Abstract
The idea of ambiguous set (AS) theory has been introduced to describe the uncertainties, imprecisions and haziness innate in information. This study generalizes the notion of AS to a single-valued ambiguous number (SVAN). We propose the concepts of partial ambiguous order set (PAOS) and lattice ambiguous set (LAS) for SVANs. Two operators, namely A-norms and A-conorms, are proposed for LAS. In this study, a degree of fitness function (DFF) and an ambiguous weighted geometric operator (AWGO) are also introduced to compare and aggregate the events in the form of SVANs. We propose a method based on A-norms, A-conorms and AWGO for solving multi-criteria group decision-making (MCGDM) problems. Finally, a real-time example of a MCGDM problem associated with the selection of cell phones by customers is presented, and its solution is suggested using the proposed method.
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