HyperNeutrosophic Set and Forest HyperNeutrosophic Set with Practical Applications in Agriculture

Abstract

The Neutrosophic Set provides a flexible mathematical framework for handling uncertainty by incorporating three distinct membership functions: truth, indeterminacy, and falsity [50]. In response to the growing complexity of real-world problems, advanced extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been introduced. These extensions offer a higher-dimensional approach to modeling uncertainty and can be formally defined in [33, 34, 35, 37, 36, 51, 32]. Since the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have only been recently defined, there remains a lack of concrete examples demonstrating their applicability. This paper aims to bridge this gap by exploring practical examples of these concepts in the field of agriculture. Additionally, we introduce two novel extensions, the Forest Hyperneutrosophic Set and the Forest SuperHyperneutrosophic Set, which further generalize the existing models to accommodate hierarchical and interconnected uncertainty structures in complex systems.