Plithogenic Fuzzy Soft Expert Set and Plithogenic Fuzzy Rough Set with Upside-Down Logic

Abstract

In 1965, Zadeh introduced the notion of a fuzzy set, which has supported decades of successful applications across diverse domains involving vagueness and uncertainty. Fuzzy sets have since been extended in many directions using a variety of concepts. Representative examples include fuzzy soft expert sets, fuzzy T-rough sets, and plithogenic sets. Fuzzy soft expert sets associate a fuzzy subset with each parameter–expert–opinion triple, thereby assigning graded membership values to decision alternatives. Fuzzy T-rough sets approximate fuzzy subsets through T-similarity relations, producing lower and upper bounds that formalize uncertainty. Plithogenic sets describe elements via attribute-dependent memberships together with a contradiction mapping between attribute values. Upside-Down Logic models structured context changes under which truth and falsity are interchanged, reversing evaluations while maintaining internal consistency across contexts. To the best of our knowledge, a unified framework that explicitly fuses the plithogenic fuzzy-set perspective with fuzzy soft expert sets and fuzzy T-rough sets has not yet been established. To address this gap, this paper revisits the Plithogenic Fuzzy Soft Expert Set, the Plithogenic Fuzzy Rough Set, and the classical fuzzy set, and examines how Upside-Down Logic can be incorporated into these settings to capture real-world reversal phenomena.

Received: 2 November 2025 | Revised: 19 January 2026 | Accepted: 24 February 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, Validation, Formal analysis, Investigation, Writing – original draft, Writing – review & editing, Project administration.