Problem solving with multiple interdependent criteria ∗

We consider multiple objective programming (MOP) problems with additive interdependences, i.e. when the states of some chosen objective are attained through supportive or inhibitory feed-backs from several other objectives. We show how the concept of interdependency can be applied to an n-party single-issue negotiation problem in which the negotiators cooperatively face a common problem or in which the parties’s interests are not diametrically opposed (variable-sum bargaining situations). 1 MOP Problems with Interdependent Objectives In their classical text Theory of Games and Economic Behavior John von Neumann and Oskar Morgenstern (1947) described the problem with interdependence; in their outline of a social exchange economy They discussed the case of two or more persons exchanging goods with each others (page 11): . . . then the results for each one will depend in general not merely upon his own actions but on those of others as well. Thus each participant attempts to maximize a function . . . of which he does not control all variables. This is certainly no maximum problem, but a peculiar and disconcerting mixture of several conflicting maximum problems. Every participant is guided by another principle and neither determines all variables which affects his interest. This kind of problem is nowhere dealt with in classical mathematics. We emphasize at the risk of being pedantic that this is no conditional maximum problem, no problem of the calculus of variations, of functional analysis, etc. It arises in full clarity, even in the most ”elementary” situations, e.g., when all variables can assume only a finite number of values. The interdependence is part of the economic theory and all market economies, but in most modelling approaches in multiple criteria decision making there seems to be an implicit assumption that objectives should be independent. This appears to be the case, if not earlier than at least at the moment when we have to select some optimal compromise among the set of nondominated decision alternatives. Milan Zeleny [26] and many others recognizes one part of the interdependence (page 1), Multiple and conflicting objectives, for example, ”minimize cost” and ”maximize the quality of service” are the real stuff of the decision maker’s or manager’s daily concerns. ∗The final version of this paper appeared in: J. Kacprzyk, H.Nurmi and M.Fedrizzi eds., Consensus under Fuzziness, The Kluwer International Series in Intelligent Technologies, Vol. 10, Kluwer Academic Publishers, Boston, 1997 231-246.