Considerations of HyperNeutrosophic Set and ForestNeutrosophic Set in Livestock Applications and Proposal of New Neutrosophic Sets

Abstract

The Neutrosophic Set offers a robust mathematical framework for handling uncertainty by incorporating three key membership functions: truth, indeterminacy, and falsity [36]. To address the growing complexity of real-world problems, advanced extensions such as the HyperNeutrosophic Set and the SuperHyperNeutrosophic Set have been developed. These higher dimensional models provide an enhanced representation of uncertainty and are formally defined in [20, 21, 22, 24, 23, 37, 19]. In addition, the TreeNeutrosophic Set and ForestNeutrosophic Set are well-established extensions of the Neutrosophic Set, broadening its applicability to structured and hierarchical data [16]. This paper explores the practical applications of the Neutrosophic Set in livestock management [28, 11, 2], highlighting its potential to enhance decision-making processes in this field. Additionally, we introduce several new variations of the Neutrosophic Set and the ForestNeutrosophic Set [16], further extending their theoretical framework and practical applicability.