Abstract
A crucial issue related to the Atanassov's intuitionistic fuzzy operators is how to determine their weights. Various weighted methods have been proposed last decades, but it seems that there is no investigation on the monotonous and proportion-invariant properties, which is decisive for aggregation and comparison of Atanassov's intuitionistic fuzzy values in group decision making. In this paper, we propose a novel weighted method, i.e., precisely weighted method, to calculate Atanassov's intuitionistic fuzzy aggregation operator weights, and prove its monotonicity and proportion-invariance. Then, we develop two weighted aggregation operators based on this new method, i.e. the Atanassov's intuitionistic fuzzy ordered precisely weighted averaging (A-IFOPWA) operator and the Atanassov's intuitionistic fuzzy ordered precisely weighted geometric (A-IFOPWG) operator. Furthermore, some of their desirable properties are investigated in detail. Finally, a practical example is provided to illustrate the precisely weighted method and the developed aggregation operators.