ALGEBRAIC HYPERSTRUCTURES AND SOCIAL RELATIONS

Abstract

The relations between the people of a certain set of individuals can be described, from a static point of view, through the arrays of Moreno.  From a dynamic point of view, however, account must be taken of the coalitions formed between people.  These coalitions can be specified or one or more alternatives can be selected while making decisions involving more decision-makers; further there are presented coordination strategies for more people in order to ensure the maximum utility in social problems modelling using cooperative games.  This paper presents how algebraic hyperstructures can be a useful mathematical tool both for the study of social relations from a static point of view and for the study of the social dynamics leading to the formation of coalitions.  It shows that, surprisingly, many properties deemed significant only from an algebraic or geometric viewpoints in a set of individuals, deep meanings from the social point of view.