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Additional info for Artificial Intelligence: A Theoretical Approach
P. , 1990; Statnikov, 1999; Tabucanon, 1988). Let us also mention examples of reviews of methods including (Buchanan, 1986; Stewart, 1992) and collections of interactive methods like (Korhonen, 2005; Shin and Ravindran, 1991; Vanderpooten and Vincke, 1989). 1 Diﬀerent Trade-oﬀ Concepts Several deﬁnitions of trade-oﬀs are available in the MCDM literature. Intuitively speaking, a trade-oﬀ is an exchange, that is, a loss in one aspect of the problem, in order to gain additional beneﬁt in another aspect.
In other words, we are not actually able to ﬁnd any Pareto optimal solution but only such solutions having a ﬁnite trade-oﬀ. However, when solving real-life problems, it is very likely that the DM is not interested in improperly Pareto optimal solutions after all. 1). , the term multiplied by ρ) to the objective function α. Alternatively, it is possible to generate provably Pareto optimal solutions by solving two problems in a row. 8). 8). ,k wi (fi (x∗ ) − zi ) , x ∈ S. One should mention that the resulting problem may be computationally badly conditioned if the problem has only one feasible solution.
However, the drawback here is that if there is a promising solution really close to the bound but on the infeasible side, it will never be found. In other words, the bounds are a very stiﬀ way of specifying preference information. In what follows, we discuss three method classes described in the introduction and outline some methods belonging to each of them. Again, proofs of theorems related to optimality as well as further details about the methods can be found in (Miettinen, 1999). 4 No-Preference Methods In no-preference methods, the opinions of the DM are not taken into consideration in the solution process.