Applied Intelligence

, Volume 49, Issue 11, pp 3909–3922 | Cite as

Aggregation framework for TSK fuzzy and association rules: interpretability improvement on a traffic accidents case

  • Sandra NemetEmail author
  • Dragan Kukolj
  • Gordana Ostojić
  • Stevan Stankovski
  • Dragan Jovanović


The number and diversity of machine learning applications causes an increasing need for understanding computational models and used data. This paper deals with a framework design of easily interpretable rules of the Takagi-Sugeno-Kang (TSK) fuzzy model. The proposed framework aggregates TSK fuzzy rules and association rules by calculating overlapping value intervals of variables appearing in both antecedent and consequent parts of fuzzy and association rules. Besides a simple insight into rule interconnections of the rule-based models, the framework provides an assessment of fuzzy rule importance, and in accordance with other rules and the complete TSK fuzzy model. The proposed framework is developed and illustrated by analysing traffic accidents with pedestrian involvement. It provides a deeper understanding of the built rule-based model, as well as more readable identification of significant accident causes. The framework can be used in many domains of analysis modelling and decision making processes where computational model understanding is crucial.


Fuzzy rules Association rules Takagi-Sugeno-Kang fuzzy model Interpretability Traffic accident analysis Fuzzy rules visualization Feature selection 



This work was partially supported by the Ministry of Education, Science and Technology Development of the Republic of Serbia under the Grant TR32034.


