Uncertainty measures for interval type-2 fuzzy sets

被引：297

作者：

Wu, Dongrui ^{[1
]}

Mendel, Jerry M. ^{[1
]}

机构：

[1] Univ So Calif, Inst Signal & Image Proc, Ming Hsieh Dept Elect Engn, Los Angeles, CA 90089 USA

来源：

INFORMATION SCIENCES | 2007年 / 177卷 / 23期

关键词：

uncertainty measure; interval type-2 fuzzy set; centroid; cardinality; fuzziness; entropy; variance; skewness;

D O I：

10.1016/j.ins.2007.07.012

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：5378 / 5393

页数：16

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