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.