A general model of ambiguous sets to a single-valued ambiguous numbers with aggregation operators

Abstract

The ambiguous sets have recently been proposed to represent inherent uncertainties, imprecision, and vague information. In this study, we generalize the concept of the 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, the ambiguous weighted geometric operator (AWGO), the ambiguous ordered weighted geometric operator (AOWGO), and the ambiguous hybrid geometric operator (AHGO), for aggregating the input information in the form of SVANs. We discuss some significant properties of the operators along with numerical examples. We develop a method based on the AWGO and AHGO for solving multi-criteria group decision-making (MCGDM) problems. Finally, a real-time example of a MCGDM problem associated with the selection of cars by customers is presented, and its solution is recommended using the proposed method.