Abstract

This paper introduces the ”anti fuzzy semigroup,” a novel algebraic structure that integrates the concepts of semigroups and anti fuzzy sets. We demonstrate, through a specific example, how a Kinship system can be represented as an anti fuzzy semigroup, effectively capturing the relationships between managers and subordinates. This appli- cation underscores the potential of anti fuzzy semigroups to model complex hierarchical structures and relationships within organizational settings. Furthermore, we investigate the representation of DNA sequences using this framework. We delve into the algebraic properties of anti fuzzy semigroups, proving that the union of two such semigroups always results in another anti fuzzy semigroup. However, we provide a counterexample to demon- strate that the intersection of two anti fuzzy semigroups may not necessarily preserve the anti fuzzy semigroup property. Finally, the Cartesian product of two anti fuzzy semigroups forms an anti fuzzy semigroup.