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Towards Data-Based Assessment of Individual Tactics Skills in Team Sports Based on Fuzzy Petri Nets
8th Vienna International Conference on Mathematical Modelling 8th Vienna International Conference on Mathematical Available onlineModelling at Vienna, www.sciencedirect.com February - 20, 2015. Vienna University of Technology, 8th Vienna18International Conference on Mathematical Modelling February 18 - 20, 2015. Vienna University of Technology, Vienna, Austria February 18 - 20, 2015. Vienna University of Technology, Vienna, Austria Austria
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IFAC-PapersOnLine 48-1 (2015) 782–783
Towards Data-Based Assessment of Individual Tactics Skills Towards Data-Based Assessment of Individual Tactics Skills Towards in Data-Based Assessment of Individual Tactics Skills Team Sports Based on Fuzzy Petri Nets in Team Sports Based on Fuzzy Petri Nets in Team Sports Based on Fuzzy Petri Nets Andrea Serafini*, Roland Leser**, Andrea Roland Leser**, Andrea Serafini*, Serafini*, Roland Leser**, Thomas Hoch***, Bernhard Moser***, Arnold Baca** Thomas Hoch***, Bernhard Moser***, Thomas Hoch***, Bernhard Moser***, Arnold Arnold Baca** Baca** *Research Institute of Symbolic Computation, Hagenberg, Austria; *Research of Computation, *Research Institute Institute of Symbolic Symbolic Computation, Hagenberg, Hagenberg, Austria; Austria; (e-mail: [email protected]). (e-mail: [email protected]). (e-mail: [email protected]). **Centre of Sport Science and University Sports, Universtiy of Vienna (e-mail: [email protected]) **Centre and University Sports, of Vienna [email protected]) **Centre of of Sport Sport Science Science *** and Software UniversityCompetence Sports, Universtiy Universtiy of Vienna (e-mail: (e-mail: [email protected]) Center Hagenberg GmbH, *** Software Competence Center Hagenberg GmbH, *** Software Competence Center Hagenberg GmbH, Austria, (e-mail: bernhard.moser,[email protected]) Austria, Austria, (e-mail: (e-mail: bernhard.moser,[email protected]) bernhard.moser,[email protected]) © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. The problem of objectively assessing activity patterns of individual players in team sports in terms of tactics skills is addressed The problem objectively assessing activity patterns of players in sports in of skills addressed Theemploying problem of ofconcepts objectively assessing activity patterns of individual individual players in team team sports in terms terms of tactics tactics skills is ishigh addressed by from fuzzy logics and state-transition graph models. This approach aims at providing level by employing concepts from fuzzy logics and state-transition graph models. This approach aims at providing high level by employingof concepts from fuzzy logics and state-transition graph models. This approach aims (2013) at providing high level descriptions activity patterns based on local positioning measurements. Mackenzie & Cushion conclude in their descriptions of activity patterns based on local positioning measurements. Mackenzie & Cushion (2013) conclude in descriptions ofabout activity patterns based onanalysis local positioning measurements. Mackenzie & Cushion (2013) conclude in their their critical review current performance (PA) research that variables are often investigated as a result of availability critical review about performance analysis (PA) that are investigated as result of critical review about current current performance analysis (PA) research research that variables variables are often often as aauseful resultinformation of availability availability rather than to develop a deeper understanding of performance. Therefore, PA studies ofteninvestigated fail to provide for rather than develop aa deeper understanding of performance. Therefore, PA often provide useful information for rather than to to practice develop due deeper performance. Therefore, PA studies studies often fail failinto toteam provide useful for the coaching to theunderstanding multifaceted, of complex and largely unpredictable behaviour sports like information football. In the the coaching practice due to complex and unpredictable behaviour in team like football. In the the coaching practice dueapproaches to the the multifaceted, multifaceted, and largely largely unpredictable team sports sports football. In and the author’s opinion holistic are neededcomplex that include more naturalistic and behaviour qualitativeinmethods such like as case studies author’s opinion holistic approaches are needed that include more naturalistic and qualitative methods such as case studies and author’s opinion holistic approaches are needed that includeapproach more naturalistic and qualitative methods such as case studies and interviews. The overall goal is to develop a data-based based on position and tracking data provided by local interviews. The is develop aa data-based approach based on position and data provided by local interviews. measurement The overall overall goal goal is to to(see, develop data-based approach based & onCushion position(2013), and tracking tracking data providedthat byallows local positioning systems e.g., Leser et al. (2011), Mackenzie Ogris et al. (2012)) positioning measurement systems (see, e.g., Leser et al. (2011), Mackenzie & Cushion (2013), Ogris et al. (2012)) that allows