Three-Mode Upside-Down Logic Within Plithogenic Double-Valued and Triple-Valued Neutrosophic Sets

In the real world, reversal phenomena are common—for example, assertions once judged false may later be recognized as true. Upside–Down Logic formalizes such reversals by contextually transforming truth and falsity (and their attendant uncertainties), thereby capturing ambiguity and temporal change in reasoning. A Plithogenic Set represents elements via attribute–driven membership and contradiction functions, extending fuzzy, intuitionistic, and neutrosophic paradigms. A Plithogenic Neutrosophic Set further models truth, indeterminacy, and falsity under explicit contradictions, enriching neutrosophic semantics with contextual sensitivity. Double–Valued Neutrosophic Logic assigns truth, falsity, and two indeterminacy components (one leaning toward truth, one toward falsity) to each proposition, whereas Triple–Valued Neutrosophic Logic adds a neutral indeterminacy component. Despite recent interest, extended forms of the Plithogenic Neutrosophic Set remain underexplored in terms of properties and concrete use–cases. To bridge this gap, this paper introduces and formalizes Plithogenic Double–Valued and Plithogenic Triple–Valued Neutrosophic Sets, establishes their fundamental properties and reduction relations, and presents application scenarios demonstrating the practical deployment of Upside–Down Logic.