On the measure based formulation of multi-criteria decision functions

The basic features and properties of a fuzzy measure are first introduced. We next discuss the Choquet integral and describe its usage in finding the aggregation of a collection of values guided by a fuzzy measure. We then show how the Choquet integral and an associated fuzzy measure can be applied to the construction of multi-criteria decision functions and describe how the associated fuzzy measure is used to model the desired multi-criteria decision function. We then look at various fuzzy measures and investigate the types of decision functions they allow us to formulate. Notable among the measures investigated here are those that allow us to model a prioritized aggregation of the criteria and a rule based aggregation of multiple criteria. Finally we show how to model linguistically specified decision functions using fuzzy measures.