positioning measurement systems based (see, e.g., Leser et al. (2011), Mackenzie & Cushion (2013), semi-structured Ogris et al. (2012)) that allows the qualification of assessments on measurements. Tactical assessments are typically and, above all, the of based on Tactical assessments are semi-structured and, all, the qualification qualification of assessments assessments based on measurements. measurements. Tactical assessments are typically typically semi-structured and, above above all, expressed in qualitative, vague and imprecisely defined linguistic concepts. Moreover, often such assessment statements rely on expressed in qualitative, vague and imprecisely defined linguistic concepts. Moreover, often such assessment statements rely on expressedcommon-sense in qualitative, and vague and imprecisely defined linguistic concepts. Moreover, oftenthe such assessment statements rely on implicit intuitive reasoning assumptions. Therefore, we postulate that knowledge representation has to implicit common-sense and intuitive reasoning assumptions. Therefore, we postulate that the knowledge representation has implicit common-sense and intuitiveK1) reasoning assumptions. we related postulate the knowledge has to to satisfy the following properties: the vagueness and Therefore, imprecision to that temporal, spatial representation and spatio-temporal satisfy the properties: K1) the and related to temporal, spatial and satisfy the following following K1) the vagueness vagueness and imprecision imprecision and spatio-temporal spatio-temporal relationships have to beproperties: expressed in a form that is appropriate for human related experts to andtemporal, users; K2)spatial the knowledge base design relationships have to in that is for experts and K2) the base design relationships to be be expressed expressed in aa form form that scenarios is appropriate appropriate for human human expertslevels; and users; users; the knowledge knowledge design should allow have a hierarchical representation of the at different abstraction K3) K2) the design has to bebase based on a should allow a hierarchical representation of the scenarios at different abstraction levels; K3) the design has to be should allow aformalism hierarchical representation of the scenarios at different abstraction levels; K3) the design has tospatio-temporal be based based on on aa well-defined and semantics that allows a formal analysis of different spatial, temporal and well-defined formalism and that aa formal of different spatial, temporal and well-defined among formalism and semantics semantics that allows allows formal analysis analysis offrom different spatial, temporal and spatio-temporal spatio-temporal relationships the objects and conclusions based thereupon. Further, the point of view of feasibility and practical relationships among the objects and conclusions based thereupon. Further, from the point of view of feasibility and practical relationshipsweamong the objects and conclusions based thereupon. Further, from the point of view of feasibility and paradigm practical usefulness, postulate that the design of the knowledge base allows D1) a modular, object-oriented programming usefulness, we postulate that the design of the knowledge base allows D1) a modular, object-oriented programming paradigm usefulness, we postulate that the design of the knowledge base allows D1) a modular, object-oriented programming paradigm based approach in the sense that the overall results from designing the knowledge bases for each player based in the that the knowledge base results from designing the knowledge bases each based approach approachand, in in thea sense sense that thetheoverall overall knowledge base results from designing the knowledge basesoffor for each player player independently second step, interaction options between the players, D2) an efficient evaluation hypotheses for independently and, second step, interaction options between D2) an efficient of for independently and, in in aaD3) second step, the the at interaction options between the the players, players, D2) anknowledge efficient evaluation evaluation of hypotheses hypotheses for real-time applications, to visualize least small or moderate-sized parts of the base by intuitive graphical real-time applications, D3) to visualize at least small or moderate-sized parts of the knowledge base by intuitive graphical real-time applications, representation models. D3) to visualize at least small or moderate-sized parts of the knowledge base by intuitive graphical representation representation models. models. Our approach is inspired by the philosophy of Carl Adam Petri (Petri (1962)) by looking for ways to decompose complex Our approach is inspired the philosophy of Petri (Petri (1962)) for to complex Our approach inspiredofby by thecomplex philosophy of Carl Carl Adam Adam Petriunits. (Petri (1962)) by by looking looking for ways waysled to todecompose decompose complex processes into ais scheme less state-transition process Mathematically, this approach the introduction of processes into a scheme of less complex state-transition process units. Mathematically, this approach led to the introduction of processes into its a scheme less complex state-transition process units. Mathematically, this approach ledexample, to the introduction of Petri nets and variants,ofwhich are directed bipartite graphs