Risk Prioritization of ``Digital Drug'' and Consumer Neurostimulation Modalities: A Reproducible Interval-Valued Fermatean Fuzzy Entropy–TOPSIS Framework

Rawan Emad El-Saadany, Faculty of Computers and Informatics, Zagazig University, Zagazig 44511, EgyptFollow
Ahmed Samy, Faculty of Computers and Informatics, Zagazig University, Zagazig 44511, EgyptFollow
Mohamed M. AbdelHafeez, Faculty of Computers and Informatics, Zagazig University, Zagazig 44511, EgyptFollow
Mahmoud M. Ismail, Faculty of Computers and Informatics, Zagazig University, Zagazig 44511, EgyptFollow

Authors' ORCIDs

Ahmed Samy: https://orcid.org/0000-0001-9862-1048

Mohamed M. AbdelHafeez: https://orcid.org/0009-0000-1032-5499

Mahmoud M. Ismail: https://orcid.org/0000-0003-2706-4621

Article Type

Research Article

Abstract

Consumer audio and multisensory stimulation technologies are increasingly accessible through streaming platforms, mobile applications, and immersive media. The expression digital drug is sometimes used for binaural-beat content intended to alter subjective states, but the term is a consumer/cultural label and does not imply pharmacological equivalence. Risk prioritization in this area is difficult because evidence is heterogeneous, several relevant criteria are qualitative, and judgments may be imprecise rather than point-valued. This paper develops a transparent interval-valued Fermatean fuzzy (IVFF) group decision framework that combines interval-preserving aggregation, Shannon entropy weighting, and TOPSIS for prioritizing digital drug risk scenarios under uncertainty. The method uses a bounded cube-based score only for entropy estimation, while the final TOPSIS stage retains the complete IVFF intervals through an endpoint-based distance metric. A normalization safeguard is introduced: entropy is computed from the bounded IVFF score before TOPSIS vector normalization, avoiding the min–max normalization issue previously identified for entropy–TOPSIS combinations. A fully disclosed illustrative case with five consumer neurostimulation modalities, eight risk criteria, and three decision-maker profiles is used for numerical verification. The resulting closeness coefficients are A5 = 0.8631, A4 = 0.7617, A2 = 0.4466, A1 = 0.2674, and A3 = 0.0000, giving the order A5 > A4 > A2 > A1 > A3. The ranking remains unchanged under ± 25% one-at-a-time criterion-weight perturbations, equal-weight ablation, scalar-score TOPSIS, and all three leave-one-decision-maker-out tests. The results demonstrate computational consistency and local robustness of the proposed decision procedure; they are not clinical incidence estimates or empirical safety claims. The complete linguistic inputs and intermediate calculations are reported to support independent reproduction.

Keywords

Digital drugs, Binaural beats, Consumer neurostimulation, Interval-valued Fermatean fuzzy sets, Entropy weighting, TOPSIS, Risk prioritization, Uncertainty

How to Cite

El-Saadany, Rawan Emad; Samy, Ahmed; AbdelHafeez, Mohamed M.; and Ismail, Mahmoud M. (2026) "Risk Prioritization of ``Digital Drug'' and Consumer Neurostimulation Modalities: A Reproducible Interval-Valued Fermatean Fuzzy Entropy–TOPSIS Framework," Neutrosophic Systems with Applications: Vol. 26: Iss. 10, Article 2. DOI: https://doi.org/10.63689/2993-7159.1372