A new cost function to solve multi-attribute decision making problems with nonseparable attributes

The authors deal with multi-attribute decision problems, assuming the existence of a utility/cost function, and the possibility of preferentially nonindependent attributes. The aim is to identify a cost function, whose structure satisfies the following three basic assumptions: it should allow a certain degree of preferential independence among the attributes; its identification should be through the use of an efficient algorithm; and it should reflect the decision maker´s behavior. An algorithm to determine the optimal cost function, when this function is positive semi-definitive quadratic or multilinear Hessian, is discussed