Simplified Extension of Zimmermann’s Model for Fuzzy Multi-Objective Linear Programming Problems

Nadia Al-Saidi; Eman Hassan  Ouda; Israa H.   Hasan

doi:10.5269/bspm.78967

Nadia Al-Saidi Division of Mathematics and Computer Applications-Department of Applied Sciences-University of Technology-Iraq.
Eman Hassan Ouda 1Collage of Applied Science, University of Technology-Iraq
Israa H. Hasan

Resumo

A crucial technique for making decisions under uncertainty, particularly when balancing multiple objectives, is fuzzy multi-objective linear programming (FMOLP). Zimmermann's max-min model, which maximizes the minimum satisfied among all fuzzy objectives to ensure equitable results, is one of the most used methods. Considering its importance, this approach often yields conservative results and increased mathematical complexity, particularly as the number of objectives increases. To overcome this limitation, we first proposed a hybrid ranking function that combines centroid-based and weighted-average measures, providing a more reliable evaluation of fuzzy numbers. Building on this idea, we extended Zimmermann’s formulation by introducing a tunable parameter that balances the minimum satisfaction level with the average satisfaction across objectives. This extension enables decision makers to smoothly adjust the trade-off between fairness and efficiency, while the hybrid ranking function ensures a more accurate ranking of fuzzy objectives.

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