In this work, we present a discrete event model that incorporates the lack of precision of variables. The make use of Fuzzy Set Theory to generate the model, and apply it on fire propagation study case. Our aim is to propose a generalization to the discrete event system specification formalism (DEVS) which be able to deal with imprecision in all of its elements (events, transition functions, state). Our approach is based on mathematical definitions of the Fuzzy Set Theory to represent and use imprecise information in the DEVS formalism.
AnglaniA., GriecoA., NucciF., SemeraroG. and TolioT., A sound analysis of fuzzy simulation results., In Proceedings of Intelligent Computation in Manufacturing Engineering 2000 citeseer.ist.psu.edu/496399.html. Capri, Naples, Italy (2000).
2.
BisgambigliaP., BisgambigliaP.A. and GualtieriJ., Cognitive simulation-based on knowledge evolution in fuzzy discrete event systems., In Fuzzy Systems (FUZZ), 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011) pp. 895–901. IEEE
3.
BisgambigliaP., InnocentiE. and GonsolinP., A new way to use Fuzzy Inference Systems in Activity-Based Cellular Modeling Simulations., In International Conference on Fuzzy Systems (FUZZ-IEEE 2017) (2017), IEEE.
4.
BisgambigliaP.-A., CapocchiL., BisgambigliaP. and GarreduS., Fuzzy Inference Models For Discrete EVent Systems., In Proceedings of the 2010 IEEE World Congress on Computational Intelligence (WCCI 2010) - IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (2010), pp688–694.
5.
BisgambigliaP.-A., CapocchiL. and de GentiliE., BisgambigliaP., Manipulation of incomplete or fuzzy Data for DEVS-based Systems., In SCS, editor, In Proceedings of the International Modeling and Simulation Multiconference (IMSM) - Conceptual Modeling Simulation (CMS) (2007), pp. 87–92.
6.
BisgambigliaP.-A. and de GentiliE., BisgambigliaP. and SantucciJ., Discrete Events System Simulation-based de-Fuzzification method. In Proceedings of The 14th IEEE Mediterranean Electrotechnical Conference (MELECON) (2008a), pp. 132–138.
7.
BisgambigliaP.-A. and de GentiliE., BisgambigliaP. and SantucciJ., Fuzzy Modeling for Discrete Events Systems. In Proceedings of The 14th IEEE Mediterranean Electrotechnical Conference (MELECON) (2008b), pp. 151–157.
8.
BisgambigliaP.-A. and de GentiliE., BisgambigliaP. and SantucciJ., Fuzzy Simulation for Discrete Events Systems., In Proceedings of the 2008 IEEE World Congress on Computational Intelligence (WCCI 2008) - IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (2008c), pp. 688–694.
9.
BisgambigliaP.-A. and de GentiliE., BisgambigliaP. and SantucciJ.-F., Fuzz-iDEVS: Towards a fuzzy toolbox for discrete event systems., In ACM, editor, Proceedings of the SIMUTools’ 09, Rome (Italie) (2009a), SIMUTools.
10.
BisgambigliaP.-A. and de GentiliE., BisgambigliaP. and SantucciJ.-F., iDEVS: New method to study inaccurate systems., In IEEE, editor Proceedings of the The Annual IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, (2009b), IEEE.
11.
BisgambigliaP.-A. and de GentiliE., SantucciJ. and BisgambigliaP., DEVS-Flou: A Discrete Events and Fuzzy Sets Theory-Based Modeling Environment., In IEEE, editor, Proceedings of the Systems and Control in Aerospace and Astronautics, (ISSCAA) (2006a), pp. 95–100.
12.
BisgambigliaP.-A., FilippiJ. and de GentiliE., A fuzzy approach of modeling evolutionary interfaces systems., In IEEE, editor,Proceedings of the ISEIM 2006, Corte (France) (2006b), pp. 98–103.
13.
CancellieriD., InnocentiE. and Leroy-CancellieriV., Wingpyro: A software platform for kinetic study of forest fuels, Fire Safety Journal58 (2013), 103–111.
14.
CassandrassC. and LafortuneS., Introduction to Discrete Event SystemsBoston, Kluwer Academic Publishers, 1999
15.
DuX., YingH. and LinF., Theory of extended fuzzy discrete-event systems for handling ranges of knowledge uncertainties and subjectivity, IEEE Transactions on Fuzzy Systems17(2) (2009), 316–328.
16.
DuX., YingH. and LinF., On modeling of fuzzy hybrid systems, Journal of Intelligent & Fuzzy Systems23(4) (2012), 129–141.
17.
DuboisD., FargierH. and FortinJ., A generalized vertex method for computing with fuzzy intervals., In IEEE, editor, Proc of the International Conference on Fuzzy Systems IEEE. Budapest, Hungary, (2004), pp. 541–546.
18.
DuboisD., FargierH. and FortinJ., The empirical variance of a set of fuzzy intervals, IEEE (2005).
19.
DuboisD. and PradeH., Fuzzy sets and systemsAcademic Press, 1980.
20.
DuboisD. and PradeH., Fuzzy set in approximate reasoning, part 1, Fuzzy set and Systems40 (1993).
21.
FortinJ., ZielinskiP., DuboisD. and FargierH., Interval analysis in scheduling., In van BeekP., editor, Proc of the 11th International Conference on Principles and Pratice of Constraint Programming (CP’05) SitgesSpain, Springer, (2005), pp. 226–240.
22.
