Abstract

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.

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