Archimedean t-Norm and t-Conorm-Based Aggregation Operators of HFNs, with the Approach of Improving Education

Abstract

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.