Background: Multiple attribute group decision making (MAGDM) is the common phenomenon
in modern life, which is to select the optimal alternative(s) from several alternatives or to
discover their ranking by aggregating the performances of each alternative under several attributes, in
which the aggregation techniques play an important role, also described in various patents.
Methods: We extend the Bonferroni mean (BM) to intuitionistic fuzzy environment and defined a
trapezoidal intuitionistic fuzzy Bonferroni harmonic mean (TrIFBHM). Some special properties are
discussed based on the trapezoidal intuitionistic fuzzy Bonferroni harmonic element (TrIFBHE).
Results: Considering the weight vector of the arguments, we develop a weighted trapezoidal intuitionistic
fuzzy Bonferroni harmonic mean (WTrIFBHM) and apply it to Multiple attribute group decision
making (MAGDM). Furthermore, a weighted trapezoidal intuitionistic fuzzy order Bonferroni harmonic
mean (WTrIFOBHM) has been defined, which is an effective tool to reveal the importance of
each attribute and the correlations among them in MAGDM problems. Finally, we develop an application
of the new approach and illustrate it with a numerical example.
Conclusion: The developed approaches for MAGDM under intuitionistic fuzzy environment have
been illustrated with a practical application. The main advantage of the WTrIFBHM is that it can explore
the importance of each attribute and the interrelationship between attribute reflected by the
TrIFBHEs, give prominence to arguments performance too high or too low, and allow the decision
makers to assign all the possible values to the alternatives so as to obtain reasonable results with more
information taken into account.