This paper presents a new multiple criteria optimization model of an assignment problem with imprecise coefficients. Besides, minimizing the total cost, total time of finishing jobs, and maximization of the overall achieved quality, we introduce a new criterion that minimizes the number of workers employed to finish all jobs. It contributes significantly in multi-job assignment to adjust the number of workers assigned to at least one job for balancing work allocation among the workers. Furthermore, we employ new diversification constraints to obtain a reasonable tradeoff between the number of workers employed and number of jobs assigned. A new interactive possibilistic programming approach is developed for trapezoidal possibility distributions, which uses $\alpha$-level sets to incorporate confidence levels of the decision maker in his fuzzy judgments leading to $\alpha$-efficient solutions. Numerical experiments are conducted using data coming from a manpower planning problem to demonstrate working of the proposed multiple criteria assignment model and effectiveness of the fuzzy interactive approach.

中文翻译：

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一种新的多准则分配问题的可能性优化模型

本文提出了一种新的具有不精确系数的分配问题的多准则优化模型。此外，为了最大限度地减少总成本、完成工作的总时间，并最大限度地提高整体质量，我们引入了一个新标准，以最大限度地减少完成所有工作所需的工人数量。调整分配给至少一项工作的工人数量以平衡工人之间的工作分配，这在多工作分配中发挥了重要作用。此外，我们采用新的多样化约束来在雇用的工人数量和分配的工作数量之间进行合理的权衡。为梯形可能性分布开发了一种新的交互式可能性编程方法，它使用 $\alpha$- 级别集将决策者的置信水平纳入其模糊判断中，从而导致 $\alpha$- 高效的解决方案。使用来自人力规划问题的数据进行数值实验，以证明所提出的多标准分配模型的工作原理和模糊交互方法的有效性。