Skip to main content
SpringerLink
Log in

Bipolar fuzzy Petri nets for knowledge representation and acquisition considering non-cooperative behaviors

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

Fuzzy Petri nets (FPNs) are a promising modeling tool for knowledge representation and reasoning. As a new type of FPNs, bipolar fuzzy Petri nets (BFPNs) are developed in this article to overcome the shortcomings and improve the performance of traditional FPNs. In order to depict expert knowledge more accurately, the BFPN model adopts bipolar fuzzy sets (BFSs), which are characterized by the satisfaction degree to property and the satisfaction degree to its counter property, to represent knowledge parameters. Because of the increasing scale of expert systems, a concurrent hierarchical reasoning algorithm is introduced to simplify the structure of BFPNs and reduce the computation complexity of knowledge reasoning algorithm. In addition, a large group expert weighting method is proposed for knowledge acquisition by taking experts’ non-cooperative behaviors into account. A realistic case of risk index evaluation system is presented to show the effectiveness and practicality of the proposed BFPNs. The result shows that the new BFPN model is feasible and efficient for knowledge representation and acquisition.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Liu HC, Liu L, Lin QL, Liu N (2013) Knowledge acquisition and representation using fuzzy evidential reasoning and dynamic adaptive fuzzy Petri nets. IEEE Trans Cybern 43(3):1059–1072

    Google Scholar 

  2. Yeung DS, Ysang ECC (1998) A multilevel weighted fuzzy reasoning algorithm for expert systems. IEEE Trans Syst Man Cybern Part A Syst Hum 28(2):149–158

    Google Scholar 

  3. Liu HC, Lin QL, Mao LX, Zhang ZY (2013) Dynamic adaptive fuzzy Petri nets for knowledge representation and reasoning. IEEE Trans Syst Man Cybern Syst 43(6):1399–1410

    Google Scholar 

  4. Yeung DS, Tsang ECC (1994) Improved fuzzy knowledge representation and rule evaluation using fuzzy Petri nets and degree of subsethood. Int J Intell Syst 9(12):1083–1100

    Google Scholar 

  5. Liu Y, Li X (2019) The application of an amended FCA method on knowledge acquisition and representation for interpreting meteorological services. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-019-01305-2

    Article  Google Scholar 

  6. Looney CG (1988) Fuzzy Petri nets for rule-based decision-making. IEEE Trans Syst Man Cybern 18(1):178–183

    Google Scholar 

  7. Chen SM, Ke JS, Chang JF (1990) Knowledge representation using fuzzy Petri nets. IEEE Trans Knowl Data Eng 2(3):311–319

    Google Scholar 

  8. Zhou KQ, Mo LP, Jin J, Zain AM (2019) An equivalent generating algorithm to model fuzzy Petri net for knowledge-based system. J Intell Manuf 30(4):1831–1842

    Google Scholar 

  9. Yeung DS, Tsang ECC (1994) Fuzzy knowledge representation and reasoning using Petri nets. Expert Syst Appl 7(2):281–289

    Google Scholar 

  10. Liu HC, Lin QL, Ren ML (2013) Fault diagnosis and cause analysis using fuzzy evidential reasoning approach and dynamic adaptive fuzzy Petri nets. Comput Ind Eng 66(4):899–908

    Google Scholar 

  11. Kiaei I, Lotfifard S (2020) Fault section identification in smart distribution systems using multi-source data based on fuzzy Petri nets. IEEE Trans Smart Grid 11(1):74–83

    Google Scholar 

  12. Shi H, Wang L, Li XY, Liu HC (2019) A novel method for failure mode and effects analysis using fuzzy evidential reasoning and fuzzy Petri nets. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-019-01262-w

    Article  Google Scholar 

  13. Li XY, Xiong Y, Duan CY, Liu HC (2019) Failure mode and effect analysis using interval type-2 fuzzy sets and fuzzy Petri nets. J Intell Fuzzy Syst 37(1):693–709

    Google Scholar 

  14. Li XY, Wang ZL, Xiong Y, Liu HC (2019) A novel failure mode and effect analysis approach integrating probabilistic linguistic term sets and fuzzy petri nets. IEEE Access 7:54918–54928

    Google Scholar 

  15. Li X, Li Y, Liu Y, Wang L (2017) Genetic expression level prediction based on extended fuzzy Petri nets. Int J Pattern Recognit Artif Intell 31(19):1750036

    Google Scholar 

  16. Hamed RI (2018) Quantitative modeling of gene networks of biological systems using fuzzy Petri nets and fuzzy sets. J King Saud Univ Sci 30(1):112–119

