Power harmonic aggregation operator with trapezoidal intuitionistic fuzzy numbers for solving MAGDM problems

Trapezoidal intuitionistic fuzzy numbers (TrIFNs) express abundant and flexible information in a suitable manner and  are very useful to depict the decision information in the procedure of decision making. In this paper, some new aggregation operators, such as, trapezoidal intuitionistic fuzzy weighted power harmonic mean (TrIFWPHM) operator, trapezoidal intuitionistic fuzzy ordered weighted power harmonic mean (TrIFOWPHM) operator, trapezoidal intuitionistic fuzzy induced ordered weighted power harmonic mean (TrIFIOWPHM) operator and trapezoidal intuitionistic fuzzy hybrid power harmonic mean (TrIFhPHM) operator are introduced to aggregate the decision information. The desirable properties of these operators are presented in detail. A prominent characteristic of these operators is that, the aggregated value by using these operators is also a TrIFN. It is observed that the proposed TrIFWPHM operator is the generalization of trapezoidal intuitionistic fuzzy weighted harmonic mean (TrIFWHM) operator, trapezoidal intuitionistic fuzzy weighted arithmetic mean (TrIFWAM) operator, trapezoidal intuitionistic fuzzy weighted geometric mean (TrIFWGM) operator and trapezoidal intuitionistic fuzzy weighted quadratic mean (TrIFWQM) operator, {it i.e.,} we can easily reduce the TrIFWPHM operator to TrIFWHM, TrIFWGM, TrIFWAM and TrIFWQM operators, depending upon the decision situation. Further, we develop an approach to multi-attribute group decision making (MAGDM) problem on the basis of the proposed aggregation operators. Finally, the effectiveness and applicability of our proposed MAGDM model, as well as comparison analysis with other approaches are illustrated with a practical example.