DENG Hui and LI Zhi, “Nondeterministic Fuzzy Simulation and Bisimulation,” Chinese Journal of Electronics, vol. 29, no. 2, pp. 297-303, 2020, doi: 10.1049/cje.2020.01.007
Citation: DENG Hui and LI Zhi, “Nondeterministic Fuzzy Simulation and Bisimulation,” Chinese Journal of Electronics, vol. 29, no. 2, pp. 297-303, 2020, doi: 10.1049/cje.2020.01.007

Nondeterministic Fuzzy Simulation and Bisimulation

doi: 10.1049/cje.2020.01.007
Funds:  This work is supported by the National Natural Science Foundation of China (No.61673310).
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  • Corresponding author: LI Zhi (corresponding author) He received the Ph.D. from Xi'an Jiaotong University. He is currently a professor and Ph.D. supervisor with Department of Automatic Control, Xidian University. His research interests include collaborative control theory and application of complex network, evolution game and neural networks. (Email:zhli@xidian.edu.cn)
  • Received Date: 2019-01-16
  • Rev Recd Date: 2019-10-22
  • Publish Date: 2020-03-10
  • As the abstraction and equivalent technologies, simulation and bisimulation have been applied to the simplifications of some classical and uncertain models structures. The studies of the more generalized simulation and bisimulation technologies have not proceeded yet. With this problem in mind, we introduce the concepts, lemmas, theorems of nondeterministic fuzzy simulation and bisimulation, as well as the relevant proofs. According to the definitions of nondeterministic fuzzy simulation and bisimulation, we propose nondeterministic fuzzy quotients and a series of quotienting algorithms to generate the minimization of nondeterministic fuzzy simulation and bisimulation. By comparison with previous quotienting algorithms, we show that our quotienting algorithms are more generalized. This kind of quotienting algorithms not only suit for Nondeterministic fuzzy Kripke structure(NFKS), but also Fuzzy Kripke structure(FKS) and classical Kripke structure.
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  • H.M. Li and W.H. Zhang, “Model checking: Theories, techniques and applications”, Acta Electronica Sinica, Vol.30, No.12A, pp.1907-1912, 2002.(in Chinese)
    M. Chechik, S. Easterbrook and V. Petrovykh, “Modelchecking over multi-valued logics”, Lecture Notes in Computer Science, Springer Verlag, Berlin, German, pp.72-98, 2001.
    M. Chechik, B. Devereux, A. Gurfinkel and S. Easterbrook,“Multi-valued symbolic model-checking”, ACM Transactions on Software Engineering and Methodology, Vol.12, No.4, pp.371-408, 2003.
    M. Chechik, B. Deverux and A. Gurfinkel, “Model-checking infinite state-space systems with fine-grained abstractions using SPIN”, Lecture Notes in Computer Science, Proceedings of the 8th SPIN Workshop on Model Checking Software, Springer, Toronto, Canada, Vol.2057, pp.16-36, 2001.
    Y.M. Li, M. Droste and L.H. Lei, “Model checking of linear-time properties in multi-valued systems”, Information Sciences, Vol.377, pp.51-74, 2017.
    C.J. Liang and Y.M. Li, “The model checking problem of computing tree logic base on generalized possibility measures”, Acta Electronica Sinica, Vol.45, No.11, pp.2641-2648, 2017.(in Chinese)
    C.J. Liang and Y.M. Li, “Model checking of fuzzy linear temporal logic based on generalized possibility measures”, Acta Electronica Sinica, Vol.45, No.12, pp.2971-2977, 2017.(in Chinese)
    Y.L. Li, Y.M. Li and Z.Y. Ma, “Computation tree logic model checking based on possibility measures”, Fuzzy Sets and Systems, Vol.262, pp.44-59, 2014.
    Y.M. Li, Y.L. Li and Z.Y. Ma, “Quantitative computation tree logic model checking based on generalized possibility measures”, IEEE Transactions on Fuzzy Systems, Vol.23, No.6, pp.2034-2047, 2015.
    X.J. Wei and Y.L. LI, “An automata-theoretic approach to L-valued computation tree logic model checking”, Chinese Journal of Electronics, Vol.28, No.2, pp.309-315, 2019.
    H.Y. Pan, Y.M. Li and Y.Z. Cao, “Lattice-valued simulations for quantitative transition systems”, International Journal of Approximate Reasoning, Vol.56, pp.28-42, 2015.
    H.Y. Pan, M. Zhang, H.Y Wu and Y.X Chen, “Quantitative analysis of lattice-valued Kripke structures”, Fundamenta Informaticae, Vol.135, pp.269-293, 2014.
    H.Y Pan, Y.Z. Cao, M. Zhang and Y.X Chen, “Simulation for lattice-valued doubly labeled transition systems”, International Journal of Approximate Reasoning, Vol.55, No.3, pp.797-811, 2014.
    Y.H. Fan and Y.M. Li, “The realizability of fuzzy linear temporal logic”, Acta Electronica Sinica, Vol.46, No.2, pp.341-346, 2018.(in Chinese)
    H.Y. Wu and Y.X Deng, “Logical characterizations of simulation and bisimulation for fuzzy transition systems”, Fuzzy Sets and Systems, Vol.301, No.6, pp.19-36, 2016.
    E. Clarke, O. Grumberg D. Peled, Model checking, The MIT Press, Cambridge, USA, pp.171-180, 1999.
    H. Deng and Z. Li, “Multi-valued bisimulation quotienting algorithms”, Journal of Intelligent & Fuzzy Systems, Vol.36, No.1, pp.37-45, 2019.
    Y.H. Fan, Y.M. Li and Z.Y. Ma, “Computation Tree Logic Model Checking for Nondeterminisitic Fuzzy Kripke Structure”, Acta Electronica Sinica, Vol.46, No.1, pp.152-159, 2018.(in Chinese)
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