainty on how to express the relationships between the collected data, it is not easy to define how to choose optimal solutions. Such problems also arise in sport, where coaches or players have many variants to choose from when conducting training or selecting the composition of players for competitions. In this paper, an objective fuzzy inference system based on fuzzy logic to evaluate players in team sports is proposed on the example of football. Based on the Characteristic Objects Method (COMET), a multi-criteria model has been developed to evaluate players on the positions of forwards based on their match statistics. The study has shown that this method can be used effectively in assessing players based on their performance. The COMET method was chosen because of its unique properties. It is one of the few methods that allow identifying the model without giving weightings of decision criteria. Symmetrical and asymmetrical fuzzy triangular numbers were used in model identification. Using the calculated derivatives in the point, it turned out that the criteria weights change in the problem state space. This prevents the use of other multi-criteria decision analysis (MCDA) methods. However, we compare the obtained model with the Technique of Order Preference Similarity (TOPSIS) method in order to better show the advantage of the proposed approach. The results from the objectified COMET model were compared with subjective rankings such as Golden Ball and player value.<\/jats:p>","DOI":"10.3390\/sym12122029","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T22:15:36Z","timestamp":1607638536000},"page":"2029","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":51,"title":["A Fuzzy Inference System for Players Evaluation in Multi-Player Sports: The Football Study Case"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7076-2519","authenticated-orcid":false,"given":"Wojciech","family":"Sa\u0142abun","sequence":"first","affiliation":[{"name":"Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence Methods and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. \u017bo\u0142nierska 49, 71-210 Szczecin, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0834-2019","authenticated-orcid":false,"given":"Andrii","family":"Shekhovtsov","sequence":"additional","affiliation":[{"name":"Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence Methods and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. \u017bo\u0142nierska 49, 71-210 Szczecin, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8522-1942","authenticated-orcid":false,"given":"Dragan","family":"Pamu\u010dar","sequence":"additional","affiliation":[{"name":"Department of Logistics, The Military Academy, The University of Defence in Belgrade, Pavla Juri\u0161i\u0107a \u0160turma 33, 11000 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4415-9414","authenticated-orcid":false,"given":"Jaros\u0142aw","family":"W\u0105tr\u00f3bski","sequence":"additional","affiliation":[{"name":"Institute of Management, University of Szczecin, Cukrowa 8, 71-004 Szczecin, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5736-4014","authenticated-orcid":false,"given":"Bart\u0142omiej","family":"Kizielewicz","sequence":"additional","affiliation":[{"name":"Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence Methods and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. \u017bo\u0142nierska 49, 71-210 Szczecin, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9324-3241","authenticated-orcid":false,"given":"Jakub","family":"Wi\u0119ckowski","sequence":"additional","affiliation":[{"name":"Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence Methods and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. \u017bo\u0142nierska 49, 71-210 Szczecin, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9657-0889","authenticated-orcid":false,"given":"Darko","family":"Bozani\u0107","sequence":"additional","affiliation":[{"name":"The Military Academy, The University of Defence in Belgrade, Pavla Juri\u0161i\u0107a \u0160turma 33, 11000 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5373-9760","authenticated-orcid":false,"given":"Karol","family":"Urbaniak","sequence":"additional","affiliation":[{"name":"Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence Methods and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. \u017bo\u0142nierska 49, 71-210 Szczecin, Poland"}]},{"given":"Bartosz","family":"Nyczaj","sequence":"additional","affiliation":[{"name":"Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence Methods and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. \u017bo\u0142nierska 