A review of recent methods for the determination of ranges of feasible solutions resulting from soft modelling analyses of multivariate data

• A review on available methods for determination of area feasible solutions (AFS).
• Comparison of the ability of each method in determining the range of feasible bands.
• Summarising the results from analysis of simulated and experimental data sets.

Soft modelling or multivariate curve resolution (MCR) are well-known methodologies for the analysis of multivariate data in many different application fields. Results obtained by soft modelling methods are very likely impaired by rotational and scaling ambiguities, i.e. a full range of feasible solutions can describe the data equally well while fulfilling the constraints of the system. These issues are severely limiting the applicability of these methods and therefore, they can be considered as the most challenging ones. The purpose of the current review is to describe and critically compare the available methods that attempt at determining the range of ambiguity for the case of 3-component systems. Theoretical and practical aspects are discussed, based on a collection of simulated examples containing noise-free and noisy data sets as well as an experimental example.

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