Extreme intuitionistic fuzzy weighted aggregation operators and their applications in optimism and pessimism decision-making processes

As a convenient and effective aggregation method, the weighted aggregation operators have been applied in some fields of real decision-makings, and many extended forms have been presented and investigated. For this reason, the intuitionistic fuzzy weighted aggregation operators, such as the intuitionistic fuzzy weighted averaging/geometric operators and the intuitionistic fuzzy ordered weighted averaging/geometric operators, are proposed and developed. However, one dilemma is that the selection principle of the different aggregation operators is indistinct and arbitrary in real decision making. Consequently, in this paper, we propose four extreme intuitionistic fuzzy weighted aggregation operators, namely, the intuitionistic fuzzy maximum weighted averaging (IFW(max)A), the intuitionistic fuzzy minimum weighted averaging (IFW(min)A), the intuitionistic fuzzy maximum weighted geometric (IFW(max)G), and the intuitionistic fuzzy minimum weighted geometric (IFW(min)G), and then study their relationships and point out their selection principles. Furthermore, the optimism and pessimism decision-making approaches are constructed and analyzed based on these new operators. Finally, an investment decision making case is provided to demonstrate the constructed optimism and pessimism decision-making processes and the proposed extreme intuitionistic fuzzy weighted aggregation operators under the intuitionistic fuzzy environment.