Intuitionistic fuzzy power geometric Heronian mean operators and their application to multiple attribute decision making

This paper investigates intuitionistic fuzzy information aggration problem with the interrelationship among the input values and the "singular point" (i.e. the input value was either too large or too small) which canot be solved by most existing aggregation operators. To accomplish this, this paper combines the geometric Heronian mean (GHM) operator with the power geometric (PG) operator under intuitionistic fuzzy environment. Then, the intuitionistic fuzzy power GHM (IFPGHM) operator and the weighted intuitionistic fuzzy power GHM (WIFPGHM) operator are presented. The new operators capture not only the correlations between the input arguments but also the relative closeness of decision making information such that they can better solve the intuitionistic fuzzy information aggregation problem with diversified connections between arguments. The desirable properties of these new extensions of GHM operator and their special cases are investigated. Finally, based on the WIFPGHM operator, we present an approach to multiple attribute decision making and illustrate that approach with a practical example.