Probabilistic model criteria with decision-theoretic rough sets

  • Authors:

  • Dun Liu;Tianrui Li;Da Ruan

  • Affiliations:

  • Department of Economics and Management, Southwest Jiaotong University, Chengdu 610031, China;Department of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China;Belgian Nuclear Research Centre (SCKCEN), Boeretang 200, 2400 Mol, Belgium and Department of Applied Mathematics and Computer Science, Ghent University, 9000 Gent, Belgium

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

In dealing with risk in real decision problems, decision-theoretic rough sets with loss functions aim to obtain optimization decisions by minimizing the overall risk with Bayesian decision procedures. Two parameters generated by loss functions divide the universe into three regions as the decision of acceptance, deferment and rejection. In this paper, we discuss the semantics of loss functions, and utilize the differences of losses replace actual losses to construct a new ''four-level'' approach of probabilistic rules choosing criteria. Ten types of probabilistic rough set models can be generated by the ''four-level'' approach and form two groups of models: two-way probabilistic decision models and three-way probabilistic decision models. A reasonable decision with these criteria is demonstrated by an illustration of oil investment.