Application of independent component analysis and TOPSIS to deal with dependent criteria in multicriteria decision problems
This addresses a specific issue in decision-making for practitioners dealing with dependent criteria, but it is incremental as it combines existing techniques.
The paper tackles the problem of biased rankings in multicriteria decision making when criteria are dependent, by proposing a novel approach that estimates independent latent criteria using independent component analysis and TOPSIS, with results validated on synthetic and actual data.
A vast number of multicriteria decision making methods have been developed to deal with the problem of ranking a set of alternatives evaluated in a multicriteria fashion. Very often, these methods assume that the evaluation among criteria is statistically independent. However, in actual problems, the observed data may comprise dependent criteria, which, among other problems, may result in biased rankings. In order to deal with this issue, we propose a novel approach whose aim is to estimate, from the observed data, a set of independent latent criteria, which can be seen as an alternative representation of the original decision matrix. A central element of our approach is to formulate the decision problem as a blind source separation problem, which allows us to apply independent component analysis techniques to estimate the latent criteria. Moreover, we consider TOPSIS-based approaches to obtain the ranking of alternatives from the latent criteria. Results in both synthetic and actual data attest the relevance of the proposed approach.