An analysis of statistical data shows that attendance in the libraries falls every year, the demand of library information as the material carrier (for example books) is greatly reduced, but the information in electronic form is in demand, and every year the figures are growing significantly. This paper presents an estimation method for separate and complex indicators of the efficiency of library and information product and service rendering depending on various factors that determine service quality, timeliness and efficiency. A fuzzy logic system to transform the primary data was designed with the "Fuzzy Logic Toolbox" software using MATLAB. The methods to rank the studied factors by their importance and effect on the criteria of the efficiency of library and information product and service rendering are given. It is shown that the quality of library and information services plays an important role in development of society and influences the global socio-economic development and wellbeing. The research application contributes to the optimization of the library helps to more efficiently organize and plan their work, as well as the right to determine the direction of further investment. In addition, it enables the management of the library to identify factors that contribute to improving the efficiency of their businesses, to study the most urgent and important needs of the market library services, and also to establish the factors that currently are essential as for institutions, and for users and consumers.