Interval Type-2 Fuzzy Sets and Systems: Overview and Outlook
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摘要: 一型模糊集可以建模单个用户的语义概念中的不确定性, 即个体内不确定性. 一型模糊系统在控制和机器学习中得到了大量成功应用. 区间二型模糊集能同时建模个体内不确定性和个体间不确定性, 因而在很多应用中显示了比一型模糊系统更好的性能, 是近年来的研究热点. 本文首先介绍了区间二型模糊集的重要概念和理论研究进展, 总结了其在决策和机器学习中的成功应用, 然后介绍了区间二型模糊系统的基本操作和理论研究进展, 并回顾了其在控制和机器学习中的典型应用. 最后, 对区间二型模糊集和模糊系统未来的研究方向进行了展望.Abstract: Type-1 fuzzy sets can model the linguistic uncertainty from a single user, i.e., intra-personal uncertainty. Type-1 fuzzy systems have been widely used in controls and machine learning applications. Interval type-2 fuzzy sets can simultaneously model both intra-personal uncertainty and inter-personal uncertainty, and hence have demonstrated better performance than type-1 fuzzy systems in many applications, becoming a hot research topic recently. This paper first introduces main concepts and theoretical research progresses of interval type-2 fuzzy sets, summarizes their successful applications in decision-making and machine learning, then introduces basic operations and theoretical research progresses of interval type-2 fuzzy systems, and reviews their typical applications in controls and machine learning. Finally, it points out several future research directions on interval type-2 fuzzy sets and systems.
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图 4 根据不同的表示定理, 计算区间二型模糊集质心所用到的嵌入一型模糊集(左边的点是由实线嵌入一型模糊集决定的质心的下界, 右边的点是由虚线嵌入一型模糊集决定的质心的上界.)
Fig. 4 Embedded type-1 fuzzy sets in computing the centroid of the interval type-2 fuzzy set, according to different representation theorems (The left dot is the lower bound of the centroid determined by the solid embedded type-1 fuzzy set, and the right dot is the upper bound determined by the dashed embedded type-1 fuzzy set.)
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