Attributes reductions of bipolar fuzzy relation decision systems

  • Ghous Ali
  • Muhammad Akram
  • José Carlos R. AlcantudEmail author
Original Article


Attribute reduction methods constitute a very important preprocessing step for artificial intelligence and pattern recognition. It has been investigated in contexts ranging from rough sets to soft sets. In this study, firstly we propose the ideas of bipolar fuzzy relation systems and bipolar fuzzy relation decision systems. They constitute intuitive extensions of various systems, for instance decision tables, relation systems, relation decision systems, fuzzy relation systems (FRSs) and fuzzy relation decision systems (FRDSs). Secondly, relying on mathematical proofs we investigate the attribute reduction problems for bipolar fuzzy relation systems and bipolar fuzzy relation decision systems and we give their corresponding reduction algorithms. Moreover, we compute the reduction algorithms for FRSs and FRDSs as particular cases of bipolar fuzzy relation systems and bipolar fuzzy relation decision systems, respectively. The experimental results prove that the concepts in this study are valid and implementable.


Bipolar fuzzy relation system Bipolar fuzzy relation decision system Fuzzy relation system Fuzzy relation decision system Attribute reduction 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest regarding the publication of the paper.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the PunjabLahorePakistan
  2. 2.BORDA Research Unit and IMEUniversity of SalamancaSalamancaSpain

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