    Google Scholar 

  17. Liu F, Chen S, Heiner M, Song H (2018) Modeling biological systems with uncertain kinetic data using fuzzy continuous Petri nets. BMC Syst Biol 12:42

    Google Scholar 

  18. Hamed RI, Ahson SI (2011) Confidence value prediction of DNA sequencing with Petri net model. J King Saud Univ Comput Inf Sci 23(2):79–89

    Google Scholar 

  19. Zhou KQ, Zain AM (2016) Fuzzy Petri nets and industrial applications: a review. Artif Intell Rev 45(4):405–446

    Google Scholar 

  20. Liu HC, You JX, Li ZW, Tian G (2017) Fuzzy Petri nets for knowledge representation and reasoning: a literature review. Eng Appl Artif Intell 60:45–56

    Google Scholar 

  21. Xu XG, Shi H, Xu DH, Liu HC (2019) Picture fuzzy Petri nets for knowledge representation and acquisition in considering conflicting opinions. Appl Sci 9(5):983

    Google Scholar 

  22. Liu HC, Xu DH, Duan CY, Xiong Y (2019) Pythagorean fuzzy Petri nets for knowledge representation and reasoning in large group context. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2019.2949342

    Article  Google Scholar 

  23. Yue W, Gui W, Chen X, Zeng Z, Xie Y (2019) Knowledge representation and reasoning using self-learning interval type-2 fuzzy Petri nets and extended TOPSIS. Int J Mach Learn Cybern 10:3499–3520

    Google Scholar 

  24. Sun XL, Wang N (2018) Gas turbine fault diagnosis using intuitionistic fuzzy fault Petri nets. J Intell Fuzzy Syst 34(6):3919–3927

    Google Scholar 

  25. Liu HC, You JX, You XY, Su Q (2016) Fuzzy Petri nets using intuitionistic fuzzy sets and ordered weighted averaging operators. IEEE Trans Cybern 46(8):1839–1850

    Google Scholar 

  26. Liu HC, Xue L, Li ZW, Wu J (2018) Linguistic Petri nets based on cloud model theory for knowledge representation and reasoning. IEEE Trans Knowl Data Eng 30(4):717–728

    Google Scholar 

  27. Akram M, Shumaiza Arshad M (2020) Bipolar fuzzy TOPSIS and bipolar fuzzy ELECTRE-I methods to diagnosis. Comput Appl Math 39(1):7

    MathSciNet  Google Scholar 

  28. Xu XR, Wei GW (2017) Dual hesitant bipolar fuzzy aggregation operators in multiple attribute decision making. Int J Knowl Based Intell Eng Syst 21(3):155–164

    Google Scholar 

  29. Zhang WR, Zhang L (2004) YinYang bipolar logic and bipolar fuzzy logic. Inf Sci 165(3):265–287

    MATH  Google Scholar 

  30. Gao H, Wei G, Huang Y (2018) Dual hesitant bipolar fuzzy Hamacher prioritized aggregation operators in multiple attribute decision making. IEEE Access 6:11508–11522

    Google Scholar 

  31. Akram M, Arshad M (2019) A novel trapezoidal bipolar fuzzy TOPSIS method for group decision-making. Group Decis Negot 28(3):565–584

    Google Scholar 

  32. Shumaiza Akram M, Al-Kenani AN (2019) Multiple-attribute decision making ELECTRE II method under bipolar fuzzy model. Algorithms 12(11):226

    MathSciNet  Google Scholar 

  33. Gao H, Wu J, Wei C, Wei G (2019) MADM method with interval-valued bipolar uncertain linguistic information for evaluating the computer network security. IEEE Access 7:151506–151524

    Google Scholar 

  34. Zhang YX, Yin X, Mao ZF (2019) Study on risk assessment of pharmaceutical distribution supply chain with bipolar fuzzy information. J Intell Fuzzy Syst 37(2):2009–2017

    Google Scholar 

  35. Akram M, Shumaiza Alkenani A (2020) Multi-criteria group decision-making for selection of green suppliers under bipolar fuzzy PROMETHEE Process. Symmetry 12:77

    Google Scholar 

  36. Wei G, Gao H, Wang J, Huang Y (2018) Research on risk evaluation of enterprise human capital investment with interval-valued bipolar 2-tuple linguistic information. IEEE Access 6:35697–35712

    Google Scholar 

  37. Shumaiza Akram M, Al-Kenani AN, Alcantud JCR (2019) Group decision-making based on the VIKOR method with trapezoidal bipolar fuzzy information. Symmetry 11(10):1313

    Google Scholar 

  38. Alghamdi MA, Alshehri NO, Akram M (2018) Multi-criteria decision-making methods in bipolar fuzzy environment. Int J Fuzzy Syst 20(6):2057–2064

