Comparison functions, operational laws and aggregation operators for ambiguous set: Application in solving multi-criteria group decision-making problem under ambiguous environment

Abstract Ambiguous set has recently been proposed to represent inherent uncertainties, imprecision, and vague information. In this study, we generalize the concept of ambiguous set to a single-valued ambiguous number (SVAN). We propose many comparison functions and operational laws for SVANs. This study also introduces three new aggregation operators, such as the ambiguous weighted geometric operator (AWGO), the ambiguous ordered weighted geometric operator (AOWGO), and the ambiguous hybrid geometric operator (AHGO), which are used to aggregate input information in the form of SVANs. We discuss some significant properties of the operators along with numerical examples. Based on the AWGO and AHGO, we develop a method for solving the multi-criteria group decision-making (MCGDM) problem. Finally, a real-time example of an MCGDM problem associated with the selection of cars by customers is presented, and its solution is recommended using the proposed method.