Abstract
Aggregation operators perform a valuable and significant role in various decision-making processes. Averaging and geometric aggregation operators are both used for capturing the interrelationships of the aggregated preferences, even if the preferences are independent. The purpose of this paper is to analyze the theory of complex linguistic fuzzy (CLF) sets and their important laws, such as algebraic laws, score values, and accuracy values, and to describe the relationship between the score and accuracy values with the help of their properties. Additionally, based on the proposed CLF information, we introduce the theory of CLF weighted averaging (CLFWA), CLF ordered weighted averaging (CLFOWA), CLF hybrid averaging (CLFHA), CLF weighted geometric (CLFWG), CLF ordered weighted geometric (CLFOWG), and CLF hybrid geometric (CLFHG) operators. The fundamental properties and some valuable results of these operators are evaluated, and their particular cases are described. Based on the presented operators, a technique for evaluating the "multi-attribute decision-making" (MADM) problems in the consideration of CLF sets is derived. The superiority of the derived technique is illustrated via a practical example, a set of experiments, and significant and qualitative comparisons. The illustration results indicate that the derived technique can be feasible and superior in evaluating CLF information. Further, it can be used for determining the interrelationships of attributes and the criteria of experts. Moreover, it is valuable and capable of evaluating the MADM problems using CLF numbers.