    Google Scholar 

  39. Wei G, Alsaadi FE, Hayat T, Alsaedi A (2018) Bipolar fuzzy Hamacher aggregation operators in multiple attribute decision making. Int J Fuzzy Systems 20(1):1–12

    MathSciNet  MATH  Google Scholar 

  40. Wei G, Wei C, Gao H (2018) Multiple attribute decision making with interval-valued bipolar fuzzy information and their application to emerging technology commercialization evaluation. IEEE Access 6:60930–60955

    Google Scholar 

  41. Li H, You JX, Liu HC, Tian G (2018) Acquiring and sharing tacit knowledge based on interval 2-tuple linguistic assessments and extended fuzzy Petri nets. Int J Uncertainty Fuzziness Knowl Syst 26(01):43–65

    MathSciNet  Google Scholar 

  42. Liu HC, Luan X, Lin W, Xiong Y (2019) Grey reasoning Petri nets for large group knowledge representation and reasoning. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2019.2949770

    Article  Google Scholar 

  43. Han Y, Lu Z, Du Z, Luo Q, Chen S (2018) A YinYang bipolar fuzzy cognitive TOPSIS method to bipolar disorder diagnosis. Comput Methods Programs Biomed 158:1–10

    Google Scholar 

  44. Gao MM, Zhou MC, Huang XG, Wu ZM (2003) Fuzzy reasoning Petri nets. IEEE Trans Syst Man Cybern Part A Syst Hum 33(3):314–324

    Google Scholar 

  45. Abu Arqub O (2017) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations. Neural Comput Appl 28(7):1591–1610

    Google Scholar 

  46. Jain AK (2010) Data clustering: 50 years beyond K-means. Pattern Recogn Lett 31(8):651–666

    Google Scholar 

  47. Dhalmahapatra K, Shingade R, Mahajan H, Verma A, Maiti J (2019) Decision support system for safety improvement: an approach using multiple correspondence analysis, t-SNE algorithm and K-means clustering. Comput Ind Eng 128:277–289

    Google Scholar 

  48. Abu Arqub O, Al-Smadi M, Momani S, Hayat T (2016) Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method. Soft Comput 20(8):3283–3302

    MATH  Google Scholar 

  49. Xu XH, Du ZJ, Chen XH, Cai CG (2019) Confidence consensus-based model for large-scale group decision making: a novel approach to managing non-cooperative behaviors. Inf Sci 477:410–427

    Google Scholar 

  50. Dong Y, Zhao S, Zhang H, Chiclana F, Herrera-Viedma E (2018) A self-management mechanism for non-cooperative behaviors in large-scale group consensus reaching processes. IEEE Trans Fuzzy Syst 26(6):3276–3288

    Google Scholar 

  51. Arqub OA, Al-Smadi M, Momani S, Hayat T (2017) Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Comput 21(23):7191–7206

    MATH  Google Scholar 

  52. Yager RR, Rybalov A (1996) Uninorm aggregation operators. Fuzzy Sets Syst 80(1):111–120

    MathSciNet  MATH  Google Scholar 

  53. Chang Y, Wu X, Chen G, Ye J, Chen B, Xu L et al (2018) Comprehensive risk assessment of deepwater drilling riser using fuzzy Petri net model. Process Saf Environ Prot 117:483–497

    Google Scholar 

Download references

Acknowledgements

The authors are very grateful to the respected editor and the anonymous referees for their insightful and constructive comments, which helped to improve the overall quality of the paper. This work was partially supported by the National Natural Science Foundation of China (No. 61773250), the Shanghai Soft Science Key Research Program (No. 19692108000), and the 2019 Yangtze River Delta High‐Quality Integration Major Issues Research Project.

Author information

Authors and Affiliations

  1. School of Management, Shanghai University, 99 Shangda Road, Shanghai, 200444, People’s Republic of China

    Xue-Guo Xu, Yun Xiong & Dong-Hui Xu

  2. College of Economics and Management, China Jiliang University, Hangzhou, 310018, People’s Republic of China

    Hu-Chen Liu

  3. School of Economics and Management, Tongji University, Shanghai, 200092, People’s Republic of China

    Hu-Chen Liu

Authors
  1. Xue-Guo Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yun Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dong-Hui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hu-Chen Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dong-Hui Xu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, XG., Xiong, Y., Xu, DH. et al. Bipolar fuzzy Petri nets for knowledge representation and acquisition considering non-cooperative behaviors. Int. J. Mach. Learn. & Cyber. 11, 2297–2311 (2020). https://doi.org/10.1007/s13042-020-01118-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-020-01118-2

Keywords

Search

Navigation