Shadowed set is a mathematical tool that processes uncertain information through three-way approximations, effectively reducing the cost of fuzzy decision-making and computation, and has been widely used in fields such as data mining, pattern recognition, and decision support. However, the existing shadowed set models are mainly based on the consideration of a single fuzzy set, lacking the comprehensive consideration of multiple fuzzy sets (multiple attributes, multiple approximation spaces) and information granules (equivalent classes), which is difficult to effectively achieve the approximate description of complex target concepts. In addition, the issues of “hard computation” and “subjectivity” in traditional rough set models also weaken the effectiveness of the three-way partitioning results. Therefore, Rough Shadowed Set (RSS) is proposed in this paper. First, analyzed the mapping relationship between rough set, shadowed set, and the three-way decision, and divided the results of the approximate partitioning of RSS into two stages. Second, in two stages, rough set is utilized to achieve comprehensive consideration of multiple attributes and information granules, shadowed set is utilized to achieve deblurring of real valued information system, and quadratic analysis and partitioning of uncertainty equivalence classes in the boundary region of rough set. Third, integrating the results of two stages to achieve the combination of the advantages of rough set and shadowed set theory, as well as a more reasonable and effective approximation of complex target concepts. Finally, the framework, definition, decision rules, algorithms, experimental analysis, and future discussions of the model are presented. The experimental results indicate that RSS has better payoff compared to traditional rough set and shadowed set models, namely higher approximate coverage and accuracy, which demonstrates the validity and rationality of RSS.

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Rough Shadowed Set: Hybridization of Rough Set and Shadowed Set

  • Man Gao,
  • Qinghua Zhang,
  • Pengren Jin,
  • Deyou Xia,
  • Guoyin Wang

摘要

Shadowed set is a mathematical tool that processes uncertain information through three-way approximations, effectively reducing the cost of fuzzy decision-making and computation, and has been widely used in fields such as data mining, pattern recognition, and decision support. However, the existing shadowed set models are mainly based on the consideration of a single fuzzy set, lacking the comprehensive consideration of multiple fuzzy sets (multiple attributes, multiple approximation spaces) and information granules (equivalent classes), which is difficult to effectively achieve the approximate description of complex target concepts. In addition, the issues of “hard computation” and “subjectivity” in traditional rough set models also weaken the effectiveness of the three-way partitioning results. Therefore, Rough Shadowed Set (RSS) is proposed in this paper. First, analyzed the mapping relationship between rough set, shadowed set, and the three-way decision, and divided the results of the approximate partitioning of RSS into two stages. Second, in two stages, rough set is utilized to achieve comprehensive consideration of multiple attributes and information granules, shadowed set is utilized to achieve deblurring of real valued information system, and quadratic analysis and partitioning of uncertainty equivalence classes in the boundary region of rough set. Third, integrating the results of two stages to achieve the combination of the advantages of rough set and shadowed set theory, as well as a more reasonable and effective approximation of complex target concepts. Finally, the framework, definition, decision rules, algorithms, experimental analysis, and future discussions of the model are presented. The experimental results indicate that RSS has better payoff compared to traditional rough set and shadowed set models, namely higher approximate coverage and accuracy, which demonstrates the validity and rationality of RSS.