  1. 1.
    Lee CC (1990) Fuzzy logic in control systems: fuzzy logic controller - part I and II. IEEE Trans Syst Man Cybern 20(2):404–435MathSciNetCrossRefGoogle Scholar
  2. 2.
    Kukolj D (2002) Design of adaptive Takagi–Sugeno–Kang fuzzy models. Appl Soft Comput 2:89–103. CrossRefGoogle Scholar
  3. 3.
    Magdalena L (2018) Designing interpretable Hierarchical Fuzzy Systems. IEEE Int. Conf. on Fuzzy Systems (FUZZ-IEEE) pp 1–8 doi:
  4. 4.
    Mencar C, Castellano G, Finelli AM (2005) Some Fundamental Interpretability Issues in Fuzzy Modeling. Joint EUSFLAT-LFA Barcelona, Spain, September 7–9 pp 100–105Google Scholar
  5. 5.
    Zhou T, Ishibuchi H, Wang S (2017) Stacked-structure-based hierarchical Takagi-Sugeno-Kang fuzzy classification through feature augmentation. IEEE Trans Emerging Top Comput Intell 1(6):421–436CrossRefGoogle Scholar
  6. 6.
    Zhang Y, Ishibuchi H, Wang S (2018) Deep Takagi–Sugeno–Kang fuzzy classifier with shared linguistic fuzzy rules. IEEE Trans Fuzzy Syst 26(3):1535–1549. CrossRefGoogle Scholar
  7. 7.
    Riid A, Rüstern E (2011) Identification of transparent, compact, accurate and reliable linguistic fuzzy models. Inf Sci 181(20):4378–4393. CrossRefzbMATHGoogle Scholar
  8. 8.
    Ho WL, Tong WL (2010) Quek C (2010) an evolving Mamdani-Takagi-Sugeno based neural-fuzzy inference system with improved interpretability-accuracy. FUZZ-IEEE.
  9. 9.
    Zhou SM, Gan JQ (2009) Extracting Takagi-Sugeno fuzzy rules with interpretable submodels via regularization of linguistic modifiers. IEEE Trans Knowl Data Eng 21(8):1191–1204. CrossRefGoogle Scholar
  10. 10.
    Driss M, Saint-Gerand T, Bensaid A, Benabdeli K, Hamadouche MA (2013) A fuzzy logic model for identifying spatial degrees of exposure to the risk of road accidents. Int. Conf. Advanced Logistics and Transport (ICALT) Sousse, pp 69–74Google Scholar
  11. 11.
    Wahaballa AM, Diab A, Gaber M, Othman AM (2017) Sensitivity of Traffic Accidents Mitigation Policies Based on Fuzzy Modeling: A Case Study. Proc. IEEE 20th Int. Conf. on Intelligent Transportation Systems (ITSC) pp 45–50Google Scholar
  12. 12.
    Hosseinpour M, Yahaya AS, Ghadiri SM, Prasetijo J (2013) Application of adaptive neuro-fuzzy inference system for road accident prediction. KSCE J Civ Eng 17(7):1761–1772. CrossRefGoogle Scholar
  13. 13.
    Yong L, Shibo Z (2009) The fuzzy regression prediction of the City road traffic accident. Int Conf on Indust Mech Autom:121–124Google Scholar
  14. 14.
    Bin C, Yong L (2009) The road safety prediction model based on the fuzzy linear regression. Int Conf on Comput Intel Nat Comput:19–21Google Scholar
  15. 15.
    Wang R, Chen Y, Li T, Li P, Sun J (2013) Classification of road safety based on fuzzy clustering. Proc IEEE 10th Int Conf Fuzzy Syst Knowl Discov (FSKD):354–358Google Scholar
  16. 16.
    Weng J, Zhu JZ, Yan X, Liu Z (2016) Investigation of work zone crash casualty patterns using association rules. Accid Anal Prev 92:92–43CrossRefGoogle Scholar
  17. 17.
    Gao Z, Pan R, Wang X, Yu R (2018) Research on automated modeling algorithm using association rules for traffic accidents. Proc IEEE Int Conf Big DataSmart Comput:127–132Google Scholar
  18. 18.
    Äyrämö S, Pirtala P, Kauttonen J, Naveed K, Karkkainen T (2009) Mining road traffic accidents. Technical Report, Reports of the Department of Mathematical Information Technology Series C. Software and Computational Engineering No. C. 2/2009
  19. 19.
    Kumar S, Toshniwal D (2015) Analysing Road Accident Data Using Association Rule Mining. Proc. of Int. Conf. on Computing Communication and Security pp 1–6Google Scholar
  20. 20.
    Viharos ZJ, Kis KB (2016) Optimal Neuro-Fuzzy model configuration. IEEE Int Conf on Syst, Man, Cybernet.
  21. 21.
    Kennedy J, Eberhart R (1995) Particle swarm optimization. Proc IEEE Int Conf Neural Netw 4:1942–1948. CrossRefGoogle Scholar
  22. 22.
    Zhao Q, Bhowmick SS (2003) Association Rule Mining: A Survey. Technical Report, CAIS Nanyang Technological University SingaporeGoogle Scholar
  23. 23.
    Agrawal R, Srikant R (1994) Fast algorithms for mining association rules. Proc. of 20th Int. Conf. Very Large Data Bases, pp 487–499Google Scholar
  24. 24.
    Takagi T, Sugeno M (1985) Fuzzy identification of systems and its application to modelling and control. IEEE Trans Syst Man Cybern 15:116–132CrossRefGoogle Scholar
  25. 25.
    Kukolj D, Levi E (2004) Identification of complex systems based on neural and Takagi-Sugeno fuzzy model. IEEE Trans Syst Man Cybern -part B 34(1):272–282CrossRefGoogle Scholar
  26. 26.
    Kukolj D, Atlagić B, Petrov M (2006) Unlabeled data clustering using a re-organizing neural network. Cybern Syst Int J 37(7):779–790. CrossRefzbMATHGoogle Scholar
  27. 27.
    Jang JR, Sun C, Mizutani E (1997) Neuro-fuzzy and soft computing. Prentice-Hall, Englewood CliffsGoogle Scholar
  28. 28.
    Golub GH, Van Loan CF (1989) Matrix computations. Johns Hopkins Univ. Press Hall, BaltimorezbMATHGoogle Scholar
  29. 29.
    Bulajić A, Jovanović D, Matović B, Bačkalić SD (2014) Identification of high-density locations with homogenous attributes of pedestrian accident in the urban area of Novi Sad. XII Int. Symposium, Road Accidents Preventions 2014:89–98Google Scholar
  30. 30.
    Alonso JM, Magdalena L (2011) HILK++: an interpretability-guided fuzzy modeling methodology for learning readable and comprehensible fuzzy rule-based classifiers. Soft Comput 15(10):1959–1980. CrossRefGoogle Scholar
  31. 31.
    Nauck DD (2003) Measuring interpretability in rule-based classification systems. Proc. of 12th IEEE INT CONF FUZZY’03, pp 196–201Google Scholar
  32. 32.
    Pancho DP, Alonso JM, Magdalena L (2013) Quest for interpretability-accuracy trade-off supported by Fingrams into the fuzzy modeling tool GUAJE. Int J Comput Intel Syst 6(1):46–60. CrossRefGoogle Scholar
  33. 33.
    Alonso JM, Magdalena L (2011) Generating understandable and accurate fuzzy rule-based systems in a java environment, LECT NOTES ARTIF INT - 9th Int. Workshop on Fuzzy Logic and Applications, LNAI6857 pp 212–219 DOI:
  34. 34.
    Wang LX, Mendel JM (1992) Generating fuzzy rules by learning from examples. IEEE Trans Syst Man Cybern 22(6):1414–1427MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.RT-RK InstituteNovi SadSerbia
  2. 2.Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia

Personalised recommendations