International Journal for Uncertainty Quantification

Interval-Valued Intuitionistic Fuzzy Power Maclaurin Symmetric Mean Aggregation Operators and their application to multiple attribute group decision making

ABSTRACT

The power average operator(PA), originally introduced by Yager, can reduce the negative impact of unreasonable evaluation values on the decision result. The Maclaurin symmetric mean(MSM), originally introduced by Maclaurin, can reflect the interrelationship among the multi-input arguments. However, in some complex decision-making situations, we need to reduce the influence of unreasonable evaluation values and reflect the interrelationship among the multi-input arguments at the same time. In this paper, in order to solve such situations, we combine the ordinary PA operator with the traditional MSM in interval-valued intuitionistic context and propose two novel interval-valued intuitionistic fuzzy aggregation operators, i.e., the interval-valued intuitionistic fuzzy power Maclaurin symmetric mean operator(IVIFPMSM) and the weighted interval-valued intuitionistic fuzzy power Maclaurin symmetric mean operator(WIVIFPMSM). Then, some desirable properties of these new proposed operators are investigated and some special cases are discussed. Further, based on these proposed operators, we develop a new approach to multiple attribute group decision making under interval-valued intuitionistic fuzzy environment. Finally, two examples are provided to illustrate the feasibility and validity of the proposed approach by comparing with other existing representative methods.