Three-Mode Upside-Down Logic Within Plithogenic Neutrosophic Sets: Handling Contradiction and Truth Inversion for Applications in Decision Science

Abstract

Reversal effects are common in real-world reasoning: a claim that is initially regarded as false may later be treated as true. Upside-Down Logic offers a formal way to model such reversals via context-dependent transformations that exchange truth and falsity, thereby capturing ambiguity and shifts in judgment over time. A (finite) Plithogenic Set describes elements through membership degrees conditioned on attribute values and is equipped with contradiction functions defined on those values, so it both subsumes and generalizes the (finite) classical fuzzy, intuitionistic, and neutrosophic frameworks. Established notions such as fuzzy sets and neutrosophic sets also admit plithogenic counterparts, including (finite) Plithogenic Fuzzy Sets and (finite) Plithogenic Neutrosophic Sets. De-Plithogenication denotes a systematic procedure for neutralizing contradictions in a plithogenic structure—for example, by resetting or transforming conflicting attribute relations into consistent, contradiction-free configurations. A Plithogenic Neutrosophic Set additionally assigns degrees of truth, indeterminacy, and falsity in the presence of such contradictions, thereby enriching neutrosophic semantics with explicit context sensitivity. We develop Three-Mode Upside-Down Logic, an enriched Upside-Down framework, alongside De-Plithogenication, and we investigate their interplay within Plithogenic Neutrosophic Sets. Because the present work is mainly theoretical, we expect future research to assess the practical effectiveness of these notions through computational experiments and related quantitative investigations.

Received: 12 September 2025 | Revised: 23 October 2025 | Accepted: 20 January 2026

Conflicts of Interest

The author declares that he has no conflicts of interest to this work.

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Author Contribution Statement

Takaaki Fujita: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization, Supervision, Project administration.