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Proceedings of the 17th Conference on Computer Science and Intelligence Systems

Annals of Computer Science and Information Systems, Volume 30

Hybridization of Fuzzy Sets and Rough Sets: Achievements and Opportunities

DOI: http://dx.doi.org/10.15439/2022F302

Citation: Proceedings of the 17th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 30, pages 714 ()

Full text

Abstract. Fuzzy rough sets are the fruit of an intense and longlasting collaboration effort between fuzzy set theory and rough set theory. Seminal research on the hybridization originated in the late 1980's, and has inspired generations of researchers from around the globe to address both theoretical and practical challenges. In this paper, we gauge the state-of-the-art in this domain and identify opportunities for further development. In particular, we highlight the potential of fuzzy quantifiers in creating new robust fuzzy rough models, we advocate closer integration with granular computing as a stepping stone for designing rule induction algorithms, and we contemplate the role of fuzzy rough sets vis-à-vis explainable artificial intelligence.

References

  1. V. Aleven, Rule-Based Cognitive Modeling for Intelligent Tutoring Systems, Springer, pp. 33–62, 2010.
  2. J. Alonso, C. Castiello, L. Magdalena, C. Mencar, Explainable fuzzy systems: paving the way from interpretable fuzzy systems to explainable AI Systems, Springer, 2021.
  3. M. Baczyński, B. Jayaram, Fuzzy implications, Springer, 2008.
  4. A. Bargiela, W. Pedrycz, The roots of granular computing, in: 2006 IEEE International Conference on Granular Computing, pp. 806–809, 2006.
  5. C. Cornelis, M. De Cock, A. Radzikowska, Vaguely quantified rough sets, in: Proceedings of 11th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC2007), Lecture Notes in Artificial Intelligence 4482, 2007, pp. 87-94.
  6. C. Cornelis, M. De Cock, A.M. Radzikowska, Fuzzy rough sets: from theory into practice, in: Handbook of Granular Computing (W. Pedrycz, A. Skowron, V. Kreinovich, eds.), Wiley, 2008, pp. 533–552.
  7. C. Cornelis, R. Jensen, A noise-tolerant approach to fuzzy-rough feature selection, in: Proc. 2008 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2008), 2008, pp. 1598–1605.
  8. C. Cornelis, R. Jensen, G. Hurtado Martín, and D. Ślęzak, Attribute selection with fuzzy decision reducts, Information Sciences, 180(2), 2010, pp. 209–224.
  9. C. Cornelis, N. Verbiest, and R. Jensen, Ordered weighted average based fuzzy rough sets, in: Proc. 5th International Conference on Rough Sets and Knowledge Technology (RSKT 2010), 2010, pp. 78–85.
  10. M. De Cock, C. Cornelis, E.E. Kerre, Fuzzy rough sets: beyond the obvious, in: Proc. 2004 IEEE Int. Conf. on Fuzzy Systems, FUZZ-IEEE’04, Volume 1, 2004, pp. 103-108.
  11. M. De Cock, C. Cornelis, E.E. Kerre, Fuzzy rough sets: the forgotten step, IEEE Transactions on Fuzzy Systems 15(1), 2007, pp. 121–130.
  12. L. D’eer, N. Verbiest, C. Cornelis, L. Godo, A comprehensive study of implicator-conjunctor based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis, Fuzzy Sets and Systems 275, 2015, pp. 1–38.
  13. C. Degang, Z. Suyun, Local reduction of decision system with fuzzy rough sets, Fuzzy Sets and Systems 161(13), 2010, pp. 1871–1883. Chen Degang, Zhao Suyun,
  14. C. Degang, Y. Yongping, W. Hui, Granular computing based on fuzzy similarity relations, Soft Computing 15(6), 2011, pp. 1161–1172.
  15. M. Delgado, M. D. Ruiz, D. Sánchez, M. A. Vila, Fuzzy association rules: general model and applications, IEEE Transactions on Fuzzy Systems 11(2), 2003, pp. 214-225.
  16. M. Delgado, M. D. Ruiz, D. Sánchez, M. A. Vila, Fuzzy quantification: a state of the art, Fuzzy Sets and Systems 242, 2014, pp. 1–30.
  17. D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems 17, 1990, pp. 91–209.