GiambasiN., EscudeB. and GhoshS., GDEVS: A Generalized Discrete Event Specification for Accurate Modeling of Dynamic Systems, Transactions of the Society for Computer Simulation International (2000), pp. 120–134.
23.
GiambiasiN. and GhoshS., Min-Max-DEVS: A new formalism for the specification of discrete event models with minmax delays,, In Proceedings of 13th European Simulation Symposium (2001), pp. 616–621.
24.
GriecoA., NucciF. and AnglaniA., Representation of fuzzy time variables in discrete event simulation, Integrated Computer-Aided Engineering4(4) (2003), 305–318.
25.
GualtieriJ.-S. and BisgambigliaP.-A., A polyphony learning software (pls) based on gesture recognition by fuzzy inference system, Journal of Intelligent & Fuzzy Systems28(4) (2015), 1795–1803.
26.
InnocentiE., BisgambigliaP.-A. and UrbaniD., Activity-based discrete event simulation of spatial production systems: Application to fisheries, In Advances in Production Management Systems. Innovative and Knowledge-Based Production Management in a Global-Local WorldSpringer, (2014), pp.240–247.
27.
InnocentiE. and CancellieriD., Randomizing activity in fire spreading simulations, In ITM Web of Conferences volume 1, EDP Sciences 2013.
28.
InnocentiE., MuzyA., HillD., AielloA. and SantucciJ.-F., Design of a multithreaded parallel model for fire spread, In 15 th European Simulation Symposium (2003), pp. 104–10.
29.
KilicE., KarasuC. and LeblebiciogluK., Fault diagnosis with dynamic fuzzy discrete event system approach, Transactions in Artificial intelligence and neural networks (14th Turkish Symposium, TAINN 2005, Izmir, Turkey, June 16-17, 2005) (revised selected papers) (2005), pp. 117–124.
30.
KwonY., ParkH., JungS. and KimT., Fuzzy-DEVS Formalisme: Concepts, Realization and Application., Proceedings AIS 1996 (1996), pp. 227–234.
31.
LeeS., LeeK.H. and LeeD., Ranking the sequences of fuzzy values, Inf Sci Inf Comput Sci160(1-4) (2004), 41–52.
32.
LinF. and YingH., Fuzzy discrete event systems and their observability, In IEEE, editor, Proceedigns of IFSA World Congress and 20th NAFIPS International ConferenceVancouver, Canada, volume 3, (2001), pp. 1271–1276.
33.
LinF. and YingH., Modeling and control of fuzzy discrete event systems, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics32(4) (2002), 408–415.
34.
LinF., YingH., MacArthurR.D., CohnJ.A., Barth-JonesD. and CraneL.R., Decision making in fuzzy discrete event systems, Inf Sci177 (2007), 3749–3763.
35.
MamdaniE., Advances in the linguistic synthesis of fuzzy controllers, International Journal of Man-Machine Studies8(6) (1976), 669–678.
36.
MatheyA.-H., KrcmarE., DragicevicS. and VertinskyI., An object-oriented cellular automata model for forest planning problems, Ecological Modelling212(3) (2008), 359–371.
37.
MooreR., Interval Analysis, 1966.
38.
QiuD. and LiuF., Fuzzy Discrete Event Systems under Fuzzy Observability and a test-algorithm, ArXiv Computer Science e-prints2006.
39.
SantoniP.-A., BalbiJ.-H., BosseurF., InnocentiE., MarcelliT., MorandiniF., NasicaF., PieriA., RinieriF. and RossiJ.-L.et al., Metrology of windland fire: Characterization of a fire spreading across the corsican scrub, congrés Environnement et Identité en Méditerranée, Université de Corse, (2004), pp. 1–8.
40.
TakagiT. and SugenoM., Fuzzy indentification of systems and its applications to modeling and control, In IEEE, editor, Proceedings in IEEE Trans On S.M.C1985.
41.
TranL. and DucksteinL., Comparison of fuzzy numbers using a fuzzy distance measure, Fuzzy Sets Syst130(3) (2002), 331–341.
42.
VangheluweH., DEVS as a Common Denominator for Multi-Formalism Hybrid Systems Modelling., In Proceedings of ISCACS 20002000.
43.
VangheluweH., The Discrete EVent System specification DEVS Formalism, Technical report, http://moncs.cs.mcgill.ca/, (2001).
44.
WeiY., QiuJ. and KarimiH.R., Reliable output feedback control of discrete-time fuzzy affine systems with actuator faults, IEEE Transactions on Circuits and Systems I: Regular Papers64(1) (2017a), 170–181.
45.
WeiY., QiuJ. and LamH.-K., A novel approach to reliable output feedback control of fuzzy-affine systems with time-delays and sensor faults, IEEE Transactions on Fuzzy Systems (2016).
46.
WeiY., QiuJ., LamH.-K. and WuL., Approaches to t– s fuzzy-affine-model-based reliable output feedback control for nonlinear ito stochastic systems, IEEE Transactions on Fuzzy Systems25(3) (2017b), 569–583.
47.
ZadehL., Fuzzy sets, Information Control8 (1965), 338–353.
48.
ZeiglerB.P., PraehoferH. and KimT.G., Theory of Modeling and Simulation, Second Edition, Inc, Academic Press, 2000.
49.
ZhangH., TamM.C. and LiH., Modeling uncertain activity duration by fuzzy number and discrete-event simulation, European Journal of Operational Research164(3) (2005), 573–695.
