Uncertainty measures for interval type-2 fuzzy sets
Uncertainty measures for interval type-2 fuzzy sets
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DOI：
10.1016/j.ins.2007.07.012
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发表时间：
2007-12-01
影响因子：
8.1
通讯作者：
Mendel, Jerry M.
中科院分区：
文献类型：
--
作者：
Wu, Dongrui;Mendel, Jerry M.
模糊度（熵）是一类模糊集不确定性的常用度量。对于区间2型模糊集（IT2 FSs），质心、基数、模糊性、方差和偏度都是不确定性的度量。卡尼克和孟德尔已经定义了it2fs的质心。本文对其他四个概念进行了定义。所有的定义都使用IT2 fs的表示定理。导出了计算IT2 FS的基数、模糊度、方差和偏度的公式。这些定义在使用不确定性原理设计IT2模糊逻辑系统以及测量两个IT2 fs之间的相似性时应该是有用的。(C) 2007爱思唯尔公司版权所有。
Fuzziness (entropy) is a commonly used measure of uncertainty for type-1 fuzzy sets. For interval type-2 fuzzy sets (IT2 FSs), centroid, cardinality, fuzziness, variance and skewness are all measures of uncertainties. The centroid of an IT2 FS has been defined by Karnik and Mendel. In this paper, the other four concepts are defined. All definitions use a Representation Theorem for IT2 FSs. Formulas for computing the cardinality, fuzziness, variance and skewness of an IT2 FS are derived. These definitions should be useful in IT2 fuzzy logic systems design using the principles of uncertainty, and in measuring the similarity between two IT2 FSs. (C) 2007 Elsevier Inc. All rights reserved.