MCDM Interactive Methods - An Overview

6. Concluding Remarks

For technical convenience, in numerical implementations of all methods presented above set Λ is usually transformed to the following form $\bar \Lambda = \{ \lambda \in \mathcal{R}^k |\lambda _i > 0,i = 1,...,k,\Sigma _{i = 1}^k \lambda _i = 1\}$. This is achieved by dividing each component of λ by the sum of all components of that λ, for all λ ∈ Λ. There is an obvious one-to-one correspondence between Λ and $\bar \Lambda$.

It is astonishing but fortunately true that the multitude of interactive MCDM methods fall just to one of three classes which correspond to three types of characterizations presented in Chapter 3. This not only allows simple presenting and smooth “marketing” the field of MCDM to potential users, but has some methodological and technical consequences for the way interactive MCDM methods can be implemented and applied in practice. In particular, the general outline of interactive MCDM methods given in this chapter is sufficient for presenting in Chapter 6 the Generic Decision Supporting Scheme.

Interactive MCDM methods are “soft” in the sense that they deny rigorous formal convergence considerations. The rationale behind this type of methods is an assumption, strongly supported by evidence from practical applications (real, not academic), that there is noway to encapsulate DM preferences into a formal, consistent, and verifiable framework. If so, the convergence issues are to be left to experimental investigations.