Methods of ranking and evaluation of the effectiveness of Social Media (SM) given and applied in this paper are the basis for the selection of online media that the public administration uses when communicating with citizens. The methodology presented is based on multicircular decision-making using the Fuzzy Analytical Hierarchical Process (fuzzy AHP) -Z number model -Fuzzy Multi-Attributive Border Approximation Area Comparison (fuzzy MABAC), which eliminates the traditional intuitive ratings of PR services. This resulted in poor use of available channels of communication or ineffective communication. Positive results of the application of presented methods are especially evident in increasing the number of channels of communication on the Internet and the realization of communication goals for greater participation of citizens in public administration. Z. Bobar et al. Ranking and Assessment of the Efficiency of Social Media using the Fuzzy AHP-z Number Model -Fuzzy MABAC -44 -where social media is seen to transform the relationship of public service and the citizenry [2]. In the process of communication with public, government institutions and businesses are not able to use the virtually unlimited number of media available on the Internet with equal efficiency. The selection of social media to be used as a communication channel ensuring reach amongst the targeted public online with desired efficiency is one of the challenges faced by these services in implementing a given communication strategy.In line with the new trends in the usage of social media for business purposes, a series of studies have examined the justification of using social media in the communication of public administration with the citizenry. Some focused on functional availability [3], benefits and risks [4], and the impact of social media use [5]. The common trait found in all these studies is the analysis and assessment of multiple social media according to a single criterion, or the analysis and evaluation of a single social media based on multiple criteria. However, communicators are often confronted with the need to choose among available social media. They have to identify the criteria and the methodology for making such a choice to reduce the risk of failure in communicating via social media.Considering the trends in social media usage and the perspective of involving such media in the activities of public administration as well as that of other organizations, the aim of this research is:1. To define the general criteria for choosing social media for communication between government bodies and the target public; and 2. To develop the methodology for social media ranking in view of the selection of a particular communication channel suited to a communication strategy.This paper examines the various options for rating and ranking social media by using parameters that influence the efficiency of communication, defined on the grounds of criteria partially used in the evaluation and ranking of social media, as well as on expert assessments...