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Possibilistic Minmax Regret Sequencing Problems With Fuzzy Parameters

机译：具有模糊参数的可能的Minmax后悔排序问题

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摘要

In this paper, a class of sequencing problems with uncertain parameters is discussed. The uncertainty is modeled by the usage of fuzzy intervals, whose membership functions are regarded as possibility distributions for the values of unknown parameters. It is shown how to use possibility theory to find robust solutions under fuzzy parameters; this paper presents a general framework, together with applications, to some classical sequencing problems. First, the interval sequencing problems with the minmax regret criterion are discussed. The state of the art in this area is recalled. Next, the fuzzy sequencing problems, in which the classical intervals are replaced with fuzzy ones, are investigated. A possibilistic interpretation of such problems, solution concepts, and algorithms for the computation of a solution are described. In particular, it is shown that every fuzzy problem can be efficiently solved if a polynomial algorithm for the corresponding interval problem with the minmax regret criterion is known. Some methods to deal with NP-hard problems are also proposed, and the efficiency of these methods is explored.
机译：本文讨论了一类参数不确定的排序问题。通过使用模糊区间对不确定性建模，模糊区间的隶属度函数被视为未知参数值的可能性分布。展示了如何使用可能性理论在模糊参数下找到鲁棒解；本文介绍了一些经典测序问题的通用框架及其应用。首先，讨论具有最小最大后悔准则的区间排序问题。回顾该领域的最新技术。接下来，研究了用经典区间替换经典区间的模糊排序问题。描述了此类问题的可能解释，解决方案概念以及用于解决方案计算的算法。特别地，示出了如果已知具有最小最大后悔准则的对应间隔问题的多项式算法，则可以有效地解决每个模糊问题。还提出了一些解决NP难问题的方法，并探讨了这些方法的有效性。

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