On shadowed hypergraphs

  • Tamunokuro Opubo William-WestEmail author
Methodologies and Application


Fuzzy hypergraphs are useful tools for representing granular structures when describing the relations between objects and set of hyperedges, at minute detail, in a specific granularity. Their merit over classical hypergraphs lies in their ability to model uncertainty that may arise with objects and/or granules incident to each other. Many previous studies on fuzzy hypergraphs seek to exploit their strong descriptive potential to analyze n-ary relations in several contexts. However, due to the very detailed numeric membership grades of their objects, fuzzy hypergraphs are sensitive to noise, which may be overwhelming in their general interpretation. To address this issue, a principle of least commitment to certain membership grades is sort by embracing a framework of shadowed sets. The specific concern of this paper is to study a noise-tolerable framework, viz. shadowed hypergraph. Our goal is to capture and quantify noisy objects in clearly marked out zones. We discuss some characteristic properties of shadowed hypergraph and describe an algorithm for transforming a given fuzzy hypergraph into its resulting shadowed hypergraph. Finally, some illustrative examples are provided to demonstrate the essence of shadowed hypergraphs.


Fuzzy sets Shadow sets Fuzzy hypergraphs 



The author sincerely wishes to thank the Editor-in-Chief Professor Antonio Di Nola, and the anonymous reviewers for their technical comments and other valuable suggestions.

Compliance with ethical standards

Conflict of interest

The author declares that there is no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by the author.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Physical SciencesAhmadu Bello UniversityZariaNigeria

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