The opioid overdose epidemic remains a critical public health crisis, particularly in the United States, leading to significant mortality and societal costs. Social media platforms like Reddit provide vast amounts of unstructured data that offer insights into public perceptions, discussions, and experiences related to opioid use. This study leverages Natural Language Processing (NLP), specifically Opioid Named Entity Recognition (ONER-2025), to extract actionable information from these platforms. Our research makes four key contributions. First, we created a unique, manually annotated dataset sourced from Reddit, where users share self-reported experiences of opioid use via different administration routes. This dataset contains 331,285 tokens and includes eight major opioid entity categories. Second, we detail our annotation process and guidelines while discussing the challenges of labeling the ONER-2025 dataset. Third, we analyze key linguistic challenges, including slang, ambiguity, fragmented sentences, and emotionally charged language, in opioid discussions. Fourth, we propose a real-time monitoring system to process streaming data from social media, healthcare records, and emergency services to identify overdose events. Using 5-fold cross-validation in 11 experiments, our system integrates machine learning, deep learning, and transformer-based language models with advanced contextual embeddings to enhance understanding. Our transformer-based models (bert-base-NER and roberta-base) achieved 97% accuracy and F1-score, outperforming baselines by 10.23% (RF=0.88).

A dozen papers have considered the concept of negation of probability distributions (pd) introduced by Yager. Usually, such negations are generated point-by-point by functions defined on a set of probability values and called here negators. Recently it was shown that Yager's negator plays a crucial role in the definition of pd-independent linear negators: any linear negator is a function of Yager's negator. Here, we prove that the sequence of multiple negations of pd generated by a linear negator converges to the uniform distribution with maximal entropy. We show that any pd-independent negator is non-involutive, and any nontrivial linear negator is strictly contracting. Finally, we introduce an involutive negator in the class of pddependent negators that generates an involutive negation of probability distributions. Keywords: Probability distribution, contracting negation, involutive negation 1. Introduction The concept of the negation of a probability distribution (pd) was introduced by Yager [1].

Recently it was introduced a negation of a probability distribution. The need for such negation arises when a knowledge-based system can use the terms like NOT HIGH, where HIGH is represented by a probability distribution (pd). For example, HIGH PROFIT or HIGH PRICE can be considered. The application of this negation in Dempster-Shafer theory was considered in many works. Although several negations of probability distributions have been proposed, it was not clear how to construct other negation. In this paper, we consider negations of probability distributions as point-by-point transformations of pd using decreasing functions defined on [0,1] called negators. We propose the general method of generation of negators and corresponding negations of pd, and study their properties. We give a characterization of linear negators as a convex combination of Yager's and uniform negators. Keywords: Probability distribution, Negation, Dempster-Shafer theory 1. Introduction The concept of negation of probability distribution (pd) was recently introduced by Yager [18].