Some interval-valued hesitant fuzzy aggregation operators based on Archimedean t-norm and t-conorm with their application in multi-criteria decision making

As a generalization of hesitant fuzzy set (HFS), interval-valued hesitant fuzzy set (IVHFS) permits an element's membership degree to be a set of several possible interval values and can therefore be used as an efficient mathematical tool for modeling people's hesitancy and uncertainty in multi-criteria decision making (MCDM). The Archimedean t-conorm and t-norm provide a generalization of a variety of other t-conorms and t-norms that include the Algebraic, Einstein, Hamacher and Frank t-conorms and t-norms as special cases. In this paper, we first present some new operational laws for interval-valued hesitant fuzzy elements (IVHFEs) based on the Archimedean t-conorm and t-norm. Then, based on these operational laws, we develop several Archimedean t-conorm- and t-norm-based interval-valued hesitant fuzzy aggregation operators, which provide a family of interval-valued hesitant fuzzy aggregation operators that include the existing interval-valued hesitant fuzzy aggregation operators based on the Algebraic and Einstein t-conorms and t-norms as special cases. Some desired properties and special cases of the developed operators are investigated in detail. Furthermore, we develop an approach to MCDM under interval-valued hesitant fuzzy environments. Finally, an illustrative example is provided to show the effectiveness and practicality of the proposed operators and approach.