A generalized effective neurosophic soft set and its applications

We introduce the concept of an effective neutrosophic soft set, which aims to capture the influence on three independent membership functions representing degrees of truth (T), indeterminacy (I) and falsity (F). We go further by presenting a generalization of the effective neutrosophic soft set, which includes the incorporation of a degree to signify the potential for an approximate value-set. This enhancement contributes to improved efficiency and realism in the concept. Notably, this innovative approach leverages the strengths of both the generalized neutrosophic set and the effective neutrosophic soft set. The subsequent sections delve into fundamental operations on the generalized effective neutrosophic soft set, providing clarity through illustrative examples and propositions. Furthermore, we demonstrate the practical application of the generalized effective neutrosophic soft set in addressing decision-making problems and medical diagnoses.