The paper substantiates the need to consider economic efficiency indicators of bank activity as fuzzy quantities. Formulations of the problem of fuzzy regression analysis and modelling, available in literary sources, have been analyzed. Three main approaches to the fuzzy regression analysis are presented. The general mathematical and meaningful formulation of problem of a fuzzy multivariate regression analysis for commercial bank competitiveness has been proposed. Sequence of its solutions is described. The example of numerical computations for one of the large Ukrainian banks is given. Results of obtained solution were analyzed from the standpoint of reliability, accuracy and compared against the classical crisp regression analysis. Finishing steps for obtaining final accurate numerical results of solution process are described. In summary, convincing arguments concerning the expediency of application of this approach to the problem of determining the competitiveness of banks are formulated and presented.