The design of an adequate culture medium is an essential step in the micropropagation process of plant species. Adjustment and balance of medium components involve the interaction of several factors, such as mineral nutrients, vitamins, and plant growth regulators (PGRs). This work aimed to shed light on the role of these three components on the plant growth and quality of micropropagated woody plants, using Actinidia arguta as a plant model. Two experiments using a five-dimensional experimental design space were defined using the Design of Experiments (DoE) method, to study the effect of five mineral factors (NH4NO3, KNO3, Mesos, Micros, and Iron) and five vitamins (Myo-inositol, thiamine, nicotinic acid, pyridoxine, and vitamin E). A third experiment, using 20 combinations of two PGRs: BAP (6-benzylaminopurine) and GA3 (gibberellic acid) was performed. Artificial Neural Networks (ANNs) algorithms were used to build models with the whole database to determine the effect of those components on several growth and quality parameters. Neurofuzzy logic allowed us to decipher and generate new knowledge on the hierarchy of some minerals as essential components of the culture media over vitamins and PRGs, suggesting rules about how MS basal media formulation could be modified to assess the quality of micropropagated woody plants.