49, 71-210 Szczecin, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Razali, N., Mustapha, A., Yatim, F.A., and Ab Aziz, R. (2017, January 6\u20137). Predicting football matches results using Bayesian networks for English Premier League (EPL). Proceedings of the Iop Conference Series: Materials Science and Engineering, International Research and Innovation Summit (IRIS2017), Melaka, Malaysia.","DOI":"10.1088\/1757-899X\/226\/1\/012099"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/j.knosys.2008.03.016","article-title":"A compound framework for sports results prediction: A football case study","volume":"21","author":"Min","year":"2008","journal-title":"Knowl. Based Syst."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Miljkovi\u0107, D., Gaji\u0107, L., Kova\u010devi\u0107, A., and Konjovi\u0107, Z. (2010, January 10\u201311). The use of data mining for basketball matches outcomes prediction. Proceedings of the IEEE 8th International Symposium on Intelligent Systems and Informatics, Subotica, Serbia.","DOI":"10.1109\/SISY.2010.5647440"},{"key":"ref_4","first-page":"171","article-title":"Robust fitting of football prediction models","volume":"22","author":"Karlis","year":"2011","journal-title":"IMA J. Manag. Math."},{"key":"ref_5","unstructured":"Deloitte (2019, November 14). Deloitte Football Money League. Available online: http:\/\/www2.deloitte.com."},{"key":"ref_6","first-page":"52","article-title":"Spanish football clubs\u2019 finances: Crisis and player salaries","volume":"5","author":"Barajas","year":"2010","journal-title":"Int. J. Sport Financ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.smr.2012.05.004","article-title":"Predicting spectators\u2019 behavioural intentions in professional football: The role of satisfaction and service quality","volume":"16","author":"Theodorakis","year":"2013","journal-title":"Sport Manag. Rev."},{"key":"ref_8","unstructured":"EGBA (2019, November 15). Sports Betting Report. Available online: http:\/\/www.egba.eu."},{"key":"ref_9","first-page":"1","article-title":"Predicting the Dutch football competition using public data: A machine learning approach","volume":"10","author":"Tax","year":"2015","journal-title":"Trans. Knowl. Data Eng."},{"key":"ref_10","unstructured":"LegalSport (2019, November 15). Rynek Zak\u0142ad\u00f3w Bukmacherskich w Polsce w 2017 Roku. Available online: http:\/\/www.legalsport.pl."},{"key":"ref_11","unstructured":"Bukmacherzy (2019, November 15). Zak\u0142ady Bukmacherskie\u2014Raport Gemius Czerwiec 2018. Available online: http:\/\/bukmacher-legalny.pl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"101","DOI":"10.14254\/2071-789X.2016\/9-2\/7","article-title":"Multistage performance modelling in digital marketing management","volume":"9","author":"Jankowski","year":"2016","journal-title":"Econ. Sociol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s11293-011-9295-x","article-title":"Effect of linguistic heterogeneity on technology transfer: An economic study of FIFA football rankings","volume":"40","author":"Yamamura","year":"2012","journal-title":"Atl. Econ. J."},{"key":"ref_14","unstructured":"FIFA (2019, September 25). FIFA\/Coca-Cola World Ranking. Available online: http:\/\/fifa.com."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2176","DOI":"10.1080\/02640414.2016.1218040","article-title":"Analysis of the predictive qualities of betting odds and FIFA World Ranking: Evidence from the 2006, 2010 and 2014 Football World Cups","volume":"34","author":"Wunderlich","year":"2016","journal-title":"J. Sport. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"839","DOI":"10.2165\/00007256-200838100-00004","article-title":"The role of motion analysis in elite soccer","volume":"38","author":"Carling","year":"2008","journal-title":"Sport. Med."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/j.dib.2018.12.015","article-title":"Generalised framework for multi-criteria method selection: Rule set database and exemplary decision support system implementation blueprints","volume":"22","author":"Jankowski","year":"2019","journal-title":"Data Brief"},{"key":"ref_18","unstructured":"Cronin, B. (2019, September 25). Poisson Distribution: Predict the Score in Soccer Betting. Available online: http:\/\/www.pinnacle.com."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.omega.2018.07.004","article-title":"Generalised framework for multi-criteria method selection","volume":"86","author":"Jankowski","year":"2019","journal-title":"Omega"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.compind.2010.10.009","article-title":"A novel fuzzy multi-criteria decision framework for sustainable supplier selection with incomplete information","volume":"62","year":"2011","journal-title":"Comput. Ind."