  18. L. Fariñas del Cerro, H. Prade, Rough sets, twofold fuzzy sets and modal logic—Fuzziness in indiscernibility and partial information, In: A. Di Nola, A.G.S. Ventre, Eds., The Mathematics of Fuzzy Systems, Verlag TUV Rheinland, Köln, 1986, pp. 103–120.
  19. A. Fernández, V. Lopez, M.J. del Jesus, F. Herrera, Revisiting evolutionary fuzzy systems: taxonomy, applications, new trends and challenges, Knowledge-Based Systems 80, 2015, pp. 109–121.
  20. I. Glöckner, Fuzzy quantifiers: a computational theory, Studies in Fuzziness and Soft Computing 193, Springer, 2008.
  21. M. Grabisch, C. Labreuche, A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid, Ann. Oper. Res. 175 (1), 2010, pp. 247–286.
  22. S. Greco, B. Matarazzo, and R. Słowiński, Rough sets theory for multicriteria decision analysis, European journal of operational research 129(1), 2001, pp. 1–47.
  23. S. Greco, M. Inuiguchi, R. Slowinski, Fuzzy rough sets and multiple-premise gradual decision rules, International Journal of Approximate Reasoning 41, 2005, 179–211.
  24. J.W. Grzymala-Busse, LERS-a system for learning from examples based on rough sets, in: Intelligent decision support, Springer, 1992, pp. 3–18.
  25. J.W. Grzymala-Busse, J. Stefanowski, Three discretization methods for rule induction, International Journal of Intelligent Systems 16(1), 2001, pp. 29–38.
  26. Q. Hu, S. An, X.Yu, D.Yu, Robust fuzzy rough classifiers, Fuzzy Sets and Systems 183(1), 2011, pp. 26–43.
  27. J. Hühn, E. Hüllermeier, FURIA: an algorithm for unordered fuzzy rule induction, Data Mining and Knowledge Discovery 19(3), 2009, pp. 293–319.
  28. M. Inuiguchi, W.Z. Wu, C. Cornelis, N. Verbiest, Fuzzy-rough hybridization, in: Springer Handbook of Computational Intelligence, 2015, pp. 425–451.
  29. R. Jensen, C. Cornelis, Q. Shen, Hybrid fuzzy-rough rule induction and feature selection, in: Proc. 2009 IEEE International Conference on Fuzzy Systems, 2009, pp. 1151–1156.
  30. R. Jensen, C. Cornelis, Fuzzy-rough instance selection, in: Proc. 19th International Conference on Fuzzy Systems (FUZZ-IEEE 2010), 2010, pp. 1776–1782.
  31. R. Jensen and C. Cornelis, Fuzzy-rough nearest neighbour classification, Transactions on rough sets, vol. XIII, 2011, pp. 56–72.
  32. E.P. Klement, R. Mesiar, E. Pap, Triangular norms, Springer, 2000.
  33. O.U. Lenz, D. Peralta, C. Cornelis, Scalable approximate FRNN-OWA classification, IEEE Transactions on Fuzzy Systems 28(5), 2020, pp. 929–938.
  34. O.U. Lenz, D. Peralta, C. Cornelis, fuzzy-rough-learn 0.1: A Python library for machine learning with fuzzy rough sets, in: Proc. International Joint Conference on Rough Sets, 2020, pp. 491–499.
  35. M.J. Lesot, G. Moyse, B. Bouchon-Meunier, Interpretability of fuzzy linguistic summaries, Fuzzy Sets and Systems 292, 2016, pp. 307–317.
  36. Y. Lin, Y. Li, C. Wang, J. Chen, Attribute reduction for multi-label learning with fuzzy rough set, Knowledge-based systems 52, 2018, pp. 51-61.
  37. C. Molnar, Interpretable machine learning, Lulu.com, 2020.
  38. G. Nápoles, C. Mosquera, R. Falcon, I. Grau, R. Bello, K. Vanhoof, Fuzzy-Rough Cognitive Networks, Neural Networks 97, 2018, pp. 19–27
  39. A. Naumoski, G. Mirceva, K. Mitreski, Novel t-norm for fuzzy-rough rule induction algorithm and its influence, in: ICT Innovations 2021. Digital Transformation, Communications in Computer and Information Science, vol. 1521. Springer, 2021, pp. 115–125.
  40. P. Ni, S. Zhao, X. Wang, H. Chen, C. Li, E.C.C.Tsang, Incremental feature selection based on fuzzy rough sets, Information Sciences 536, 2020, pp.185–204.
  41. M. Palangetić, C. Cornelis, S. Greco, R. Słowiński, Fuzzy extensions of the dominance-based rough set approach, International Journal of Approximate Reasoning 129, 2021, pp. 1–19.
  42. M. Palangetić, C. Cornelis, S. Greco, R. Słowiński, Granular representation of OWA-based fuzzy rough sets, Fuzzy Sets and Systems, in press.
