Especially, if [omega] = [(1/n,1/n, ..., 1/n).sup.T], then the FPWG operator reduces to a fuzzy power geometric (FPG) operator:
It can be easily proved that the FPWG operator has the following properties similar to the FPWA operator.
From the definitions of the FPWA and FPWG operators, it can be seen that the fundamental characteristics of these two operators is that they weight all the given triangular fuzzy numbers, and weighting vectors depend upon the input arguments and allow values being aggregated to support and reinforce each other.
Then, we utilize the FPWA (or FPWG, FPWHA, FPWQA) operator to develop an approach to multiple attribute group decision making problems with triangular fuzzy information, which can be described as following:
Utilising the FPWA (or FPWG, FPWHA, FPWQA) operator to aggregate all the individual decision matrices into the collective decision matrix, the aggregating results are shown in Tables 10-13.
In this paper, based on the ideal of power aggregation, proposed eight triangular fuzzy power aggregation operators were proposed: the fuzzy power weighted average (FPWA) operator, the fuzzy power weighted geometric (FPWG) operator, fuzzy power weighted harmonic average (FPWHA), fuzzy power weighted quadratic average (FPWQA), the fuzzy power ordered weighted average (FPOWA) operator, the fuzzy power ordered weighted geometric (FPOWG) operator, fuzzy power ordered weighted harmonic average (FPOWHA) and fuzzy power ordered weighted quadratic average (FPOWQA).