The article proposes a solution to the scientific task, which consists of determining the competitive positions of restaurant business enterprises using mathematical modelling. The importance of its use for evaluating the competitiveness of restaurant business enterprises is emphasized, which provides the possibility and feasibility of carrying out a number of changes related to the reorientation of the enterprise to strategic advantages. The purpose of the work is to justify and improve methodological approaches for determining competitive advantages and marketing strategies of restaurant business enterprises by means of mathematical modelling. In order to visualize the obtained results, a model for assessing the level of use of the company's competitive potential was built using a mathematical apparatus of fuzzy logic. The developed model focuses not only on satisfying the needs and interests of consumers but also helps to form the demand for the products and services they need, taking into account the factors that influence their decision-making. The analysis and formation of the system of competitive advantages of restaurant enterprises are based on the indicators of competitiveness given in the study and the graphical presentation of the obtained models based on data sets of these indicators. The Analytical Hierarchy Process (AHP) method was used to perform a relative assessment of competitiveness, which allows to build a multi-parameter hierarchical model that reflects the level of competition of restaurants and makes it possible to calculate the fuzzy value of the integral level of competition. It is proposed to use the apparatus of game theory to choose alternative marketing strategies for increasing the competitiveness of restaurants. The results of the study indicate the need for constant adaptation of enterprises and flexibility to respond to the changing global circumstances of the business environment.