},{"key":"ref_21","first-page":"102","article-title":"Prioritization of the factors effecting privatization in sport clubs: With AHP & TOPSIS methods-emphasis in football","volume":"2","author":"Salimi","year":"2012","journal-title":"Int. J. Acad. Res. Bus. Soc. Sci."},{"key":"ref_22","first-page":"83","article-title":"Decision making with the analytic hierarchy process","volume":"1","author":"Saaty","year":"2008","journal-title":"Int. J. Serv. Sci."},{"key":"ref_23","first-page":"190","article-title":"A mathematical model using AHP priorities for soccer player selection: A case study","volume":"27","author":"Ozceylan","year":"2016","journal-title":"S. Afr. J. Ind. Eng."},{"key":"ref_24","first-page":"239","article-title":"Who really won the FIFA 2014 Golden Ball Award?: What sports can learn from multi-criteria decision analysis","volume":"16","author":"Mu","year":"2016","journal-title":"Int. J. Sport Manag. Mark."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Cooper, W.W., Seiford, L.M., and Tone, K. (2000). Data envelopment analysis. Handbook on Data Envelopment Analysis, Springer.","DOI":"10.1007\/b109347"},{"key":"ref_26","first-page":"108","article-title":"Ranking football teams with AHP and TOPSIS methods","volume":"4","author":"Kiani","year":"2012","journal-title":"Int. J. Decis. Sci. Risk Manag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1057\/jors.1988.112","article-title":"Ranking of sports teams via the AHP","volume":"39","year":"1988","journal-title":"J. Oper. Res. Soc."},{"key":"ref_28","first-page":"159","article-title":"Football match results prediction using artificial neural networks; the case of Iran Pro League","volume":"1","author":"Arabzad","year":"2014","journal-title":"J. Appl. Res. Ind. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1080\/02640414.2019.1702280","article-title":"Evaluation of soccer players under the Moneyball concept","volume":"38","year":"2020","journal-title":"J. Sports Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/S0377-2217(02)00684-7","article-title":"Team formation: Matching quality supply and quality demand","volume":"148","author":"Boon","year":"2003","journal-title":"Eur. J. Oper. Res."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"10408","DOI":"10.1016\/j.eswa.2011.02.104","article-title":"Decision-making in sport management based on the OWA operator","volume":"38","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1016\/j.asoc.2012.07.031","article-title":"Multi-objective optimization and decision making approaches to cricket team selection","volume":"13","author":"Ahmed","year":"2013","journal-title":"Appl. Soft Comput."},{"key":"ref_33","unstructured":"Lourens, M. (2009). Integer Optimization for the Selection of a Twenty20 Cricket Team. [Ph.D. Thesis, Nelson Mandela Metropolitan University]."},{"key":"ref_34","first-page":"81","article-title":"Selecting a limited overs cricket squad using an integer programming model","volume":"28","author":"Gerber","year":"2006","journal-title":"S. Afr. J. Res. Sport Phys. Educ. Recreat."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"S369","DOI":"10.1080\/17461391.2012.705333","article-title":"Cricket team selection using data envelopment analysis","volume":"14","author":"Amin","year":"2014","journal-title":"Eur. J. Sport Sci."},{"key":"ref_36","unstructured":"Omkar, S., and Verma, R. (2003, January 1\u20133). Cricket team selection using genetic algorithm. Proceedings of the International Congress on Sports Dynamics (ICSD2003), Melbourne, Australia."},{"key":"ref_37","first-page":"51","article-title":"Statistical based multi-criteria decision making analysis for performance measurement of batsmen in Indian Premier League","volume":"3","author":"Dey","year":"2012","journal-title":"Int. J. Adv. Res. Comput. Sci."},{"key":"ref_38","first-page":"563","article-title":"A MCDM approach for evaluating bowlers performance in IPL","volume":"2","author":"Dey","year":"2011","journal-title":"J. Emerg. Trends Comput. Inf. Sci."},{"key":"ref_39","first-page":"1","article-title":"Decision making in best player selection: An integrated approach with AHP and Extended TOPSIS methods based on WeFA Freamwork in MAGDM problems","volume":"4","author":"Nikjo","year":"2015","journal-title":"Int. J. Res. Ind. Eng."