In a decision problem, let a be a feasible alternative from the set of all feasible alternatives A. Each alternative is measured against n attributes (X1,..., Xn). The decision maker's (DM) problem is to choose an a in A that “maximizes” the payoff vector of scores [X1(a), ..., Xn (a)] = Xva. We define a real-valued, scalar function v(·), the value function, as follows. The function has the property that v(Xva) > vv(Xvb) if and only if the DM prefers alternative a to alternative b; and v(Xva) = vv(Xvb) if and only if the DM is indifferent between alternative a and alternative b. The DM's decision problem is now the selection of an alternative that maximizes v(Xv) over all alternatives.