Nonadditivity index and capacity identification method in the context of multicriteria decision making

Nonadditivity is an essential property of the capacities defined on the sets of decision criteria. Nonadditivity extends the additivity of traditional probability measures and enables capacities to flexibly represent the interaction phenomenon between the decision criteria. We propose the nonadditivity index to quantify the degree and kind of nonadditivity of a capacity, discuss some properties of this index, and present some tools to help decision makers determine the nonadditivity index of given subset. The nonadditivity index based capacity identification method is proposed and formulated in terms of linear constraints representing the decision makers' explicit or implicit preferences. A linear programming model is formulated as an aid for an optimal capacity identification. The proposed capacity identification method is illustrated on an example.