A New Ranking Method of Alternatives for Group Decision Making in Social Networks

Group decision-making (GDM) is a process that consists of choosing the best alternative or a set of alternatives from all possible, taking into account the opinions of the group of people. This technology is well researched and applied not for the first decade, however, traditional algorithms did not intend to work with a large amount of data. It means, that during assessment of alternatives each expert chooses a limited set of data that interested him. In addition, each of experts may have his own rating scale. The problem becomes critical when the number of alternatives and experts evaluating them is large, as it is happening in social network contexts. The article offers a review and a formal description of a new GDM approach in social networks. With the use of set-theoretical operations, method of alternatives ranking in the group assessment of social networks is formalized. A theorem on the conversion from the rating scale of linguistic term set (LTS) into basic LTS (BLTS) rating scale is proved. Using the UML language, a formal model was developed and a key algorithm for conversion of numerical ranks from the LTS scale into the BLTS scale was proposed. A method for extrapolating the values of ranks when the network is scaled is developed, for example, when the number of experts is modified. A case for numerical demonstration of the algorithm is presented.