Granular Computing

, Volume 4, Issue 1, pp 27–38 | Cite as

Induction of shadowed sets from fuzzy sets

  • Adeku Musa Ibrahim
  • Tamunokuro Opubo William-West
Original Paper


A new method for computing a threshold value of an \(\alpha\)-cut for the induction of shadowed sets from fuzzy sets is proposed by modifying the formula for balance of uncertainty; which is required for transforming a fuzzy set into its resulting shadowed set. In order to reach a compromise between retention of the original amount of information in a fuzzy set and the optimality of a specific threshold level, the proposed method anchors on the average of the balance of uncertainties under various feasible \(\alpha\)-cuts. We describe and exemplify an algorithm which illustrates our proposed method. Finally, a number of randomly generated fuzzy sets are used as test samples to compare and point out the advantage of the proposed method over existing method.


Fuzzy set Shadowed set Uncertainty Three-way decision 



The authors are thankful to the Editors-in-Chief: Professor Withold Pedrycz and Professor Shyi-Ming Chen for their technical comments and to the anonymous Reviewers for their suggestions, which have improved the quality of this paper.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest toward the publication of this manuscript.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Adeku Musa Ibrahim
    • 1
  • Tamunokuro Opubo William-West
    • 1
  1. 1.Department of MathematicsAhmadu Bello UniversityZariaNigeria

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