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Shadowed sets with higher approximation regions
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DOI：10.1007/s00500-020-04992-8.png)
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Abstract
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This paper mainly discusses three points involving shadowed set approximation of a given fuzzy set. Firstly, a principle of uncertainty balance, which guarantees that preservation of uncertainty in the induced shadowed set is studied. Secondly, an alternative formulation for determining the optimum partition thresholds of shadowed sets is suggested. This formulation helps us study principle of uncertainty balance in shadowed sets with higher approximation regions. Thirdly, five-region shadowed set, which effectively deals with the issue of uncertainty balance, is introduced. We provide a closed-form formula for determining its optimum partition thresholds and generalize it to n(>= 5)-region shadowed sets. Finally, some examples from synthetic and real dataset are provided to demonstrate the feasibility of the suggested methods.
Keywords:
Fuzzy set
Shadowed set
Three-way approximation
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