Background: Non-small cell lung cancer is defined at the molecular level by mutations and alterations to oncogenes, including AKT1, ALK, BRAF, EGFR, HER2, KRAS, MEK1, MET, NRAS, PIK3CA, RET, and ROS1. A better understanding of non-small cell lung cancer requires a thorough consideration of these oncogenes. However, the complexity of the problem arises from high-dimensional gene vector space, which complicates the identification of cluster boundaries, and hence gene expression cluster membership. This paper aims to analyze potential biological biomarkers for tumorigenesis in lung cancer based on different treatment solutions. Results: Genes BRAF, RET, and ROS1 show an overexpression transition by one cluster from non-treatment to treatment states, followed by a stabilization in the 3 treatment states at the same cluster. Genes MET, ALK, and PIK3CA show an overexpression transition by two clusters from non-treatment to treatment states, followed by a stabilization in the 3 treatment states at the same cluster. SME1 shows an under-expression transition by two clusters from non-treatment to the treatment states, a stabilization in the 3 treatment states at the same cluster. Conclusions: We present a novel fusion-based approach for gene expression profiling of non-small cell lung cancer under non-thermal plasma treatment. The main contribution of the proposed approach is to exploit Dempster-Shafer evidence theory-based data fusion to combine information from different samples in the considered dataset. This minimizes uncertainty and enhances the reliability and validity of decisions, leading to a better description of genes related to non-small cell lung cancer. We also propose use of fuzzy c-means-with-range clustering to track changes of genes' states under different non-thermal plasma treatments. INDEX TERMS Gene expression, Dempster Shafer, evidence theory, data fusion, clustering, non-small cell lung cancer.

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Machine learning (ML)-based algorithms are playing an important role in cancer diagnosis and are increasingly being used to aid clinical decision-making. However, these commonly operate as ‘black boxes’ and it is unclear how decisions are derived. Recently, techniques have been applied to help us understand how specific ML models work and explain the rational for outputs. This study aims to determine why a given type of cancer has a certain phenotypic characteristic. Cancer results in cellular dysregulation and a thorough consideration of cancer regulators is required. This would increase our understanding of the nature of the disease and help discover more effective diagnostic, prognostic, and treatment methods for a variety of cancer types and stages. Our study proposes a novel explainable analysis of potential biomarkers denoting tumorigenesis in non-small cell lung cancer. A number of these biomarkers are known to appear following various treatment pathways. An enhanced analysis is enabled through a novel mathematical formulation for the regulators of mRNA, the regulators of ncRNA, and the coupled mRNA–ncRNA regulators. Temporal gene expression profiles are approximated in a two-dimensional spatial domain for the transition states before converging to the stationary state, using a system comprised of coupled-reaction partial differential equations. Simulation experiments demonstrate that the proposed mathematical gene-expression profile represents a best fit for the population abundance of these oncogenes. In future, our proposed solution can lead to the development of alternative interpretable approaches, through the application of ML models to discover unknown dynamics in gene regulatory systems.