This study explores key characteristics associated with neutrosophic prime ideals. In particular, it is shown that the image corresponding to these ideals contains exactly two different elements. The work also extends the concept of classical prime ideals by incorporating neutrosophic logic. A new approach to identifying prime ideals using neutrosophic points is introduced. Furthermore, the paper compares various definitions of neutrosophic prime ideals and examines the connections between them. Finally, an application is used to illustrate the role of neutrosophic prime ideals in decision-making processes.

The concept of $F-$filters is introduced in an almost distributive lattice(ADL) and their properties are studied. A set of equivalent conditions is established for every proper $F-$filter of an ADL to become a prime $F-$filter. For any $F-$filter $U$ of an ADL, ${\mathcal{O}}^F(U)$ is defined, and it is proved that ${\mathcal{O}}^F(U)$ is an $F-$filter if $U$ is prime. It is also derived that each minimal prime $F-$filter belonging to ${\mathcal{O}}^F(U)$ is contained in $U$, and ${\mathcal{O}}^F(U)$ is the intersection of all the minimal prime $F-$filters contained in $U.$ The concept of $F-$normal ADL is defined and characterized in terms of the prime $F-$filters and minimal prime $F-$filters, as well as relative annihilators with respect to $F$.