Evaluating the Efficiency of DMUs with Uncertain Data and Minimized Undesirable Outputs using Belief Degree

Abstract

Evaluating decision-making units often requires managingundesirable outputs that hinder performance. While reducing these outputsenhances efficiency, complete elimination is impractical. Most existingmodels rely on precise data, but real-world scenarios often involveuncertainty from expert opinions. Among the approaches, Liu’s uncertaintytheory is effective in handling such imprecise data. This studyintroduces two models: one identifies the minimum unavoidable undesirableoutputs while maintaining other inputs and outputs, and anotherevaluates efficiency by incorporating uncertain data in the presence ofundesirable outputs. Utilizing the directional distance function withindividual-proportion weak disposability, we convert uncertain modelsinto deterministic equivalents using belief degrees as a problem-solvingmeasure. We also analyzed the influence of desirable and undesirableoutputs on inefficiency, showing that efficiency increases with higherbelief degrees and deviates from deterministic values. To validate ourapproach, we developed an uncertain version of a deterministic practical problem and presented the findings. These insights provide decisionmakerswith a structured methodology to manage undesirable outputsand improve efficiency assessments in uncertain environments.