Currently, systems based on multidimensional membership functions are being actively researched and developed. Most algorithms for determining the parameters of fuzzy membership functions are developed on the basis of one-dimensional membership functions. The fuzzy rules generated by these algorithms often overlap and cannot act as independent rules. The overlap of fuzzy rules in fuzzy systems does not allow one to evaluate the reliability of individual fuzzy rules and at the same time creates limitations in extracting knowledge from fuzzy systems. In this article, a neuro-fuzzy neural system will be built based on a multidimensional Gaussian membership function with the ability to describe the relationship of interaction between input variables, and at the same time, the generated fuzzy rules are capable of independent operation.