Biased Survival Analysis of Gastric and Prostate Cancer Patients Using Fuzzy Soft Theory and Fuzzy Inference Systems: Mamdani and Sugeno Models

Abstract

This study introduces a novel mathematical framework for biased survival analysis by integrating Fuzzy Soft Set Theory with Mamdani and Sugeno Fuzzy Inference Systems (FIS). Motivated by the limitations of conventional survival models in addressing uncertainty, imprecision, and selection bias commonly observed in ontological datasets we construct a parameterized fuzzy soft set representation of clinical variables associated with gastric and prostate cancer patients. Each soft set element encodes fuzzified linguistic assessments (e.g., tumor stage, age, PSA level), enabling robust modelling of partial and vague information. We develop and apply both Mamdani-type and Sugeno-type fuzzy inference mechanisms to this fuzzy soft representation, formulating mathematically consistent rule bases and membership functions. The Mamdani system allows rule-based linguistic inference, whereas the Sugeno system offers crisp functional mappings for computational evaluation. Using real-world clinical data, the proposed hybrid approach demonstrates resilience to bias and enhances interpretability without sacrificing predictive accuracy. The numbers show big improvements in accuracy and reliability (errors stayed very small, RMSE ≤ 0.21) even under different conditions.