Reduction of an information system

  • Muhammad ShabirEmail author
  • Rani Sumaira Kanwal
  • Muhammad Irfan Ali
Methodologies and Application


Notion of soft binary relation is studied here. Some properties of lower and upper approximations with the help of soft equivalence relations are given. Actually, approximations of a subset by a soft binary relation give rise to two soft sets. This new setting is very clear and provides approximations related to every parameter/attribute under consideration. For any subset X,  there is an associated fuzzy subset with respect to each parameter. These fuzzy sets are very helpful in decision-making problems. Parametric reduction helps to reduce the size of data. A technique has been presented for this purpose.


Soft sets Rough sets Fuzzy sets Soft rough sets Decision making Parametric reduction 



Authors are thankful to anonymous reviewers and the editors for their very nice suggestions which enhanced the quality of this paper by a great deal.

Compliance with ethical standards

Conflict of interest

All the authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.


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Copyright information

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

Authors and Affiliations

  • Muhammad Shabir
    • 1
    Email author
  • Rani Sumaira Kanwal
    • 1
  • Muhammad Irfan Ali
    • 2
  1. 1.Department of MathematicsQuaid-i-Azam universityIslamabadPakistan
  2. 2.Islamabad Model College for Boys G-11/1IslamabadPakistan

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