made up by state and transition nodes. For in a chemical Petri nets and which are bipartite graphs made by transition nodes. example, in chemical Petri netschemical and its its variants, variants, which are directed directedby bipartite graphschemical made up upreactions by state state and and transition nodes. For For between example,the in aastates. chemical process substances are represented states while are treated as transitions The process chemical substances are represented by states while chemical reactions are treated as transitions between the states. The process chemical are represented by states chemical reactions are treated transitions the states. dynamics of such substances nets are modelled by so-called tokenswhile which are handed over from states as to other statesbetween via transition rules.The As dynamics of such are by tokens which are handed over to via rules. dynamics such nets netsexecutable are modelled modelled by so-called so-called which arefor handed over from from states states to other other states states via transition transition rules. As As a formal, of graphical, technique Petritokens nets are used the specification, modelling and analysis of concurrent, aa formal, executable technique nets used specification, modelling analysis of concurrent, formal, graphical, graphical, executable technique Petri Petri nets are are(1998)). used for forForthe the modelling and and analysis discrete-event dynamic systems (Rozenburg & Engelfriet an specification, overview of applications see, e.g., Chenofetconcurrent, al. (1990), discrete-event dynamic systems (Rozenburg & Engelfriet (1998)). For an overview of applications see, e.g., Chen et al. discrete-event systems Engelfriet (1998)). Forand an overview of(Jensen applications see,Cardoso e.g., Chen al. (1990), (1990), Christensen & dynamic Kristensen (2003)(Rozenburg or Girault &&Valk (2003). Petri nets its variants (1991), et alet(1996), Pan Christensen & (2003) or & Valk Petri and (Jensen Cardoso et al (1996), Pan Christensen & Kristensen Kristensen (2003) or Girault Girault & outlined Valk (2003). (2003). Petri nets nets[K1]-[K3] and its its variants variants (Jensen (1991), (1991), Cardoso (1996),event Pan & Sun (2007), Jensen et al. (2007)) meet the requirements and [D1]-[D3]. However, sucheta al discrete & Sun Jensen et meet the requirements [K1]-[K3] and [D1]-[D3]. However, such aa discrete & Sun (2007), (2007), et al. al. (2007)) (2007)) the outlined outlined [K1]-[K3] andsystems [D1]-[D3]. However, discrete event event dynamic systemJensen formalism can onlymeet be applied in a requirements reasonable way when the behaviour can such be decomposed into dynamic system formalism can only be applied in a reasonable way when the systems behaviour can be decomposed into dynamic system formalism can only be applied in transitions. a reasonable way whenthat theallsystems behaviour and can conditions be decomposed separate states with well-defined conditions for state This means states, transitions need tointo be separate states with well-defined conditions for state This that all transitions and conditions need be separate withand well-defined conditions forbrings state transitions. transitions. This means means thatwhat all states, states, transitions and and conditions needinto tothe be known instates advance be well defined. This us to the central question are adequate states transitions known in advance and be defined. This brings us the central question what adequate states and transitions in the known andLet beuswell well defined. us to to of theevents central whatofare are states in For the context in of advance team sport. point out thatThis the brings discreteness is question also a matter theadequate abstraction leveland andtransitions the context. context of team sport. Let us point out that the discreteness of events is also a matter of the abstraction level and the context. For context sport.of Let us possession point out that of events also a matter of the abstraction level and thee.g., context. example,ofatteam the level ball wethe candiscreteness easily decompose theisscenario into the players’ positions (states), playerFor A example, at the level possession we can easily decompose the scenario into positions (states), e.g., player example, theapproaching level of of ball ballthe possession we B can decompose into the the players’ players’ positions (states), e.g., player player A A possesses at ball goal, player is easily approaching playerthe A,scenario some interactions (transition), e.g. duel between A possesses ball approaching the goal, player B approaching player A, some interactions (transition), e.g. duel between player A possesses ball leads approaching goal, player B is isthe approaching player some interactions (transition), e.g. duel between A and B, which to new the states, e.g., B wins ball. On this levelA,the process of possessing, losing and winning theplayer ball can and B, to states, e.g., B the ball. On this the of losing and winning ball and B, which which leads leads to new new B wins winsand theone ball.can Onmake this level level the process process of possessing, possessing, losing the andnumber winningofthe the ball can can be adequately described by states, a Petrie.g., net model statistical evaluations by e.g. counting successful be adequately described by a Petri net model and one can make