Annals of Communications in Mathematics

AbstractThis 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.

AbstractThis paper introduces the novel concepts of semi 2-metric space and interval- valued semi 2-metric space. We establish the fundamental properties of these structures and examine their relationships with existing metric space generalizations. Additionally, it proposes the concept of cubic semi 2-metric spaces by integrating the principles of cubic sets with semi 2-metric spaces. Furthermore, the paper examines the structure of general- ized quasi-pseudometric spaces on L-M -semigroup and investigates the characteristics of the quasi-pseudometric space associated with L-M -semigroup.