},{"key":"ref_40","first-page":"19","article-title":"Analysis of selection indicators of badminton players by the Delphi method and analytic hierarchy process","volume":"7","author":"Huang","year":"2015","journal-title":"Int. J. Comput. Sci. Inf. Technol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"6106","DOI":"10.1016\/j.eswa.2014.03.036","article-title":"Multi-criteria assessment and ranking system of sport team formation based on objective-measured values of criteria set","volume":"41","author":"Dadelo","year":"2014","journal-title":"Expert Syst. Appl."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1111\/exsy.12002","article-title":"Development of a fuzzy decision support framework for complex multi-attribute decision problems: A case study for the selection of skilful basketball players","volume":"31","year":"2014","journal-title":"Expert Syst."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Blanco, V., Salmer\u00f3n, R., and G\u00f3mez-Haro, S. (2018). A multicriteria selection system based on player performance. Case study: The Spanish ACB Basketball League. arXiv.","DOI":"10.1007\/s10726-018-9583-9"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1260\/1747-9541.10.1.21","article-title":"Decision support for evaluating player performance in rugby union","volume":"10","author":"Calder","year":"2015","journal-title":"Int. J. Sports Sci. Coach."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1080\/24748668.2014.11868742","article-title":"Professional baseball team starting pitcher selection using AHP and TOPSIS methods","volume":"14","author":"Chen","year":"2014","journal-title":"Int. J. Perform. Anal. Sport"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"23","DOI":"10.9790\/6737-0401012329","article-title":"Weighting the positions and skills of volleyball sport by using AHP: A real life application","volume":"4","author":"Budak","year":"2017","journal-title":"IOSR J. Sports Phys. Educ."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Budak, G., Kara, \u0130., \u0130\u00e7, Y.T., and Kas\u0131mbeyli, R. (2017, January 26\u201328). Optimization of Harmony in Team Formation Problem for Sports Clubs: A real life volleyball team application. Proceedings of the MathSport International 2017 Conference, Padua, Italy.","DOI":"10.30845\/ijast.v8n2a2"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1007\/s10462-016-9511-9","article-title":"Comparative analysis of MCDM methods for the assessment of mortality in patients with acute coronary syndrome","volume":"48","author":"Piegat","year":"2017","journal-title":"Artif. Intell. Rev."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1002\/mcda.1525","article-title":"The Characteristic Objects Method: A New Distance-based Approach to Multicriteria Decision-making Problems","volume":"22","year":"2015","journal-title":"J. Multi. Criteria Decis. Anal."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Urbaniak, K., W\u0105tr\u00f3bski, J., and Sa\u0142abun, W. (2020). Identification of Players Ranking in E-Sport. Appl. Sci., 10.","DOI":"10.3390\/app10196768"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"3524","DOI":"10.1016\/j.procs.2020.09.034","article-title":"MCDA based approach to sports players\u2019 evaluation under incomplete knowledge","volume":"176","author":"Kizielewicz","year":"2020","journal-title":"Procedia Comput. Sci."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2491","DOI":"10.1016\/j.procs.2019.09.424","article-title":"Identification of the football teams assessment model using the COMET method","volume":"159","author":"Palczewski","year":"2019","journal-title":"Procedia Comput. Sci."},{"key":"ref_53","first-page":"353","article-title":"The Search of the Optimal Preference Values of the Characteristic Objects by Using Particle Swarm Optimization in","volume":"Volume 193","author":"Wieckowski","year":"2020","journal-title":"Smart Innovation, Systems and Technologies, Proceedings of the 12th KES International Conference on Intelligent Decision Technologies (KES-IDT, 2020), Virtual Conference, 17\u201319 June 2020"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"3581","DOI":"10.1016\/j.procs.2020.09.028","article-title":"Effects of the selection of characteristic values on the accuracy of results in the COMET method","volume":"176","author":"Kizielewicz","year":"2020","journal-title":"Procedia Comput. Sci."},{"key":"ref_55","first-page":"62","article-title":"Reduction in the number of comparisons required to create matrix of expert judgment in the comet method","volume":"5","year":"2014","journal-title":"Manag. Prod. Eng. Rev."