In my opinion, the most real human multi-criteria functions are nonlinear (linearity is a special ideal feature of the dependences).
The significance of the component is not constant in the domain and the components are dependent. Additionaly, linear or linear-like
multi-criteria models are used in many internationally known methods. The proof of the nonlinearity is presented by Kahneman and Tversky (1979).
KAHNEMAN, D. and TVERSKY, A. (1979) PROSPECT THEORY - ANALYSIS OF DECISION UNDER RISK, Econometrica, 47(2), pp. 263 - 291.
Thank you for answering. I agree with your answer in the vast majority. I think that linear approach may cause majority of MCDM methods shortcomings. For e.g., if we assume linearity of human MCDM function, results will be vulnerable on rank reversals. I know that the results of a decision analysis process rarely "make the decision", but I think MCDM methods should be given the most reliable result. Additionally, in my opinion "similar rank orderings of results" are insufficient. For e.g. in AHP a new alternative can cause rank reversals. In that way we obtain a new rank where the best option became the worst and vice versa.