In this study a new hybrid aggregation operator named as the generalized intuitionistic fuzzy hybrid Choquet averaging(GIFHCA) operator is defined.Meantime,some desirable properties are studied, and several important cases are examined.Furthermore,we define the generalized Shapley GIFHCA (GS-GIFHCA) operator,which does not only overall consider the importance of elements and their ordered positions,but also globally reflect the correlations among them and their ordered positions.In order to simplify the complexity of solving a fuzzy measure,we further define the generalizedλ-Shapley GIFHCA(GλS-GIFHCA) operator.
In the framework of games with coalition structure,we introduce probabilistic Owen value which is an extension of the Owen value and probabilistic Shapley value by considering the situation that not all priori unions are able to cooperate with others.Then we use five axioms of probabilistic efficiency,symmetric within coalitions,symmetric across coalitions applying to unanimity games,strong monotone property and linearity to axiomatize the value.
