The aim of this paper is to develop the calculus of hesitant fuzzy numbers (HFNs), have been recently proposed as the newest extension of hesitant fuzzy sets. At first, based on the willingness of decision maker to each part of HFNs, a new method has been proposed to compare them. Then, several t-norm and t-conorm-based aggregation operators of HFNs, i.e., algebraic t-norm and t-conorm, Einstein t-norm and t-conorm, Hamacher t-norm and t-conorm, Frank t-norm and t-conorm have been defined, and some of their mathematical properties are also discussed. As the special cases of the above t-norm and t-conorm-based aggregation operators of HFNs, Archimedean t-norm and t-conorm-based HFN weighted averaging operator, Archimedean t-norm and t-conorm-based HFN weighted geometric operator, Archimedean t-norm and t-conorm-based HFN ordered weighted averaging operator, and Archimedean t-norm and t-conorm-based HFN ordered weighted geometric operator have been proposed. The new problem of improving the process of educational activities under the Covid-19 epidemic conditions, for instance, has been defined as a multi-attribute group decision-making (MAGDM) problem, in which students are its options, courses are its criteria, and teachers are members of the decision-making team. Then, the scores of final exams and teachers’ assessments merged together as HFNs, and a new method has been proposed based on the before mentioned operators to solve the resulting MAGDM problem. A numerical example, the results of which are also analyzed, is responsible for explaining what is proposed in this article. Finally, subsequent studies in this area are briefly stated.

本文的目的是开发犹豫模糊数 (HFN) 的微积分，最近被提出作为犹豫模糊集的最新扩展。首先，基于决策者对HFN各部分的意愿，提出了一种新的比较方法。然后，几个牛逼范数和牛逼-conorm基于HFNs聚集经营，即代数牛逼范数和牛逼-conorm，爱因斯坦牛逼范数和牛逼-conorm，HAMACHER牛逼范数和牛逼-conorm，弗兰克牛逼范数和Ť-conorm 已经定义，并且还讨论了它们的一些数学特性。作为上述的特殊情况下吨范数和吨HFNs的-conorm基于聚合运营商，阿基米德吨范数和吨-conorm基于HFN加权平均的，阿基米德吨范数和吨-conorm基于HFN加权几何操作符, Archimedean t -norm 和t -conorm-b​​ased HFN 有序加权平均算子，以及 Archimedean t -norm 和t已经提出了基于-conorm的HFN有序加权几何算子。例如，在 Covid-19 流行情况下改进教育活动过程的新问题已被定义为多属性群体决策（MAGDM）问题，其中学生是其选择，课程是其标准，教师是决策团队的成员。然后，将期末考试成绩和教师评估结果合并为 HFN，并基于上述算子提出了一种新方法来解决由此产生的 MAGDM 问题。一个数值例子，其结果也被分析，负责解释本文中提出的内容。最后，简要说明该领域的后续研究。