Uncertainty measures for general type-2 fuzzy sets
Uncertainty measures for general type-2 fuzzy sets
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DOI：
10.1016/j.ins.2010.09.020
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发表时间：
2009-10
期刊：
影响因子：
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通讯作者：
Daoyuan Zhai;J. Mendel
中科院分区：
文献类型：
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作者：
Daoyuan Zhai;J. Mendel
以往对区间二型模糊集(IT2 FSS)定义了五个不确定性度量，即质心、基数、模糊性、方差和偏度。基于最近发展的一般T2 FS的α平面表示，本文将这些定义推广到这类T2 FS，更重要的是，得到了以较低的复杂度计算所有不同不确定性度量的统一策略。计算了具有不同形状的不确定足迹和不同类型的二级隶属函数的T2模糊综合评判的不确定度，并给出了算例。对这些例子进行了观察和总结，并提出了一种针对一般T2 FS的汇总区间不确定度度量，以简化解释。本文还对准2类(QT2)、IT2和T2 FSS的不确定性度量进行了比较研究，以检验用QT2甚至IT2 FSS近似T2 FSS的可行性。
Five uncertainty measures have previously been defined for interval Type-2 fuzzy sets (IT2 FSs), namely centroid, cardinality, fuzziness, variance and skewness. Based on a recently developed α-plane representation for a general T2 FS, this paper generalizes these definitions to such T2 FSs and, more importantly, derives a unified strategy for computing all different uncertainty measures with low complexity. The uncertainty measures of T2 FSs with different shaped Footprints of Uncertainty and different kinds of secondary membership functions (MFs) are computed and are given as examples. Observations and summaries are made for these examples, and a Summary Interval Uncertainty Measure for a general T2 FS is proposed to simplify the interpretations. Comparative studies of uncertainty measures for Quasi-Type-2 (QT2), IT2 and T2 FSs are also performed to examine the feasibility of approximating T2 FSs using QT2 or even IT2 FSs.