Fuzzy sets were initially proposed to address ambiguities and uncertainties. However, in certain cases, the fuzzy sets show some degree of uncertainty and risk, when the available data are either obtained from unreliable sources or related to future events. To solve this problem, the R-numbers methodology has been recently developed as a powerful approach to model the risk of fuzzy sets and numbers due to risk factors. In R-numbers, only the variability of x values has been taken into account in risk modeling of the fuzzy sets, but not their membership function. Moreover, one source of risk factors related to fuzzy sets and numbers merely has been considered. Therefore, this study presents a new concept called R-sets, in which different risk cases of a membership function due to both future events and unreliable information sources are investigated, and the governing mathematical relations are presented. Subsequently, to overcome previous limitations of R-numbers, the R-sets are applied to develop a decision-making method, and it is tested by using a case study.

中文翻译：

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R-sets，基于风险的信息融合和决策的综合模糊集风险建模

模糊集最初是为了解决歧义和不确定性而提出的。然而，在某些情况下，当可用数据是从不可靠的来源获得或与未来事件相关时，模糊集显示出一定程度的不确定性和风险。为了解决这个问题，最近开发了 R 数方法作为一种强大的方法来模拟由于风险因素引起的模糊集和数字的风险。在 R 数中，在模糊集的风险建模中只考虑了 x 值的可变性，而没有考虑它们的隶属函数。此外，仅考虑了与模糊集和数字相关的风险因素的一种来源。因此，本研究提出了一个称为 R-sets 的新概念，其中调查了由于未来事件和不可靠信息源导致的隶属函数的不同风险案例，并提出了控制数学关系。随后，为了克服先前 R 数的局限性，将 R 集应用于开发决策方法，并通过案例研究对其进行了测试。