Uncertainty measurement for neighborhood based soft covering rough graphs with applications

  • Noor Rehman
  • Nasir Shah
  • Muhammad Irfan Ali
  • Choonkil ParkEmail author
Original Paper


Soft set theory and rough set theory are two newer tools to discuss uncertainty. Soft graphs are a nice way to depict certain information. In order to discuss uncertainty in soft graphs, a new type of graphs called neighborhood based soft covering rough graphs is introduced. We have discussed the uncertainty measures associated with neighborhood based soft covering rough graphs such as roughness measure, entropy measure and granularity. Some important properties of these uncertainty measures are investigated and the relationships between such measures are established. These properties will help to understand the essence of uncertainty measurement and in measuring the quality of a decision rule.


Soft set theory Uncertainty measure Soft graph Soft covering rough graph Information entropy Granularity 

Mathematics Subject Classification

08A72 54A40 03B52 20N25 



C. Park was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2017R1D1A1B04032937). The authors are thankful to the reviewers and the editors for their close attention and constructive suggestions to improve the quality of the manuscript.

Compliance with ethical standards

Conflict of interest

The authors of this paper declare that they have no conflict of interest.


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Copyright information

© The Royal Academy of Sciences, Madrid 2019

Authors and Affiliations

  • Noor Rehman
    • 1
  • Nasir Shah
    • 2
  • Muhammad Irfan Ali
    • 3
  • Choonkil Park
    • 4
    Email author
  1. 1.Department of Mathematics and StatisticsBacha Khan University CharsaddaKPKPakistan
  2. 2.Department of Mathematics and StatisticsRiphah International UniversityIslamabadPakistan
  3. 3.Department of MathematicsIslamabad Model College for GirlsIslamabadPakistan
  4. 4.Research Institute for Natural SciencesHanyang UniversitySeoulKorea

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