Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon openaccess Rule induction based on rough sets from information tables having continuous domains

  • Author(s): Michinori Nakata 1 ; Hiroshi Sakai 2 ; Keitarou Hara 3
    • View affiliations
  • Source: Volume 4, Issue 4, December 2019, p. 237 – 244
    DOI:  10.1049/trit.2019.0025 , Online ISSN 2468-2322
This is an open access article published by the IET, Chinese Association for Artificial Intelligence and Chongqing University of Technology under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/)
Received 30/03/2019, Accepted 23/09/2019, Revised 20/08/2019, Published 04/10/2019

Information tables having continuous domains are handled by neighborhood rough sets. Two approximations in complete information tables are extended to handle incomplete information. Consequently, four approximations are obtained: certain and possible lower ones and certain and possible upper ones without computational complexity. These extended approximations create the same results as the ones from possible world semantics by using possible indiscernibility relations. Therefore, the extension is justified. In complete information tables two types of single rules that an object supports are obtained: consistent and inconsistent ones. The single rule has low applicability. To increase applicability, a series of single rules are brought into one combined rule with an interval value. In incomplete information tables four kinds of single rules are obtained. From them, four kinds of combined rules are obtained: certain and consistent, possible and consistent, certain and inconsistent, and possible inconsistent ones. A combined rule has higher applicability than the single rules from which it is assembled.

Inspec keywords: rough set theory; approximation theory

Other keywords: incomplete information tables; consistent ones; possible indiscernibility relations; upper approximation; inconsistent ones; lower approximation; possible lower approximations; combined rule; consistent rules; complete information tables; possible upper ones; inconsistent rules; extended approximations; continuous domains; possible upper approximations; single rule; rule induction; possible world semantics; neighbourhood rough sets; possible ones; possible lower ones

Subjects: Combinatorial mathematics; Knowledge engineering techniques

References

    1. 1)
      • [23]. Zimányi, E., Pirotte, A.: ‘Imperfect information in relational databases’, in Motro, A., Smets, P. (Eds.): ‘Uncertainty management in information systems: from needs to solutions’ (Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997), pp. 35–87.
    2. 2)
      • [11]. Nakata, M., Sakai, H.: ‘Applying rough sets to information tables containing missing values’. Proc. 39th Int. Symp. on Multiple-Valued Logic, Naha, Okinawa, Japan, 2009, Changchun, Jilin, China, 2009, pp. 286–291.
    3. 3)
      • [13]. Nakata, M., Sakai, H.: ‘Rough sets handling missing values probabilistically interpreted’, Lect. Notes Artif. Intell., 2005, 3641, pp. 325–334.
    4. 4)
      • [18]. Abiteboul, S., Hull, R., Vianu, V.: ‘Foundations of databases’ (Addison-Wesley Publishing Company, Reading, Massachusetts, USA, 1995).
    5. 5)
      • [1]. Pawlak, Z.: ‘Rough sets: theoretical aspects of reasoning about data’ (Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991).
    6. 6)
    7. 7)
      • [17]. Skowron, A., Stepaniuk, J.: ‘Tolerance approximation spaces’, Fundam. Inform., 1996, 27, pp. 245–253.
    8. 8)
      • [3]. Yang, Y., Webb, I. G., Wu, X.: ‘Discretization methods’, in Maimon, O., Rokachan, L. (Eds.): ‘Data mining and knowledge discovery handbook’ (Springer, Berlin, Germany, 2005), pp. 113–130.
    9. 9)
    10. 10)
      • [4]. Grzymala-Busse, J.W.: ‘Mining numerical data – a rough set approach’, Trans. Rough Sets, 2010, XI, pp. 1–13.
    11. 11)
    12. 12)
    13. 13)
    14. 14)
    15. 15)
    16. 16)
    17. 17)
      • [5]. Lin, T.Y.: ‘Neighborhood systems: a qualitative theory for fuzzy and rough sets’, Adv. Mach. Intell. Soft Comput., 1977, IV, pp. 132–155.
    18. 18)
      • [22]. Paredaens, J., De Bra, P., Gyssens, M., et al: ‘The structure of the relational database model’ (Springer-Verlag, Berlin, Germany, 1989).
    19. 19)
      • [8]. Yang, X., Zhang, M., Dou, H., et al: ‘Neighborhood systems-based rough sets in incomplete information system’, Inf. Sci., 2011, 24, pp. 858–867.
    20. 20)
    21. 21)
    22. 22)
      • [10]. Zhao, B., Chen, X., Zeng, Q.: ‘Incomplete hybrid attributes reduction based on neighborhood granulation and approximation’. 2009 Int. Conf. on Mechatronics and Automation, 2009, pp. 2066–2071.
    23. 23)
http://iet.metastore.ingenta.com/content/journals/10.1049/trit.2019.0025
Loading

Related content

content/journals/10.1049/trit.2019.0025
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
Print this page
This is a required field
Please enter a valid email address