In this paper, we propose a novel operational law for calculating the credibility distributions of monotone functions of independent regular fuzzy numbers to study the project scheduling problem with partially (or fully) fuzzy activity durations. In this regard, we formulate three corresponding types of fuzzy models, namely the $\alpha$-cost minimization, the credibility maximization and the time-cost trade-off models, and show that they can be converted into crisp ones, and then be efficiently solved. Specifically, for the first model, its optimal solution is represented analytically, and thus determined precisely. The second and third ones can be solved exactly for small and medium, and approximately with high accuracy within reasonable time for large scale projects. Several numerical experiments on the public instance sets from the project scheduling problem library (PSPLIB) illustrate clearly the accuracy and efficiency of our treatment.

在本文中，我们提出了一种计算独立正则模糊数单调函数的可信度分布的新运算法则，以研究具有部分（或完全）模糊活动持续时间的项目调度问题。在这方面，我们制定了三种相应类型的模糊模型，即$\alpha$-成本最小化、可信度最大化和时间成本权衡模型，并表明它们可以转化为清晰的模型，然后被有效地解决。具体来说，对于第一个模型，其最优解是解析表示的，因此可以精确确定。第二个和第三个对于中小型项目可以准确地解决，对于大型项目可以在合理的时间内以高精度近似地解决。来自项目调度问题库 (PSPLIB) 的公共实例集的几个数值实验清楚地说明了我们处理的准确性和效率。