An Enhanced Fuzzy Two-Phase Method for Solving Fully Fuzzy Linear Programming Problems without Initial Feasible Basis

Fully fuzzy linear programming (FFLP) problems, where all coefficients and variables are fuzzy numbers, frequently lack an initial fuzzy basic feasible solution (FBFS). This paper proposes an enhanced fuzzy two-phase method using triangular fuzzy numbers (TFNs) throughout. Phase I minimizes the fuzzy sum of artificial variables via a modified fuzzy simplex tableau and centroid-distance ranking function, ensuring convergence to a feasible fuzzy basis without premature defuzzification. Phase II then optimizes the original fuzzy objective using the obtained basis. Theorems prove fuzzy feasibility restoration in Phase I, optimality transfer to Phase II, and finite termination. Numerical illustrations show narrower fuzzy solution intervals (15-35% improvement) compared to defuzzified or traditional two-phase approaches. The method advances operations research under high uncertainty, such as supply chain planning with vague resources. Future directions include type-2 fuzzy extensions and machine learning for adaptive ranking.