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Shekhovtsov, A., Ko\u0142odziejczyk, J., and Sa\u0142abun, W. (2020). Fuzzy Model Identification Using Monolithic and Structured Approaches in Decision Problems with Partially Incomplete Data. Symmetry, 12.","DOI":"10.3390\/sym12091541"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"2137","DOI":"10.1016\/j.procs.2018.07.238","article-title":"On Analysis of e-Banking Websites Quality\u2013Comet Application","volume":"126","author":"Chmielarz","year":"2018","journal-title":"Procedia Comput. Sci."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Sa\u0142abun, W., Ziemba, P., and W\u0105tr\u00f3bski, J. (2016). The rank reversals paradox in management decisions: The comparison of the ahp and comet methods. Smart Innovation, Systems and Technologies, Proceedings of the International Conference on Intelligent Decision Technologies, Puerto de la Cruz, Spain, 15\u201317 June 2016, Springer.","DOI":"10.1007\/978-3-319-39630-9_15"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"2222","DOI":"10.1016\/j.procs.2020.09.259","article-title":"How the normalization of the decision matrix influences the results in the VIKOR method?","volume":"176","year":"2020","journal-title":"Procedia Comput. Sci."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Sa\u0142abun, W., W\u0105tr\u00f3bski, J., and Shekhovtsov, A. (2020). Are MCDA Methods Benchmarkable? A Comparative Study of TOPSIS, VIKOR, COPRAS, and PROMETHEE II Methods. Symmetry, 12.","DOI":"10.3390\/sym12091549"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"3591","DOI":"10.1016\/j.procs.2020.09.027","article-title":"Why TOPSIS does not always give correct results?","volume":"176","author":"Paradowski","year":"2020","journal-title":"Procedia Comput. Sci."},{"key":"ref_62","first-page":"40","article-title":"The mean error estimation of TOPSIS method using a fuzzy reference models","volume":"7","year":"2013","journal-title":"J. Theor. Appl. Comput. Sci."},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Jankowski, J., Sa\u0142abun, W., and W\u0105tr\u00f3bski, J. (2017). Identification of a multi-criteria assessment model of relation between editorial and commercial content in web systems. Multimedia and Network Information Systems, Springer.","DOI":"10.1007\/978-3-319-43982-2_26"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"3555","DOI":"10.1016\/j.procs.2020.09.031","article-title":"Handling economic perspective in multicriteria model-renewable energy resources case study","volume":"176","author":"Kizielewicz","year":"2020","journal-title":"Procedia Comput. Sci."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.asoc.2014.03.014","article-title":"A comparison between Fuzzy AHP and Fuzzy TOPSIS methods to supplier selection","volume":"21","author":"Junior","year":"2014","journal-title":"Appl. Soft Comput."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"2243","DOI":"10.1016\/j.procs.2020.09.274","article-title":"How to choose the optimal single-track vehicle to move in the city? Electric scooters study case","volume":"176","author":"Kizielewicz","year":"2020","journal-title":"Procedia Comput. Sci."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"2232","DOI":"10.1016\/j.procs.2020.09.260","article-title":"How to handling with uncertain data in the TOPSIS technique?","volume":"176","year":"2020","journal-title":"Procedia Comput. Sci."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"131","DOI":"10.31181\/dmame2003131r","article-title":"Application of hybrid model fuzzy AHP-VIKOR in selection of the most efficient procedure for rectification of the optical sight of the long-range rifle","volume":"3","author":"Radovanovic","year":"2020","journal-title":"Decis. Making Appl. Manag. Eng."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"2294","DOI":"10.1016\/j.procs.2019.09.404","article-title":"The fuzzy TOPSIS applications in the last decade","volume":"159","author":"Palczewski","year":"2019","journal-title":"Procedia Comput. Sci."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Bashir, Z., Rashid, T., W\u0105tr\u00f3bski, J., Sa\u0142abun, W., and Malik, A. (2018). Hesitant probabilistic multiplicative preference relations in group decision making. Appl. Sci., 8.","DOI":"10.3390\/app8030398"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1109\/TFUZZ.2011.2170076","article-title":"Hesitant fuzzy linguistic term sets for decision making","volume":"20","author":"Rodriguez","year":"2011","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.ejor.2006.04.009","article-title":"Multi-criteria decision-making methods based on intuitionistic fuzzy sets","volume":"179","author":"Liu","year":"2007","journal-title":"Eur. J. Oper. Res."