Dominance-based fuzzy rough set analysis of uncertain and possibilistic data tables

  • Authors:

  • Tuan-Fang Fan;Churn-Jung Liau;Duen-Ren Liu

  • Affiliations:

  • Department of Computer Science and Information Engineering, National Penghu University of Science and Technology, Penghu 880, Taiwan;Institute of Information Science, Academia Sinica, Taipei 115, Taiwan;Institute of Information Management, National Chiao-Tung University, Hsinchu 300, Taiwan

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2011

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Abstract

In this paper, we propose a dominance-based fuzzy rough set approach for the decision analysis of a preference-ordered uncertain or possibilistic data table, which is comprised of a finite set of objects described by a finite set of criteria. The domains of the criteria may have ordinal properties that express preference scales. In the proposed approach, we first compute the degree of dominance between any two objects based on their imprecise evaluations with respect to each criterion. This results in a valued dominance relation on the universe. Then, we define the degree of adherence to the dominance principle by every pair of objects and the degree of consistency of each object. The consistency degrees of all objects are aggregated to derive the quality of the classification, which we use to define the reducts of a data table. In addition, the upward and downward unions of decision classes are fuzzy subsets of the universe. Thus, the lower and upper approximations of the decision classes based on the valued dominance relation are fuzzy rough sets. By using the lower approximations of the decision classes, we can derive two types of decision rules that can be applied to new decision cases.