Abstract
The available data for real-world decision-making problems are usually associated with all sorts of ambiguities and uncertainties. A common solution to such problems is the use of fuzzy sets. However, there are cases in which the fuzzy sets and fuzzy numbers may have some degree of uncertainty and error when available data either come from unreliable sources or refer to events in the future. These situations result in some deviation between the available data and the determined values. Therefore, for a better modeling of the risks and errors associated with fuzzy numbers this paper aims at presenting a novel concept herein referred to as R-numbers. First, all possible configurations of risk modeling are investigated in order to propose and develop an R-numbers-based model and their related mathematical relationships. Eventually, R-numbers will be used to develop a multi-criteria decision-making approach that will be applied to different real-world decision problems.
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