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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
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    References listed on IDEAS

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    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.
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