  43. M. Palangetić, C. Cornelis, S. Greco, R. Słowiński, A novel machine learning approach to data inconsistency with respect to a fuzzy relation, https://arxiv.org/abs/2111.13447 [cs.AI].
  44. Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences 11(5), 1982, pp. 341–356.
  45. Z. Pawlak, A. Skowron, Rudiments of rough sets, Information Sciences 177(1), 2007, pp. 3–27.
  46. Z. Pawlak, A. Skowron, Rough sets: some extensions. Information Sciences 177(1), 2007, pp. 28–40.
  47. Z. Pawlak, A. Skowron, Rough sets and boolean reasoning, Information Sciences 177(1), 2007, pp. 41–73.
  48. E. Ramentol, S. Vluymans, N. Verbiest, Y. Caballero, R. Bello, C. Cornelis, F. Herrera, IFROWANN: imbalanced fuzzy-rough ordered weighted average nearest neighbor classification, IEEE Transactions on Fuzzy Systems 23(5), 2015, pp. 1622–1637.
  49. A.M. Radzikowska, E.E. Kerre, A comparative study of fuzzy rough sets, Fuzzy Sets and Systems 126, 2002, pp. 137–156.
  50. A. Theerens, O.U. Lenz, C. Cornelis, Choquet-based fuzzy rough sets, International Journal of Approximate Reasoning, in press.
  51. N. Verbiest, C. Cornelis, F. Herrera, FRPS: a fuzzy rough prototype selection method, Pattern Recognition 46(10), 2013, pp. 2770–2782.
  52. N. Verbiest, E. Ramentol, C. Cornelis, F. Herrera, Preprocessing Noisy Imbalanced Datasets using SMOTE enhanced with Fuzzy Rough Proto- type Selection 22, 2014, pp. 511–517.
  53. S. Vluymans, L. D’eer, Y. Saeys, C. Cornelis, Applications of fuzzy rough set theory in machine learning: a survey, Fundamenta Informaticae 142(1-4), 2015, pp. 53–86.
  54. S. Vluymans, D. Sánchez Tarragó, Y. Saeys, C. Cornelis, F. Herrera, Fuzzy rough classifiers for class imbalanced multi-instance data, Pattern Recognition 53, 2016, pp. 36–45.
  55. S. Vluymans, A. Fernández, Y. Saeys, C. Cornelis, F. Herrera, Dynamic affinity-based classification of multi-class imbalanced data with one-vs-one decomposition: a fuzzy rough approach, Knowledge and Information Systems 6(1), 2018, pp. 55–84.
  56. S. Vluymans, C. Cornelis, F. Herrera, Y. Saeys, Multi-label classification using a fuzzy rough neighborhood consensus, Information Sciences 433-434, 2018, pp. 96–114.
  57. S. Vluymans, N. Mac Parthalain , C. Cornelis, Y. Saeys, Weight selection strategies for ordered weighted average based fuzzy rough sets, Information Sciences 501, 2019, pp. 155–171.
  58. R.R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transactions on systems, Man, and Cybernetics 18(1), 1988, pp. 183–190.
  59. R.R. Yager, Quantifier guided aggregation using OWA operators, International Journal of Intelligent Systems 11(1), 1996, pp. 49–73.
  60. J.T. Yao, A.V. Vasilakos, W. Pedrycz, Granular computing: perspectives and challenges, IEEE Transactions on Cybernetics 43(6), 2013, pp. 1977–1989.
  61. Y. Yao, Granular computing using neighborhood systems, Advances in soft computing, Springer, 1999, pp. 539–553.
  62. Y. Yao, Three-way decisions with probabilistic rough sets, Information Sciences 180(3), 2010, pp. 341–353.
  63. L.A. Zadeh, Fuzzy sets, Information and Control 8, 1965, pp. 338–353.
  64. L.A. Zadeh, A computational approach to fuzzy quantifiers in natural languages, in: Computational linguistics, Elsevier, 1983, pp. 149–184.
  65. L.A. Zadeh, Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy sets and systems 90(2), 1997, pp. 111–127.
  66. S. Zhao, E.C.C. Tsang, D. Chen, X. Wang, Building a rule-based classifier—a fuzzy-rough set approach, IEEE Transactions on Knowledge and Data Engineering 22(5), 2009, pp. 624-638.
  67. S. Zhao, Z. Dai, X. Wang, P. Ni, H. Chen, C. Li, An accelerator for rule induction in fuzzy rough theory, IEEE Transactions on Fuzzy Systems 29(12), 2021, pp. 3635-3649.
  68. W. Ziarko, Variable precision rough set model, Journal of computer and system sciences 46(1), 1993, pp. 39–59.