2026/06/15 by Vikas V. Sharma, Mohit Kumar
Mathematics · #math.GM
To address computational intensity and crisp weight limitations in the alpha-cut intervals based Fuzzy Best-Worst Method (alpha-FBWM), this research proposes the Linear alpha-cut intervals based Fuzzy Best-Worst Method (Linear alpha-FBWM). By reformulating the non-linear optimization into a single linear programming model, the framework directly determines criteria weights as Triangular Fuzzy Numbers (TFNs) to retain uncertainty. To evaluate weight alignment with decision-makers' initial fuzzy preferences, an Ordinal Preference Violation (OPV) metric is introduced based on the prominence effect. Numerical examples demonstrate that Linear alpha-FBWM minimizes logical violations and matches or outperforms the original alpha-FBWM. To efficiently handle large-scale datasets, we extend this into the Linear alpha-cut intervals based Parsimonious Fuzzy Best-Worst Method (Linear alpha-PFBWM), embedding the linear formulation. This model allows initial alternative ratings as fuzzy numbers and computes non-reference alternative priorities via fuzzy interpolation without early defuzzification. The framework is validated using a literature example and a real-world warehouse selection case study involving 20 alternatives across Gujarat for a multinational paint firm. The integrated approach reduced the required expert evaluations from 185 to 20 initial ratings and 35 pairwise comparisons. This 81.08% reduction in pairwise comparisons proves the framework to be an efficient, reliable, and scalable tool for complex industrial decision-making.