Variable Precision Rough Set Model Based on Set Pair Homeopathic Similarity Relationship

Abstract

  Due to the complexity and uncertainty of the objective world, as well as the limitation of human understanding, it has been difficult for the classical rough set method to deal with incomplete information system with noise data, ambiguity and other informational uncertainties. In view of this, the thought and method of the set pair theory and variable precision rough set are used in this paper to construct a novel variable precision rough set model. After scrutinizing the advantages and limitations of the models previously established based on the set pair similarity relationship, we define the set pair homeopathic similarity relationship based on threshold connection degree. Then we employ this new concept to substitute the equivalence relationship of the variable precision rough set so that a novel variable precision rough set model based on the set pair homeopathic similarity relationship is established. Upon developing the properties of this model, we construct an example to show the feasibility and effectiveness of our novel model.