This paper presents a novel application called the rational valued cyclic characters group, which extensively utilizes fuzzy partial differential equations in medicine and engineering. Among adult malignancies, acute interstitial pneumonia represents approximately 6% of cases, making it the most prevalent malignancy among individuals under 20. In recent years, The use of mathematical models to supplement experimental biological models in cancer research has increased. This paper proposes a new approach to address these challenges by developing a method based on filtering and optimizing radiographic images of damaged cells and differentiating parameters. The method utilizes the newly introduced rational valued cyclic group characters and partial fuzzy transformation. Notably, the suggested transform demonstrates significantly enhanced intelligibility compared to the fuzzy partial Laplace transform. Furthermore, this approach facilitates the analysis and categorization of disease progression and its impact on a patient’s response to treatment.