Balanced Relations Equations

In this paper, it is introduced a new type of relation equations, which are based on the concept of balanced fuzzy sets. We present the idea of balanced fuzzy equations. Relationships of this type allow for a much better way of reasoning, which is based not only on the analysis of positive factors but of both positive and negative factors. The motivation for this approach is the achievements of Nobel Prize winners in cognitive science: Amos Tversky and Daniel Kahneman. Theirs prospect theory give us explanation of human economic choices. Based on their scientific achievements, we know that human decision-making is influenced by both positive and negative information.Using this theory we develop methods for solving different types of balanced relational equations. We present numerical examples along with their practical applications. Furthermore, we extend the notion of the S − T product for balanced norms and conorms and present how to solve balanced systems.