Abstract
Human decision-making is an essential direction of current research. Fuzzy sets and relations have been used to model human behavior, reasoning, and decision-making over the years. Since social science research shows that omitting or zeroing out negative information does not fully describe human behavior and decision-making, the concept of balanced sets and relations was developed in response to this problem. Balanced sets and relations are mathematical concepts that support both positive and negative data analysis. Balanced sets of equations are considered to find relationships between different sets. In this article, the idea of balanced systems of equations is presented. The paper discusses the existence and how to determine their set of solutions. A method for solving balanced systems of equations with balanced MAX and MIN operations is given.
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