Extracting Rules from Specifications and Their Modeling using Colored Fuzzy Petri-Nets

Document Type : Original Article

Authors

Department of Software Engineering, Faculty of Electrical and Computer, University of Kashan, Kashan, Iran

Abstract

In this paper, the rules governing the behavior of the system are extracted from the system specifications and then they are modeled by Petri-nets. The set of these rules forms the knowledge base of the system, which provides the ability of making inferences. Each rule consists of several premises and a conclusion. When there are many rules and the premises in different rules overlap, it is possible to prevent the repetition of premises using a hierarchical structure by the inference engine and thus reduce the number of checks required to reach the conclusion. When these rules have many and fuzzy variables, they take a complex form, and it becomes difficult to understand and deduce their behavior. To better understand this complexity, it is appropriate to visualize it using fuzzy petri-nets. So far, many different methods based on fuzzy Petri nets have been presented to model fuzzy rules. But these methods either do not support a large number of rules and variables or do not consider matters like the role of conditional propositions in the occurrence of the conclusion propositions, the probability of the conclusion propositions, the threshold value for the conditional propositions and the conclusions, the certainty factor for the rule or for the conditional propositions. In this paper, by extending our previous work, we present a model based on fuzzy Petri nets that covers the two mentioned cases. Finally, we present the proposed model for a secure water refinement system and the attacks against it.