},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Bashir, Z., W\u0105tr\u00f3bski, J., Rashid, T., Sa\u0142abun, W., and Ali, J. (2017). Intuitionistic-fuzzy goals in zero-sum multi criteria matrix games. Symmetry, 9.","DOI":"10.3390\/sym9080158"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.asoc.2008.05.005","article-title":"Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets","volume":"9","author":"Ashtiani","year":"2009","journal-title":"Appl. Soft Comput."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1007\/s00170-009-2241-2","article-title":"Extension of VIKOR method based on interval-valued fuzzy sets","volume":"47","author":"Vahdani","year":"2010","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_76","doi-asserted-by":"crossref","unstructured":"Faizi, S., Sa\u0142abun, W., Ullah, S., Rashid, T., and Wi\u0119ckowski, J. (2020). A New Method to Support Decision-Making in an Uncertain Environment Based on Normalized Interval-Valued Triangular Fuzzy Numbers and COMET Technique. Symmetry, 12.","DOI":"10.3390\/sym12040516"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1007\/s00500-013-1109-4","article-title":"A PROMETHEE-based outranking method for multiple criteria decision analysis with interval type-2 fuzzy sets","volume":"18","author":"Chen","year":"2014","journal-title":"Soft Comput."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"4948","DOI":"10.1016\/j.apm.2012.10.006","article-title":"A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets","volume":"37","author":"Zhang","year":"2013","journal-title":"Appl. Math. Model."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"3813","DOI":"10.1007\/s10462-019-09780-x","article-title":"Pythagorean fuzzy MCDM method based on CoCoSo and CRITIC with score function for 5G industry evaluation","volume":"53","author":"Peng","year":"2020","journal-title":"Artif. Intell. Rev."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1016\/j.scs.2018.05.034","article-title":"WASPAS and TOPSIS based interval type-2 fuzzy MCDM method for a selection of a car sharing station","volume":"41","author":"Deveci","year":"2018","journal-title":"Sustain. Cities Soc."},{"key":"ref_81","doi-asserted-by":"crossref","unstructured":"Riaz, M., Sa\u0142abun, W., Farid, H.M.A., Ali, N., and W\u0105tr\u00f3bski, J. (2020). A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management. Energies, 13.","DOI":"10.3390\/en13092155"},{"key":"ref_82","first-page":"235","article-title":"The use of fuzzy logic to evaluate the nonlinearity of human multi-criteria used in decision making","volume":"88","year":"2012","journal-title":"Prz. Elektrotech."},{"key":"ref_83","doi-asserted-by":"crossref","unstructured":"Wi\u0119ckowski, J., Kizielewicz, B., and Ko\u0142odziejczyk, J. (2020). Finding an Approximate Global Optimum of Characteristic Objects Preferences by Using Simulated Annealing. Smart Innovation, Systems and Technologies, Proceedings of the International Conference on Intelligent Decision Technologies, Split, Croatia, 17\u201319 June 2020, Springer.","DOI":"10.1007\/978-981-15-5925-9_31"},{"key":"ref_84","doi-asserted-by":"crossref","unstructured":"Kizielewicz, B., and Sa\u0142abun, W. (2020). A New Approach to Identifying a Multi-Criteria Decision Model Based on Stochastic Optimization Techniques. Symmetry, 12.","DOI":"10.3390\/sym12091551"},{"key":"ref_85","doi-asserted-by":"crossref","unstructured":"Wi\u0119ckowski, J., Kizielewicz, B., and Ko\u0142odziejczyk, J. (2020). Application of Hill Climbing Algorithm in Determining the Characteristic Objects Preferences Based on the Reference Set of Alternatives. Smart Innovation, Systems and Technologies, Proceedings of the International Conference on Intelligent Decision Technologies, Split, Croatia, 17\u201319 June 2020, Springer.","DOI":"10.1007\/978-981-15-5925-9_29"},{"key":"ref_86","doi-asserted-by":"crossref","unstructured":"Sa\u0142abun, W., Karczmarczyk, A., and W\u0105tr\u00f3bski, J. (2018, January 18\u201321). Decision-making using the hesitant fuzzy sets COMET method: An empirical study of the electric city buses selection. Proceedings of the 2018 IEEE Symposium Series on Computational Intelligence (SSCI), Bangalore, India.","DOI":"10.1109\/SSCI.2018.8628864"},{"key":"ref_87","doi-asserted-by":"crossref","unstructured":"Sa\u0142abun, W., Karczmarczyk, A., W\u0105tr\u00f3bski, J., and Jankowski, J. (2018, January 18\u201321). Handling data uncertainty in decision making with COMET. Proceedings of the 2018 IEEE Symposium Series on Computational Intelligence (SSCI), Bangalore, India.","DOI":"10.1109\/SSCI.2018.8628934"},{"key":"ref_88","doi-asserted-by":"crossref","unstructured":"Faizi, S., Sa\u0142abun, W., Rashid, T., Zafar, S., and W\u0105tr\u00f3bski, J. (2020). Intuitionistic fuzzy sets in multi-criteria group decision making problems using the characteristic objects method. Symmetry, 12.","DOI":"10.3390\/sym12091382"},{"key":"ref_89","first-page":"536492","article-title":"Identification of a multicriteria decision-making model using the characteristic objects method","volume":"2014","author":"Piegat","year":"2014","journal-title":"Appl. Comput. Intell. Soft Comput."