A Probabilistic Plithogenic Neutrosophic Rough Set  for Uncertainty-Aware Food Safety Analysis

Ruixuan Chen; Qun Liu; Yucang Zhang; Wuyin Weng

Authors

Ruixuan Chen College of Ocean Food and Biological Engineering, Jimei University, Xiamen, 361021, Fujian, China
Qun Liu College of Ocean Food and Biological Engineering, Jimei University, Xiamen, 361021, Fujian, China
Yucang Zhang College of Ocean Food and Biological Engineering, Jimei University, Xiamen, 361021, Fujian, China
Wuyin Weng College of Ocean Food and Biological Engineering, Jimei University, Xiamen, 361021, Fujian, China

Keywords:

—Plithogenic sets, Neutrosophic sets, Food safety, Risk assessment, Uncertainty modeling, Indeterminacy, Uncertainty-aware analysis.

Abstract

Ensuring food safety amid increasing complexity and uncertainty in supply chains
demands advanced solution for modeling multi-source, imprecise, and contradictory information. In
this paper, we propose a novel Probabilistic Plithogenic Neutrosophic Rough Set (P²NRS) that
synergistically integrates plithogenic, neutrosophic set (NS), rough set, and probabilistic theories in
unified framework. This framework contributes effective capturing of aleatory randomness,
epistemic indeterminacy, and contradiction across multiple food safety risk criteria, enabling a
comprehensive uncertainty-aware analysis. Our research settles theoretical foundations of P²NRS
through providing formal definition of essential concepts including probabilistic NS membership,
contradiction degree distributions, and rough approximations, and develop set-theoretic,
approximation, and aggregation operations under this enriched model. By the end, we presented a
real-world case study on milk batch risk assessment that demonstrates the framework’s practical
applicability, the findings explain the expressivity as well as potential of P²NRS as a powerful tool
for food safety managers and decision makers.

DOI: 10.5281/zenodo.16658838