Shadowed sets with higher approximation regions

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...

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Bibliographic Details
Published in:Soft computing (Berlin, Germany) Germany), 2020-11, Vol.24 (22), p.17009-17033
Main Authors: Ibrahim, M. A., William-West, T. O., Kana, A. F. D., Singh, D.
Format: Article
Language:English
Subjects:
Approximation
Artificial Intelligence
Computational Intelligence
Control
Engineering
Fuzzy sets
Mathematical analysis
Mathematical Logic and Foundations
Mechatronics
Methodologies and Application
Optimization
Principles
Robotics
Thresholds
Uncertainty
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Summary: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.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-020-04992-8