A comparative structure-affinity study of anthraquinone dyes adsorption on cellulose fibre is presented in this paper. We used receptor-dependent 4D-QSAR methods based on grid and neural (SOM) methodology coupled with IVEPLS procedure. The applied RD 4D-QSAR approach focuses mainly on the ability of mapping dye properties to verify the concept of tinctophore in dye chemistry. Moreover, the stochastic SMV procedure to investigate the predictive ability of the method for a large population of 4D-QSAR models was employed. The obtained findings were compared with the previously published RI 3D/4D-QSAR models for the corresponding anthraquinone trainings sets. The neutral (protonated) and anionic (deprotonated) forms of anthraquinone scaffold were examined in order to deal with the uncertainty of the dye ionization state. The results are comparable to both the neutral and anionic dye sets regardless of the occupancy and charge descriptors applied, respectively. It is worth noting that the SOM-4D-QSAR behaves comparably to the cubic counterpart which is observed in each training/test subset specification (4D-QSAR-Jo vs SOM- 4D-QSARo and 4D-QSAR-Jq vs SOM-4D-QSARq). Additionally, an attempt was made to specify a common set of variables contributing significantly to dye-fiber binding affinity; it was simultaneously performed for some arbitrary chosen SMV models. The presented RD 4D-QSAR methodology together with IVE-PLS procedure provides a robust and predictive modeling technique, which facilitates detailed specification of the molecular motifs significantly contributing to the fiber-dye affinity.