Multi-criteria decision making (MCDM) technique and approach have been a trending topic in decision making and systems engineering to choosing the probable optimal options. The primary purpose of this article is to develop prioritized operators to multi-criteria decision making (MCDM) based on Archimedean t-conorm and t-norms (At-CN&t-Ns) under interval-valued dual hesitant fuzzy (IVDHF) environment. A new score function is defined for finding the rank of alternatives in MCDM problems with IVDHF information based on priority levels of criteria imposed by the decision maker. This paper introduces two aggregation operators: At-CN&t-N-based IVDHF prioritized weighted averaging (AIVDHFPWA), and weighted geometric (AIVDHFPWG) aggregation operators. Some of their desirable properties are also investigated in details. A methodology for prioritization-based MCDM is derived under IVDHF information. An illustrative example concerning MCDM problem about a Chinese university for appointing outstanding oversea teachers to strengthen academic education is considered. The method is also applicable for solving other real-life MCDM problems having IVDHF information.

The linguistic q-rung orthopair fuzzy (L q-ROF) set is an important implement in the research area in modelling vague decision information by incorporating the advantages of q- rung orthopair fuzzy sets and linguistic variables. This paper aims to investigate the multicriteria decision group decision making (MCGDM) with L q-ROF information. To do this, utilizing Hamacher t-norm and t-conorm, some L q-ROF prioritized aggregation operators viz., L q- ROF Hamacher prioritized weighted averaging, and L q-ROF Hamacher prioritized weighted geometric operators are developed in this paper. The defined operators can effectively deal with different priority levels of attributes involved in the decision making processes. In addition, Hamacher parameters incorporated with the proposed operators make the information fusion process more flexible. Some prominent characteristics of the developed operators are also wellproven. Then based on the proposed aggregation operators, an MCGDM model with L q-ROF context is framed. A numerical example is illustrated in accordance with the developed model to verify its rationality and applicability. The impacts of Hamacher and rung parameters on the achieved decision results are also analyzed in detail. Afterwards, a comparative study with other representative methods is presented in order to reflect the validity and superiority of the proposed approach.