statistical evaluations by e.g. counting the number of successful be adequately described by a Petri netevaluations model and one can make evaluations by e.g.circumstances counting the number of successful duels of a player. Obviously, such become morestatistical informative when taking and spatio-temporal duels of Obviously, such become more informative when taking circumstances and duels of aa player. player. such evaluations evaluations become informative when circumstances and spatio-temporal spatio-temporal characteristics of theObviously, duels into account, e.g., whether theremore is much pressing or not;taking duration of the duel; speed of the players; characteristics of the duels into account, e.g., whether there is much pressing or not; duration of the duel; speed of the characteristics theetc. duels into account, e.g., whether there is much or not; duration the duel; speed the players; players; location on the of field Pressing is an example for an attribute whosepressing occurrence is not crisplyofdefined rather it isoffuzzy (Zadeh location on the field etc. Pressing is an example for an attribute whose occurrence is not crisply defined rather it is fuzzy (Zadeh location on the field etc. Pressing is an example for an attribute whose is not crisply defined rather it isinfuzzy (Zadeh (1965), Zadeh (1975)). Also, though spatio-temporal variables like occurrence location, duration, speed etc. are crisp nature, for (1965), Zadeh (1975)). Also, though spatio-temporal variables like location, duration, speed etc. in for (1965), (1975)). though purposes spatio-temporal location, duration, speedinformative etc. are are crisp crisp in nature, nature, for statisticalZadeh evaluation and Also, interpretation clustersvariables like “shortlike versus long duel” are more in order to provide statistical statistical evaluation evaluation and and interpretation interpretation purposes purposes clusters clusters like like “short “short versus versus long long duel” duel” are are more more informative informative in in order order to to provide provide
2405-8963 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review©under of International Federation of Automatic Copyright 2015,responsibility IFAC 782Control. Copyright © 2015, IFAC 782 10.1016/j.ifacol.2015.05.183 Copyright © 2015, IFAC 782
MATHMOD 2015 February 18 - 20, 2015. Vienna, Austria Andrea Serafini et al. / IFAC-PapersOnLine 48-1 (2015) 782–783
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discrete distinguishable descriptions of situations. This motivates the introduction of fuzzy spatio-temporal relations. Ribaric & Hrkac (2012) proposes a high-level Petri net in the context of robot soccer where the states are qualified by evaluating fuzzy spatio-temporal relations. We extend this concept by taking fuzzy context attributes into account and discuss its feasibility and usefulness. In particular, we address the question whether such a context-sensitive spatio-temporal modelling approach is feasible for real soccer scenarios from the point of view of setting up and running such models from a practical engineering point of view and meeting the requirements [K1]-[K3] and [D1]-[D3]. On a theoretical level, however, the feasibility issue also comprises questions regarding verifiability, completeness, stability, expressiveness and model-calibration. In a first step we tackle these questions by specifying experimental test scenarios that take local positioning measurement data and human trainer based assessments into account. In a second step we conduct a semi-formal analysis based on simulations. For this purpose, oneversus-one football games with defined game situations are considered in order to generate a representative quantity of data sets. Simultaneously, expert oriented judgements of individual player performances are collected from coaches. By means of interviews and content analyses the criteria for the expert judgements are gathered (Tenenbaum & Driscoll (2005)). As an example, for the action “pass” the criteria preparation, decision and quality as well as the difficulty of the situation (defined by the opponent pressing and the size of the passing gap) are considered. Keywords: Discrete and Discrete-Event Systems, Discretisation of Continuous Systems, Modelling Fuzzy Systems and Fuzzy Modelling, Petri Nets, Fitting Models to Real Processes, Uncertainties in Systems and in Modelling, Multiscale Modelling
REFERENCES Alvarez-Alvarez, A., Trivino, G., Cordon, O. (2012). Human Gait Modeling Using a Genetic Fuzzy Finite State Machine. In Proc. of 2012 IEEE Transactions on Fuzzy Systems, 20(2), pp. 205-223. Christensen, S., Kristensen, L.M. (2003). State Space Analysis of Hierarchical Coloured Petri Nets. In W.v.d. Aalst, J.