An investigation of ambiguous sets and their application to decision-making from partial order to lattice ambiguous sets

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.