Symmetric Trapezoidal Fuzzy Numbers in Fully Fuzzy Linear Programming: A Double Parametric Perspective

This study proposes a novel method for solving Fully Fuzzy Linear Programming (FFLP) problems, with coefficients represented as Symmetric Trapezoidal Fuzzy Numbers (STrFNs). Unlike traditional methods that reduce fuzzy constraints to crisp equivalents, this approach preserves the complexity of uncertainty by employing a double-parametric representation using $\alpha$ and $\beta$ parameters. The method reformulates the FFLP problem into a parametric framework via Double parametric form (DPF) or Bi-parametric form (BPF) and solves it using the simplex algorithm for varying ($\alpha, \beta$) combinations. The suggested method has been evaluated on representative FFLP situations, demonstrating enhanced accuracy and adaptability, while it requires greater computer resources than conventional crisp-based methods. The proposed method demonstrates enhanced accuracy and adaptability in numerical experiments, making it highly suitable for applications in logistics, finance, and operations, where managing inherent uncertainty is crucial.