-M. Colom, F. Kordon, G. Kotsis, and D. Moldt. Petri Net Approaches for Modelling and Validation. LINCOM Studies in Computer Science, No. 1, pp. 1-16. S. M. Chen, J. S. Ke, J. F. Chang (1990). Knowledge representation using fuzzy Petri nets, IEEE Trans. Knowledge and Data Engineering, vol. 2, no. 3, pp. 311-319. J. Cardoso, R. Valette, D. Dubois (1996). Fuzzy Petri net: An overview, In Proc. 13th IFAC World Congr., pp. 443-448. Jensen, K. (1991). Coloured Petri Nets: A High-level Language for System Design and Analysis. In G. Rozenberg (Ed.): Advances in Petri Nets 1990, Lecture Notes in Computer Science, vol. 483, Springer-Verlag, pp. 342-416. Jensen, K., Kristensen, L. M., Wells, L. M. (2007). Coloured Petri Nets and CPN Tools for Modelling and Validation of Concurrent Systems, International Journal on Software Tools for Technology Transfer, vol. 9, nr. 3/4, pp. 213-254. C. Girault, R. Valk (2003). Petri Nets for Systems Engineering. Springer-Verlag. Leser, R., Baca, A., Ogris, G. (2011). Local Positioning Systems in (Game) Sports. Sensors, 11, pp. 9778-9797. Mackenzie, R., Cushion, C. (2013). Accuracy of the LPM tracking system considering dynamic position changes. Journal of Sports Sciences, 31, pp. 639-676. Ogris, G., Leser, R., Horsak, B., Kornfeind, P., Heller, M., Baca, A. (2012). Accuracy of the LPM tracking system considering dynamic position changes. Journal of Sports Sciences, 30, pp. 1503-1511. Petri, C.A. (1962). Kommunikation mit Automaten. Dissertation, Institut für instrumentelle Mathematik der Universität Bonn. H. Pan, J. Sun (2007): Complex Knowledge System Modeling Based on Hierarchical Fuzzy Petri Net. In Proc. 2007 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology - Workshops (WI-IATW '07). IEEE Computer Society, Washington, DC, USA, pp. 31-34. G. Rozenburg, J. Engelfriet (1998). Elementary Net Systems, in: W. Reisig, G. Rozenberg (Eds.), Lectures on Petri Nets I: Basic Models - Advances in Petri Nets, volume 1491 of Lecture Notes in Computer Science, Springer, pp. 12-121. S. Ribaric, T. Hrkac (2012). A model of fuzzy spatio-temporal knowledge representation and reasoning based on high-level Petri nets, Information Systems, Volume 37, Issue 3, pp. 238-256. Tenenbaum, G., Driscoll, M. (2005). Methods of Research in Sport Sciences: Quantitative and Qualitative Approaches. Oxford: Meyer & Meyer. Zadeh, L. A. (1965). Fuzzy Sets. Information and Control, 8(3), pp. 338-353. Zadeh, L. A. (1975). Fuzzy Logic and Approximate Reasoning, Synthese, 30(3-4), pp. 407-428.
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Towards Data-Based Assessment of Individual Tactics Skills Towards Data-Based Assessment of Individual Tactics Skills Towards in Data-Based Assessment of Individual Tactics Skills Team Sports Based on Fuzzy Petri Nets in Team Sports Based on Fuzzy Petri Nets in Team Sports Based on Fuzzy Petri Nets Andrea Serafini*, Roland Leser**, Andrea Roland Leser**, Andrea Serafini*, Serafini*, Roland Leser**, Thomas Hoch***, Bernhard Moser***, Arnold Baca** Thomas Hoch***, Bernhard Moser***, Thomas Hoch***, Bernhard Moser***, Arnold Arnold Baca** Baca** *Research Institute of Symbolic Computation, Hagenberg, Austria; *Research of Computation, *Research Institute Institute of Symbolic Symbolic Computation, Hagenberg, Hagenberg, Austria; Austria; (e-mail: [email protected]). (e-mail: [email protected]). (e-mail: [email protected]). **Centre of Sport Science and University Sports, Universtiy of Vienna (e-mail: [email protected]) **Centre and University Sports, of Vienna [email protected]) **Centre of of Sport Sport Science Science *** and Software UniversityCompetence Sports, Universtiy Universtiy of Vienna (e-mail: (e-mail: [email protected]) Center Hagenberg GmbH, *** Software Competence Center Hagenberg GmbH, *** Software Competence Center Hagenberg GmbH, Austria, (e-mail: bernhard.moser,[email protected]) Austria, Austria, (e-mail: (e-mail: bernhard.moser,[email protected]) bernhard.moser,[email protected]) © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. The problem of objectively assessing activity patterns of individual players in team sports in terms of tactics skills is addressed The problem objectively assessing activity patterns of players in sports in of skills addressed Theemploying problem of ofconcepts objectively assessing activity patterns of individual individual players in team team sports in terms terms of tactics tactics skills is ishigh addressed by from fuzzy logics and state-transition graph models. This approach aims at providing level by employing concepts from fuzzy logics and state-transition graph models. This approach aims at providing high level by employingof concepts from fuzzy logics and state-transition graph models. This approach aims (2013) at providing high level descriptions activity patterns based on local positioning measurements. Mackenzie & Cushion conclude in their descriptions of activity patterns based on local positioning measurements. Mackenzie & Cushion (2013) conclude in descriptions ofabout activity patterns based onanalysis local positioning measurements. Mackenzie & Cushion (2013) conclude in their their critical review current performance (PA) research that variables are often investigated as a result of availability critical review about performance analysis (PA) that are investigated as result of critical review about current current performance analysis (PA) research research that variables variables are often often as aauseful resultinformation of availability availability rather than to develop a deeper understanding of performance. Therefore, PA studies ofteninvestigated fail to provide for rather than develop aa deeper understanding of performance. Therefore, PA often provide useful information for rather than to to practice develop due deeper performance. Therefore, PA studies studies often fail failinto toteam provide useful for the coaching to theunderstanding multifaceted, of complex and largely unpredictable behaviour sports like