Cubic bipolar fuzzy ordered weighted geometric aggregation operators and their application using internal and external cubic bipolar fuzzy data

  • Muhammad RiazEmail author
  • Syeda Tayyba Tehrim


In the present study, we discuss the concept of internal cubic bipolar fuzzy (ICBF) sets and external cubic bipolar fuzzy (ECBF) sets. We also discuss some properties of ICBF-sets and ECBF-sets under both \(\mathcal {P}\)-Order and \(\mathcal {R}\)-Order. We present examples and counterexamples to support our concepts. Furthermore, we see the importance of ICBF-sets and EBCF-sets in multiple attribute decision making. We proposed two cubic bipolar fuzzy ordered weighted geometric aggregation operators, including, \(\mathcal {P}\)-CBFOWG operator and \(\mathcal {R}\)-CBFOWG operator to aggregate cubic bipolar fuzzy information with both perspectives, i.e., ICBF data and ECBF data. Finally, we present a multiple attribute decision making problem to examine the useability and capability of these operators and a comparison between ICBF information and ECBF information.


Internal cubic bipolar fuzzy sets External cubic bipolar fuzzy sets Properties of ICBF-sets and ECBF-sets \(\mathcal {P}\)-CBFOWG and \(\mathcal {R}\)-CBFOWG operators Multiple attribute decision making 

Mathematics Subject Classification

90B50 03E72 



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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the PunjabLahorePakistan

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