| Abstract: |
Fuzzy methodologies in linear programming problems (FLPPs) concern the intrinsic indeterminacy and vagueness of real-world decision environments. While classical linear programming works on certain crisp, defined coefficients and constraints, real world scenarios related to supply chain management, production planning, financial portfolio allocation or resource distribution rarely abide by specific instances. This empirical research applies fuzzy set theory in the context of linear programming problem settings using triangular (TFNs) and trapezoidal fuzzy numbers (TrFNs) as models for uncertain objective function coefficients and constraints parameters. Leveraging a three-phase dataset developed from 180 simulated optimization runs of six sectors, the research quantitatively assesses solution quality, computational efficiency and constraint adherence rates of fuzzy LP models against crisp LP counterparts. An empirical evaluation of Zimmermann's fuzzy programming methodology, the Bellman Zadeh decision framework and ranking-based defuzzification techniques. Statistical analyses (ANOVA, regression, and paired t-tests) confirm that FLPPs obtain significantly better objective function values than those computed for imprecision levels greater than 15% of parameter magnitude (p < 0.001). In addition, it is noted that with the presence of uncertain data, triangular fuzzy number-based models have a 18.7% improvement in mean constraint satisfaction compared to classical models. The results provide a strong evidence-based background to utilising fuzzy LP in industrial optimisation scenarios, alongside quantitative benchmarks for method selection. |
