IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v271y2018i2d10.1007_s10479-018-2905-0.html
   My bibliography  Save this article

Bi-criteria optimization problems for decision rules

Author

Listed:
  • Fawaz Alsolami

    (King Abdulaziz University)

  • Talha Amin

    (King Abdullah University of Science and Technology)

  • Igor Chikalov

    (King Abdullah University of Science and Technology)

  • Mikhail Moshkov

    (King Abdullah University of Science and Technology)

Abstract

We consider bi-criteria optimization problems for decision rules and rule systems relative to length and coverage. We study decision tables with many-valued decisions in which each row is associated with a set of decisions as well as single-valued decisions where each row has a single decision. Short rules are more understandable; rules covering more rows are more general. Both of these problems—minimization of length and maximization of coverage of rules are NP-hard. We create dynamic programming algorithms which can find the minimum length and the maximum coverage of rules, and can construct the set of Pareto optimal points for the corresponding bi-criteria optimization problem. This approach is applicable for medium-sized decision tables. However, the considered approach allows us to evaluate the quality of various heuristics for decision rule construction which are applicable for relatively big datasets. We can evaluate these heuristics from the point of view of (i) single-criterion—we can compare the length or coverage of rules constructed by heuristics; and (ii) bi-criteria—we can measure the distance of a point (length, coverage) corresponding to a heuristic from the set of Pareto optimal points. The presented results show that the best heuristics from the point of view of bi-criteria optimization are not always the best ones from the point of view of single-criterion optimization.

Suggested Citation

  • Fawaz Alsolami & Talha Amin & Igor Chikalov & Mikhail Moshkov, 2018. "Bi-criteria optimization problems for decision rules," Annals of Operations Research, Springer, vol. 271(2), pages 279-295, December.
    • Handle: RePEc:spr:annopr:v:271:y:2018:i:2:d:10.1007_s10479-018-2905-0
    DOI: 10.1007/s10479-018-2905-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-018-2905-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-018-2905-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2001. "Rough sets theory for multicriteria decision analysis," European Journal of Operational Research, Elsevier, vol. 129(1), pages 1-47, February.
    2. Peter Hammer & Tibérius Bonates, 2006. "Logical analysis of data—An overview: From combinatorial optimization to medical applications," Annals of Operations Research, Springer, vol. 148(1), pages 203-225, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lejeune, Miguel & Lozin, Vadim & Lozina, Irina & Ragab, Ahmed & Yacout, Soumaya, 2019. "Recent advances in the theory and practice of Logical Analysis of Data," European Journal of Operational Research, Elsevier, vol. 275(1), pages 1-15.
    2. Caserta, Marco & Reiners, Torsten, 2016. "A pool-based pattern generation algorithm for logical analysis of data with automatic fine-tuning," European Journal of Operational Research, Elsevier, vol. 248(2), pages 593-606.
    3. Wen-Min Lu & Qian Long Kweh & Chung-Wei Wang, 2021. "Integration and application of rough sets and data envelopment analysis for assessments of the investment trusts industry," Annals of Operations Research, Springer, vol. 296(1), pages 163-194, January.
    4. Pang, Jifang & Liang, Jiye, 2012. "Evaluation of the results of multi-attribute group decision-making with linguistic information," Omega, Elsevier, vol. 40(3), pages 294-301.
    5. Eduardo Fernández & José Rui Figueira & Jorge Navarro, 2023. "A theoretical look at ordinal classification methods based on comparing actions with limiting boundaries between adjacent classes," Annals of Operations Research, Springer, vol. 325(2), pages 819-843, June.
    6. Doumpos, M. & Marinakis, Y. & Marinaki, M. & Zopounidis, C., 2009. "An evolutionary approach to construction of outranking models for multicriteria classification: The case of the ELECTRE TRI method," European Journal of Operational Research, Elsevier, vol. 199(2), pages 496-505, December.
    7. Skorupski, Jacek & Uchroński, Piotr, 2017. "A fuzzy model for evaluating metal detection equipment at airport security screening checkpoints," International Journal of Critical Infrastructure Protection, Elsevier, vol. 16(C), pages 39-48.
    8. Pierre Hansen & Christophe Meyer, 2011. "A new column generation algorithm for Logical Analysis of Data," Annals of Operations Research, Springer, vol. 188(1), pages 215-249, August.
    9. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 246-276, April.
    10. repec:dau:papers:123456789/4080 is not listed on IDEAS
    11. Becchio, Cristina & Bottero, Marta Carla & Corgnati, Stefano Paolo & Dell’Anna, Federico, 2018. "Decision making for sustainable urban energy planning: an integrated evaluation framework of alternative solutions for a NZED (Net Zero-Energy District) in Turin," Land Use Policy, Elsevier, vol. 78(C), pages 803-817.
    12. Elnaz Gholipour & B'ela Vizv'ari & Zolt'an Lakner, 2020. "Reconstruction Rating Model of Sovereign Debt by Logical Analysis of Data," Papers 2011.14112, arXiv.org.
    13. Fernandez, Eduardo & Navarro, Jorge & Bernal, Sergio, 2010. "Handling multicriteria preferences in cluster analysis," European Journal of Operational Research, Elsevier, vol. 202(3), pages 819-827, May.
    14. Pawel Lezanski & Maria Pilacinska, 2018. "The dominance-based rough set approach to cylindrical plunge grinding process diagnosis," Journal of Intelligent Manufacturing, Springer, vol. 29(5), pages 989-1004, June.
    15. Tsoukias, Alexis, 2008. "From decision theory to decision aiding methodology," European Journal of Operational Research, Elsevier, vol. 187(1), pages 138-161, May.
    16. Choudhary, Devendra & Shankar, Ravi, 2012. "An STEEP-fuzzy AHP-TOPSIS framework for evaluation and selection of thermal power plant location: A case study from India," Energy, Elsevier, vol. 42(1), pages 510-521.
    17. McKenna, R. & Bertsch, V. & Mainzer, K. & Fichtner, W., 2018. "Combining local preferences with multi-criteria decision analysis and linear optimization to develop feasible energy concepts in small communities," European Journal of Operational Research, Elsevier, vol. 268(3), pages 1092-1110.
    18. García Cáceres, Rafael Guillermo & Aráoz Durand, Julián Arturo & Gómez, Fernando Palacios, 2009. "Integral analysis method - IAM," European Journal of Operational Research, Elsevier, vol. 192(3), pages 891-903, February.
    19. Bouyssou, Denis & Pirlot, Marc, 2009. "An axiomatic analysis of concordance-discordance relations," European Journal of Operational Research, Elsevier, vol. 199(2), pages 468-477, December.
    20. Azam, Nouman & Zhang, Yan & Yao, JingTao, 2017. "Evaluation functions and decision conditions of three-way decisions with game-theoretic rough sets," European Journal of Operational Research, Elsevier, vol. 261(2), pages 704-714.
    21. Nikolaos Argyris & Alec Morton & José Rui Figueira, 2014. "CUT: A Multicriteria Approach for Concavifiable Preferences," Operations Research, INFORMS, vol. 62(3), pages 633-642, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:271:y:2018:i:2:d:10.1007_s10479-018-2905-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.