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Soft Computing
Published in: Soft Computing 4/2014

01-04-2014 | Methodologies and Application

A new approach to similarity and inclusion measures between general type-2 fuzzy sets

Authors: Tao Zhao, Jian Xiao, YiXing Li, XueSong Deng

Published in: Soft Computing | Issue 4/2014

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Abstract

Interval type-2 fuzzy similarity and inclusion measures have been widely studied. In this paper, the axiomatic definitions of general type-2 fuzzy similarity and inclusion measures are given on the basis of interval type-2 fuzzy similarity and inclusion measures. To improve the shortcomings of the existing general type-2 fuzzy similarity and inclusion measures, we define two new general type-2 fuzzy similarity measures and two new general type-2 fuzzy inclusion measures based on \(\alpha \)-plane representation theory, respectively, and discuss their related properties. Unlike some existing measures, one of the proposed similarity and inclusion measures are expressed as type-1 fuzzy sets, and therefore these definitions are consistent with the highly uncertain nature of general type-2 fuzzy sets. The theoretical proof is also given to illustrate that the proposed measures are natural extensions of the most popular type-1 fuzzy measures. In the end, the performances of the proposed similarity and inclusion measures are examined.
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Metadata
Title
A new approach to similarity and inclusion measures between general type-2 fuzzy sets
Authors
Tao Zhao
Jian Xiao
YiXing Li
XueSong Deng
Publication date
01-04-2014
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 4/2014
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-013-1101-z

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