We review recent literature on three aspects of fuzzy measures: their representations, learning optimal fuzzy measures and random generation of various types of fuzzy measures. These three aspects are interdependent: methods of learning fuzzy measures depend on their representation, and may also include random generation as one of the steps, on the other hand different representations also affect generation methods, while random generation plays an important role in simulation studies for post-hoc analysis of sets of measures learned from data and problem-specific constraints. Explicit modelling of interactions between the decision variables is a distinctive feature of integrals based on fuzzy measures, but its price is high computational complexity. To extend their range of applicability efficient representations and computational techniques are required. All three mentioned aspects provide mathematical and computational tools for novel applications of fuzzy measures and integrals in decision making and information fusion, allow scaling up significantly the domain of applicability and reduce their complexity.

中文翻译：

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模糊测度的表示、优化和生成

我们回顾了最近关于模糊测度三个方面的文献：它们的表示、学习最优模糊测度以及各种类型模糊测度的随机生成。这三个方面是相互依赖的：学习模糊测度的方法取决于其表示，并且还可能包括随机生成作为步骤之一，另一方面不同的表示也会影响生成方法，而随机生成在模拟研究中起着重要作用对从数据和特定问题的约束中学到的措施进行事后分析。决策变量之间相互作用的显式建模是基于模糊测度的积分的显着特征，但其代价是计算复杂度较高。为了扩展其适用范围，需要有效的表示和计算技术。所有提到的三个方面都为模糊测量和积分在决策和信息融合中的新颖应用提供了数学和计算工具，允许显着扩大适用范围并降低其复杂性。