information football. In the the coaching practice due to complex and unpredictable behaviour in team like football. In the the coaching practice dueapproaches to the the multifaceted, multifaceted, and largely largely unpredictable team sports sports football. In and the author’s opinion holistic are neededcomplex that include more naturalistic and behaviour qualitativeinmethods such like as case studies author’s opinion holistic approaches are needed that include more naturalistic and qualitative methods such as case studies and author’s opinion holistic approaches are needed that includeapproach more naturalistic and qualitative methods such as case studies and interviews. The overall goal is to develop a data-based based on position and tracking data provided by local interviews. The is develop aa data-based approach based on position and data provided by local interviews. measurement The overall overall goal goal is to to(see, develop data-based approach based & onCushion position(2013), and tracking tracking data providedthat byallows local positioning systems e.g., Leser et al. (2011), Mackenzie Ogris et al. (2012)) positioning measurement systems (see, e.g., Leser et al. (2011), Mackenzie & Cushion (2013), Ogris et al. (2012)) that allows positioning measurement systems based (see, e.g., Leser et al. (2011), Mackenzie & Cushion (2013), semi-structured Ogris et al. (2012)) that allows the qualification of assessments on measurements. Tactical assessments are typically and, above all, the of based on Tactical assessments are semi-structured and, all, the qualification qualification of assessments assessments based on measurements. measurements. Tactical assessments are typically typically semi-structured and, above above all, expressed in qualitative, vague and imprecisely defined linguistic concepts. Moreover, often such assessment statements rely on expressed in qualitative, vague and imprecisely defined linguistic concepts. Moreover, often such assessment statements rely on expressedcommon-sense in qualitative, and vague and imprecisely defined linguistic concepts. Moreover, oftenthe such assessment statements rely on implicit intuitive reasoning assumptions. Therefore, we postulate that knowledge representation has to implicit common-sense and intuitive reasoning assumptions. Therefore, we postulate that the knowledge representation has implicit common-sense and intuitiveK1) reasoning assumptions. we related postulate the knowledge has to to satisfy the following properties: the vagueness and Therefore, imprecision to that temporal, spatial representation and spatio-temporal satisfy the properties: K1) the and related to temporal, spatial and satisfy the following following K1) the vagueness vagueness and imprecision imprecision and spatio-temporal spatio-temporal relationships have to beproperties: expressed in a form that is appropriate for human related experts to andtemporal, users; K2)spatial the knowledge base design relationships have to in that is for experts and K2) the base design relationships to be be expressed expressed in aa form form that scenarios is appropriate appropriate for human human expertslevels; and users; users; the knowledge knowledge design should allow have a hierarchical representation of the at different abstraction K3) K2) the design has to bebase based on a should allow a hierarchical representation of the scenarios at different abstraction levels; K3) the design has to be should allow aformalism hierarchical representation of the scenarios at different abstraction levels; K3) the design has tospatio-temporal be based based on on aa well-defined and semantics that allows a formal analysis of different spatial, temporal and well-defined formalism and that aa formal of different spatial, temporal and well-defined among formalism and semantics semantics that allows allows formal analysis analysis offrom different spatial, temporal and spatio-temporal spatio-temporal relationships the objects and conclusions based thereupon. Further, the point of view of feasibility and practical relationships among the objects and conclusions based thereupon. Further, from the point of view of feasibility and practical relationshipsweamong the objects and conclusions based thereupon. Further, from the point of view of feasibility and paradigm practical usefulness, postulate that the design of the knowledge base allows D1) a modular, object-oriented programming usefulness, we postulate that the design of the knowledge base allows D1) a modular, object-oriented programming paradigm usefulness, we postulate that the design of the knowledge base allows D1) a modular, object-oriented programming paradigm based approach in the sense that the overall results from designing the knowledge bases for each player based in the that the knowledge base results from designing the knowledge bases each based approach approachand, in in thea sense sense that thetheoverall overall knowledge base results from designing the knowledge basesoffor for each player player independently second step, interaction options between the players, D2) an efficient evaluation hypotheses for independently and, second step, interaction options between D2) an efficient of for independently and, in in aaD3) second step, the the at interaction options between the the players, players, D2) anknowledge efficient evaluation evaluation