Keywords

References

[1] N. Majma and S.M. Babamir, "Model-Based Monitoring and Adaptation of Pacemaker Behavior Using Hierarchical Fuzzy Colored Petri-Nets," IEEE Trans. Syst. Man Cybern. Syst., vol. 50, no. 9, pp. 3344-3357, 2018, doi: 10.1109/TSMC.2018.2861718.
[2] S.M. Chen, J.S. Ke, and J.F. Chang, "Knowledge representation using fuzzy Petri nets," IEEE Trans. Knowl. Data Eng., vol. 2, no. 3, pp. 311-319, 1990, doi: 10.1109/69.60794.
[3] S.M. Chen, "Fuzzy backward reasoning using fuzzy Petri nets," IEEE Trans. Syst. Man Cybern., Part B, vol. 30, no. 6, pp. 846-856, 2000, doi: 10.1109/3477.891146. 
[4] S.M. Chen, "Weighted fuzzy reasoning using weighted fuzzy Petri nets," IEEE Trans. Knowl. Data Eng., vol. 14, no. 2, pp. 386-397, 2002, doi: 10.1109/69.991723. 
[5] J. Leena, R. B. Soney, and T. V. Manoj, "Knowledge representation using fuzzy Petri nets-revisited," IEEE Trans. Knowl. Data Eng., vol. 10, no. 4, pp. 666-667, 1998, doi: 10.1109/69.706063. 
[6] Z. Suraj, "A new class of fuzzy Petri nets for knowledge representation and reasoning," Fundam. Informaticae, vol. 128, no. 1-2, pp. 193-207, 2013, doi: 10.3233/FI-2013-941. 
[7] K.Q. Zhou, A. Mohd Zain, and L.P. Mo, "A decomposition algorithm of fuzzy Petri net using an index function and incidence matrix," Expert Syst. Appl., vol. 42, no. 8, pp. 3980-3990, 2015, doi: 10.1016/j.eswa.2014.12.048. 
[8] H.C. Liu, Q.L. Lin, L.X. Mao, and Z.Y. Zhang, "Dynamic adaptive fuzzy Petri nets for knowledge representation and reasoning," IEEE Trans. Syst. Man Cybern. Syst., vol. 43, no. 6, pp. 1399-1410, 2013, doi: 10.1109/TSMC.2013.2256125. 
[9] H.C. Liu, L. Liu, Q.L. Lin, and N. Liu, "Knowledge Acquisition and Representation Using Fuzzy Evidential Reasoning and Dynamic Adaptive Fuzzy Petri Nets," IEEE Trans. Cybern., vol. 43, no. 3, pp. 1059-1072, 2013, doi: 10.1109/TSMCB.2012.2223671. 
[10] H.C. Liu, Q.L. Lin, M.L. Ren, "Fault diagnosis and cause analysis using fuzzy evidential reasoning approach and dynamic adaptive fuzzy Petri nets," Comput. Ind. Eng., vol. 66, no. 4, pp. 899-908, 2013, doi: 10.1016/j.cie.2013.09.004. 
[11] H.C. Liu, J.X. You, X.Y. You, and Q. Su, "Fuzzy Petri nets using intuitionistic fuzzy sets and ordered weighted averaging operators," IEEE Trans. Cybern., vol. 46, no. 8, pp. 1839-1850, 2016, doi: 10.1109/TCYB.2015.2455343. 
[12] H.C. Liu, J.X. You, X.Y. You, and Q. Su, "Linguistic reasoning Petri nets for knowledge representation and reasoning," IEEE Trans. Syst. Man Cybern. Syst., vol. 46, no. 4, pp. 499-511, 2016, doi: 10.1109/TSMC.2015.2445732. 
[13] H.C. Liu, D.H. Xu, C.Y. Duan, and Y. Xiong, "Pythagorean Fuzzy Petri Nets for Knowledge Representation and Reasoning in Large Group Context," IEEE Trans. Syst. Man Cybern. Syst., pp. 1-11, 2021, doi: 10.1109/TSMC.2019.2949342. 
[14] H.C. Liu, X. Yun, X. Luan, and M. Zhou, "A New Linguistic Petri Net for Complex Knowledge Representation and Reasoning," IEEE Trans. Knowl. Data Eng., pp. 1-11, 2022, doi: 10.1109/TKDE.2020.2997175. 
[15] X. Li, W. Yu, and F.L. Rosano, "Dynamic knowledge inference and learning under adaptive fuzzy Petri net framework," IEEE Trans. Syst. Man Cybern., Part C, vol. 30, no. 4, pp. 442-450, 2000, doi: 10.1109/5326.897071. 
[16] V.R.L. Shen, "Knowledge representation using high-level fuzzy Petri nets," IEEE Trans. Syst. Man Cybern., Part A, vol. 36, no. 6, pp. 1220-1227, 2006, doi: 10.1109/TSMCA.2006.878968. 
[17] M.H. Ha, Y. Li, and X.F. Wang, "Fuzzy knowledge representation and reasoning using a generalized fuzzy petri net and a similarity measure," Soft Comput., vol. 11, no. 4, pp. 323-327, 2007, doi: 10.1007/s00500-006-0084-4. 
[18] X.Y. Shen, Y.J. Lei, and C.H. Li, "Intuitionistic fuzzy petri nets model and reasoning algorithm," in 6th Int. Conf. Fuzzy Syst. Knowl. Discov., Tianjin, China, 2009, doi: 10.1109/FSKD.2009.105. 
[19] J. Yuan, C. Liu, B. Jiang, Y. Shan, and W. Shang, "A forward concurrent reasoning approach for rule-based systems using fuzzy colored Petri nets," in 8th World Congress Intell. Control Autom., Jinan, China, 2010, doi: 10.1109/WCICA.2010.5554461. 
[20] F.X. Meng , Y.J. Lei, B. Zhang, X.Y. Shen, and J.Y. Zhao, "Intuitionistic fuzzy Petri nets for knowledge representation and reasoning," J. Digit. Inf. Manag., vol. 14, no. 2, pp. 104-113, 2016.
[21] R. Akhoondi and R. Hossini, “A Novel Fuzzy-Genetic Differential Evolutionary Algorithm for Optimization of A Fuzzy Expert Systems Applied to Heart Disease Prediction,” Soft Comput. J., vol. 6, no. 2, pp. 32-47, 2017, dor: 20.1001.1.23223707.1396.6.2.3.7 [In Persian].
[22] H. Abbasi, M. Shamsi, and A. Rasuli-Kenari, “Approaches of user activity detection and a new fuzzy logic-based method to determine the risk amount of user unusual activity in the smart home,” Soft Comput. J., vol. 9, no. 2, pp. 2-13, 2020, doi: 10.22052/scj.2021.242812.0 [In Persian].
[23] E. Afarande and R. Hosseini, “An automatic Model for Managing Uncertainty and Rule Extraction in Form of Fuzzy Rules using Genetic Algorithm,” Soft Comput. J., vol. 9, no. 1, pp. 14-25, 2020, doi: 10.22052/scj.2021.111449 [In Persian].
[24] C.L. Heitmeyer, "Software Cost Reduction," in Encyclopedia of Software Engineering, John Wiley & Sons, Inc., 2002. 
[25] S.M. Babamir and S. Jalili, "An approach for dynamic and logic-based verification of distributed systems", in 11th Annual Conf. Comput. Soc. Iran, Tehran, 2005 [In Persian].
[26] J. Goh, S. Adepu, K.N. Junejo, and A. Mathur, "A Dataset to Support Research in the Design of Secure Water Treatment Systems," in 11th Int. Conf. Crit. Inf. Infrastructures Secur., France, 2016, doi.org/10.1007/978-3-319-71368-7_8.
Soft Computing Journal
Volume 11, Issue 1 - Serial Number 21
September 2022
Pages 22-47

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History

  • Receive Date: 03 July 2022
  • Revise Date: 27 October 2022
  • Accept Date: 04 November 2022

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