Table 1.
Summary of literature review
| Aggregation operators |
Proposed by | Findings | Gaps |
|---|---|---|---|
|
Weighted Geometric (WG) |
Aczel and Saaty (1983) |
Offer simple multiplicative weighting method Synthesizing ratio judgments in AHP method |
Cannot capture the complex decision situations Did not consider the interdependencies among input arguments |
|
Weighted Average (WA) |
Dong and Wong (1987) | Offer simple additive weighting method | |
|
Ordered weighted average (OWA) |
Yager (1988) |
A parameterized operator that provides aggregations between maximum and minimum the arithmetic average, and the median criteria The weight vector of input arguments is according to the rearranged ordered position of all the input arguments |
Did not consider the information when the relationship among input arguments are in the hesitant, indeterminant and bipolar situations |
|
Ordered weighted geometric (OWG) |
Chiclana et al. (2000) | Extended from WG and OWA | |
| Einstein | Wang and Liu (2011) | Introduce the Einstein operations in WG and OWG for intuitionistic fuzzy set | Did not consider the interrelationship among input arguments |
|
Choquet integral |
Choquet (1953) | A generalization form to the WA and able to take into account the importance of a criterion, as well as the interactions between criteria |
Did not consider the overall interaction among input decision makers The computation is long and complicated |
| Hamacher | Hamacher (1978) | The Hamacher t-norm and t-conorm are more flexible and a generalized form to the algebraic operators and Einstein t-norm and t-conorm respectively |
Did not consider the interrelationship among input arguments Did not express decision makers’ hesitancy and bipolar judgmental thinking during evaluation process |
|
Prioritized average (PA) |
Xu and Yager (2006) | Modelling the importance of the relationship among criteria by knowing the priority among the criteria and unnecessary to provide weight vectors | Suppose that the input arguments are mutually independent |
|
Heronian mean (HM) |
Beliakov et al. (2007) | Capturing the correlations of the aggregated arguments | Did not consider the hesitant, bipolar and indeterminate informations |
|
Bonferroni Mean (BM) |
Bonferroni (1950) |
An extension of the arithmetic means and geometric means Reflect the interdependence of the individual input arguments |
Did not reflect the overall interaction among decision makers Did not consider the hesitant, bipolar and indeterminate informations |