of hypotheses hypotheses for real-time applications, to visualize least small or moderate-sized parts of the base by intuitive graphical real-time applications, D3) to visualize at least small or moderate-sized parts of the knowledge base by intuitive graphical real-time applications, representation models. D3) to visualize at least small or moderate-sized parts of the knowledge base by intuitive graphical representation representation models. models. Our approach is inspired by the philosophy of Carl Adam Petri (Petri (1962)) by looking for ways to decompose complex Our approach is inspired the philosophy of Petri (Petri (1962)) for to complex Our approach inspiredofby by thecomplex philosophy of Carl Carl Adam Adam Petriunits. (Petri (1962)) by by looking looking for ways waysled to todecompose decompose complex processes into ais scheme less state-transition process Mathematically, this approach the introduction of processes into a scheme of less complex state-transition process units. Mathematically, this approach led to the introduction of processes into its a scheme less complex state-transition process units. Mathematically, this approach ledexample, to the introduction of Petri nets and variants,ofwhich are directed bipartite graphs made up by state and transition nodes. For in a chemical Petri nets and which are bipartite graphs made by transition nodes. example, in chemical Petri netschemical and its its variants, variants, which are directed directedby bipartite graphschemical made up upreactions by state state and and transition nodes. For For between example,the in aastates. chemical process substances are represented states while are treated as transitions The process chemical substances are represented by states while chemical reactions are treated as transitions between the states. The process chemical are represented by states chemical reactions are treated transitions the states. dynamics of such substances nets are modelled by so-called tokenswhile which are handed over from states as to other statesbetween via transition rules.The As dynamics of such are by tokens which are handed over to via rules. dynamics such nets netsexecutable are modelled modelled by so-called so-called which arefor handed over from from states states to other other states states via transition transition rules. As As a formal, of graphical, technique Petritokens nets are used the specification, modelling and analysis of concurrent, aa formal, executable technique nets used specification, modelling analysis of concurrent, formal, graphical, graphical, executable technique Petri Petri nets are are(1998)). used for forForthe the modelling and and analysis discrete-event dynamic systems (Rozenburg & Engelfriet an specification, overview of applications see, e.g., Chenofetconcurrent, al. (1990), discrete-event dynamic systems (Rozenburg & Engelfriet (1998)). For an overview of applications see, e.g., Chen et al. discrete-event systems Engelfriet (1998)). Forand an overview of(Jensen applications see,Cardoso e.g., Chen al. (1990), (1990), Christensen & dynamic Kristensen (2003)(Rozenburg or Girault &&Valk (2003). Petri nets its variants (1991), et alet(1996), Pan Christensen & (2003) or & Valk Petri and (Jensen Cardoso et al (1996), Pan Christensen & Kristensen Kristensen (2003) or Girault Girault & outlined Valk (2003). (2003). Petri nets nets[K1]-[K3] and its its variants variants (Jensen (1991), (1991), Cardoso (1996),event Pan & Sun (2007), Jensen et al. (2007)) meet the requirements and [D1]-[D3]. However, sucheta al discrete & Sun Jensen et meet the requirements [K1]-[K3] and [D1]-[D3]. However, such aa discrete & Sun (2007), (2007), et al. al. (2007)) (2007)) the outlined outlined [K1]-[K3] andsystems [D1]-[D3]. However, discrete event event dynamic systemJensen formalism can onlymeet be applied in a requirements reasonable way when the behaviour can such be decomposed into dynamic system formalism can only be applied in a reasonable way when the systems behaviour can be decomposed into dynamic system formalism can only be applied in transitions. a reasonable way whenthat theallsystems behaviour and can conditions be decomposed separate states with well-defined conditions for state This means states, transitions need tointo be separate states with well-defined conditions for state This that all transitions and conditions need be separate withand well-defined conditions forbrings state transitions. transitions. This means means thatwhat all states, states, transitions and and conditions needinto tothe be known instates advance be well defined. This us to the central question are adequate states transitions known in advance and be defined. This brings us the central question what adequate states and transitions in the known andLet beuswell well defined. us to to of theevents central whatofare are states in For the context in of advance team sport. point out thatThis the brings discreteness is question also a matter theadequate abstraction leveland andtransitions the context. context of team sport. Let us point out that the discreteness of events is also a matter of the abstraction level and the context. For context sport.of Let us possession point out that of events also a matter of the abstraction level and thee.g., context. example,ofatteam the level ball wethe candiscreteness easily decompose theisscenario into