},{"key":"ref_90","doi-asserted-by":"crossref","unstructured":"Papathanasiou, J., and Ploskas, N. (2018). Multiple Criteria Decision Aid, Springer.","DOI":"10.1007\/978-3-319-91648-4"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"13051","DOI":"10.1016\/j.eswa.2012.05.056","article-title":"A state-of the-art survey of TOPSIS applications","volume":"39","author":"Behzadian","year":"2012","journal-title":"Expert Syst. Appl."},{"key":"ref_92","doi-asserted-by":"crossref","unstructured":"Sa\u0142abun, W., and Urbaniak, K. (2020). A new coefficient of rankings similarity in decision-making problems. Lecture Notes in Computer Science, Proceedings of the International Conference on Computational Science, Amsterdam, The Netherlands, 3\u20135 June 2020, Springer.","DOI":"10.1007\/978-3-030-50417-5_47"},{"key":"ref_93","doi-asserted-by":"crossref","unstructured":"Shekhovtsov, A., Kozlov, V., Nosov, V., and Sa\u0142abun, W. (2020). Efficiency of Methods for Determining the Relevance of Criteria in Sustainable Transport Problems: A Comparative Case Study. Sustainability, 12.","DOI":"10.3390\/su12197915"},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"3718","DOI":"10.1016\/j.procs.2020.09.015","article-title":"Do distance-based multi-criteria decision analysis methods create similar rankings?","volume":"176","author":"Shekhovtsov","year":"2020","journal-title":"Procedia Comput. Sci."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"3730","DOI":"10.1016\/j.procs.2020.09.014","article-title":"A comparative case study of the VIKOR and TOPSIS rankings similarity","volume":"176","author":"Shekhovtsov","year":"2020","journal-title":"Procedia Comput. Sci."},{"key":"ref_96","unstructured":"Parrish, R. (2019, November 28). The Advantages of Short Soccer Players. Available online: http:\/\/www.sportsrec.com."},{"key":"ref_97","unstructured":"Eskilson, J. (2019, November 28). En Route: The Golden age Group of Player Development. Available online: http:\/\/\/www.goal.com."},{"key":"ref_98","unstructured":"Hughes, C. (1990). The Winning Formula: The Football Association Book of Soccer Tactics and Skills, William Collins Sons e Co. Ltd."},{"key":"ref_99","first-page":"806","article-title":"Goal scoring in soccer: A polar coordinate analysis of motor skills used by Lionel Messi","volume":"7","author":"Barreira","year":"2016","journal-title":"Front. Psychol."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"808","DOI":"10.1016\/j.humov.2013.06.002","article-title":"Match performance and physical capacity of players in the top three competitive standards of English professional soccer","volume":"32","author":"Bradley","year":"2013","journal-title":"Hum. Mov. Sci."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1123\/jsep.30.1.95","article-title":"Game management, context effects, and calibration: The case of yellow cards in soccer","volume":"30","author":"Unkelbach","year":"2008","journal-title":"J. Sport Exerc. Psychol."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"149","DOI":"10.31181\/dmame2003149z","article-title":"Objective methods for determining criteria weight coefficients: A modification of the CRITIC method","volume":"3","year":"2020","journal-title":"Decis. Mak. Appl. Manag. Eng."},{"key":"ref_103","unstructured":"Guardian, T. (2019, December 20). Diego Maradona: Lionel Messi Winning Golden Ball is a \u2018Marketing Plan\u2019. Available online: http:\/\/www.theguardian.com."},{"key":"ref_104","unstructured":"Macvillano (2019, December 20). Jordi Alba\u2019s Harsh Criticism of the Golden Ball. Available online: http:\/\/fcbarcelonasport.com."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/12\/2029\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:42:16Z","timestamp":1760179336000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/12\/2029"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,8]]},"references-count":104,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["sym12122029"],"URL":"https:\/\/doi.org\/10.3390\/sym12122029","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,8]]}}}