This research introduces an innovative methodology for optimizing multi-objective mathematical models under uncertainty by incorporating multiple utility functions for each objective, thereby advancing beyond conventional single-utility approaches. This enhanced framework more accurately captures real-world decision-making complexity, where assigning a singular utility function to an objective often proves inadequate. To manage the inherent uncertainty in utility specification, we develop a fuzzy probabilistic system that yields a fuzzy nonlinear programming formulation. Given the limitations of traditional optimization techniques in handling such models, we implement a defuzzification procedure using the α-cut technique to convert conditional utility functions into precise representations. This transformation produces a solvable crisp nonlinear model that can be addressed using established optimization algorithms.

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Fuzzy Multi-objective Optimization by α-Cut Method

  • Hamed Fazlollahtabar

摘要

This research introduces an innovative methodology for optimizing multi-objective mathematical models under uncertainty by incorporating multiple utility functions for each objective, thereby advancing beyond conventional single-utility approaches. This enhanced framework more accurately captures real-world decision-making complexity, where assigning a singular utility function to an objective often proves inadequate. To manage the inherent uncertainty in utility specification, we develop a fuzzy probabilistic system that yields a fuzzy nonlinear programming formulation. Given the limitations of traditional optimization techniques in handling such models, we implement a defuzzification procedure using the α-cut technique to convert conditional utility functions into precise representations. This transformation produces a solvable crisp nonlinear model that can be addressed using established optimization algorithms.