the players’ positions (states), playerFor A example, at the level possession we can easily decompose the scenario into positions (states), e.g., player example, theapproaching level of of ball ballthe possession we B can decompose into the the players’ players’ positions (states), e.g., player player A A possesses at ball goal, player is easily approaching playerthe A,scenario some interactions (transition), e.g. duel between A possesses ball approaching the goal, player B approaching player A, some interactions (transition), e.g. duel between player A possesses ball leads approaching goal, player B is isthe approaching player some interactions (transition), e.g. duel between A and B, which to new the states, e.g., B wins ball. On this levelA,the process of possessing, losing and winning theplayer ball can and B, to states, e.g., B the ball. On this the of losing and winning ball and B, which which leads leads to new new B wins winsand theone ball.can Onmake this level level the process process of possessing, possessing, losing the andnumber winningofthe the ball can can be adequately described by states, a Petrie.g., net model statistical evaluations by e.g. counting successful be adequately described by a Petri net model and one can make statistical evaluations by e.g. counting the number of successful be adequately described by a Petri netevaluations model and one can make evaluations by e.g.circumstances counting the number of successful duels of a player. Obviously, such become morestatistical informative when taking and spatio-temporal duels of Obviously, such become more informative when taking circumstances and duels of aa player. player. such evaluations evaluations become informative when circumstances and spatio-temporal spatio-temporal characteristics of theObviously, duels into account, e.g., whether theremore is much pressing or not;taking duration of the duel; speed of the players; characteristics of the duels into account, e.g., whether there is much pressing or not; duration of the duel; speed of the characteristics theetc. duels into account, e.g., whether there is much or not; duration the duel; speed the players; players; location on the of field Pressing is an example for an attribute whosepressing occurrence is not crisplyofdefined rather it isoffuzzy (Zadeh location on the field etc. Pressing is an example for an attribute whose occurrence is not crisply defined rather it is fuzzy (Zadeh location on the field etc. Pressing is an example for an attribute whose is not crisply defined rather it isinfuzzy (Zadeh (1965), Zadeh (1975)). Also, though spatio-temporal variables like occurrence location, duration, speed etc. are crisp nature, for (1965), Zadeh (1975)). Also, though spatio-temporal variables like location, duration, speed etc. in for (1965), (1975)). though purposes spatio-temporal location, duration, speedinformative etc. are are crisp crisp in nature, nature, for statisticalZadeh evaluation and Also, interpretation clustersvariables like “shortlike versus long duel” are more in order to provide statistical statistical evaluation evaluation and and interpretation interpretation purposes purposes clusters clusters like like “short “short versus versus long long duel” duel” are are more more informative informative in in order order to to provide provide
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discrete distinguishable descriptions of situations. This motivates the introduction of fuzzy spatio-temporal relations. Ribaric & Hrkac (2012) proposes a high-level Petri net in the context of robot soccer where the states are qualified by evaluating fuzzy spatio-temporal relations. We extend this concept by taking fuzzy context attributes into account and discuss its feasibility and usefulness. In particular, we address the question whether such a context-sensitive spatio-temporal modelling approach is feasible for real soccer scenarios from the point of view of setting up and running such models from a practical engineering point of view and meeting the requirements [K1]-[K3] and [D1]-[D3]. On a theoretical level, however, the feasibility issue also comprises questions regarding verifiability, completeness, stability, expressiveness and model-calibration. In a first step we tackle these questions by specifying experimental test scenarios that take local positioning measurement data and human trainer based assessments into account. In a second step we conduct a semi-formal analysis based on simulations. For this purpose, oneversus-one football games with defined game situations are considered in order to generate a representative quantity of data sets. Simultaneously, expert oriented judgements of individual player performances are collected from coaches. By means of interviews and content analyses the criteria for the expert judgements are gathered (Tenenbaum & Driscoll (2005)). As an example, for the action “pass” the criteria preparation, decision and quality as well as the difficulty of the situation (defined by the opponent pressing and the size of the passing gap) are considered. Keywords: Discrete and Discrete-Event Systems, Discretisation of Continuous Systems, Modelling Fuzzy Systems and Fuzzy Modelling, Petri Nets, Fitting Models to Real Processes, Uncertainties in Systems and in Modelling, Multiscale Modelling
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