The ongoing research in the field of decision-making can be analyzed from different perspectives. Research trends indicate that multi-attribute decision-making (MADM) methods have a significant impact on engineering and management scientific areas. Since many of the problems existing in the mentioned areas are associated with a certain level of uncertainty, type 2 fuzzy sets represent a common solution for the enhancement of conventional MADM methods. In this way, the decision-makers are encouraged to use linguistic expressions for the assessment of attributes’ relative importance and their values. The purpose of this paper is to review a determination of attributes’ relative importance, and their values, as well as the extension of ranking methods with type 2 fuzzy sets. The papers are systematically adjoined to groups consisting of hybrid models with the following characteristics: (1) indicating the procedure for modeling attribute relative importance and their values, (2) determining the extension of MADM methods with type 2 fuzzy sets to determine attributes’ vector weights, and (3) the extension of MADM for attributes ranking with type 2 fuzzy sets. This study reviewed a total of 42 papers in the domain of engineering and management published from 2013 to 2023 in different journals indexed by the Springer, Science Direct, Emerald, Wiley, ProQuest, Taylor, and Francis research platforms.