The triangular intuitionistic fuzzy number (TIFN) is a special intuitionistic fuzzy set defined on the real number set. The multi-criteria group decision making (MCGDM) with the prioritization among the criteria is called the prioritized MCGDM. The aim of this paper is to develop some prioritized geometric operators for TIFNs and apply to the prioritized MCGDM problems with TIFNs. Firstly, the weighted possibility means of TIFNs are defined and hereby a new lexicographic approach is given to rank the TIFNs sufficiently considering the risk preference of decision maker. Then, three kinds of prioritized geometric operators for TIFNs are developed including the prioritized weighted geometric (TIFPWG) operator, prioritized ordered weighted geometric (TIFPOWG) operator and prioritized hybrid weighted geometric (TIFPHWG) operator of TIFNs. Utilized the TIFPWG operator, the criteria values of alternatives are aggregated into the individual overall values of alternatives, which are further integrated into the collective ones by the TIFPHWG operator. The ranking order of alternatives is generated according to the collective overall values of alternatives. Finally, the system analyst selection example is analyzed to demonstrate the applicability and validity of the proposed method.
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