An advancement in complex neutrosophic soft field theory

The notion of a field is a basic algebraic structure widely used in different areas of mathematics. A complex neutrosophic soft set is a specialised hybrid model that merges the features of soft sets and neutrosophic sets within a complex framework, employing sets as a key component. By merging the properties of complex neutrosophic soft sets with foundational field theory concepts, this paper introduces fields in uncertain environments. In contrast to existing neutrosophic soft fields, the proposed model incorporates complex-valued truth, indeterminacy and falsity membership grades, enabling the representation of both magnitude and phase information in uncertain environments. Therefore, the proposed structure can be regarded as a natural extension and generalisation of neutrosophic soft field which is considered as a special case of a complex neutrosophic soft field when the complex-valued membership functions are reduced to real values (i.e., with zero phase components). Throughout this detailed study, we aim to deepen our understanding of complex neutrosophic soft fields and their characteristics, thereby advancing algebraic analysis and its real-world applications for managing uncertainties and imprecision.