Three-Mode Upside-Down Logic within Plithogenic Neutrosophic Set

Abstract

In the real world, many reversal phenomena occur, such as statements once considered false later becoming recognized as true. Upside-Down Logic provides a framework to formalize such reversals by inverting truth and falsity through contextual transformations, thus capturing ambiguity and dynamic changes in reasoning processes.

A Plithogenic Set models elements via attribute-based membership and contradiction functions, extending the established frameworks of fuzzy, intuitionistic, and neutrosophic sets. De-Plithogenication is the process of systematically neutralizing contradictions in plithogenic structures, resetting or transforming attribute relationships into consistent, contradiction-free states. A Plithogenic Neutrosophic Set further represents truth, indeterminacy, and falsity degrees under contradictions, enriching neutrosophic sets with context-sensitive semantics.

In this paper, we define and study Three-Mode Upside-Down Logic, an improved version of Upside-Down Logic, together with De-Plithogenication, and investigate their behavior within the framework of Plithogenic Neutrosophic Sets.