Cart (Loading....) | Create Account
Close category search window
 

On the geometry of join and meet calculations for general type-2 fuzzy sets

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Mendel, J.M. ; Signal & Image Process. Inst., Univ. of Southern California, Los Angeles, CA, USA

The union and intersection of general type-2 fuzzy sets (T2 FSs) are fundamental computations for such FSs. In the past, algorithms were developed for the union and intersection computations using vertical-slice and horizontal-slice representations of T2 FSs. The vertical-slice representation of a T2 FS traces its origins back to Zadeh [32] and requires computing the join or meet, whereas the horizontal-slice representation of a T2 FS is very recent, traces its origins to Liu [14], and requires computing the join and meet only for interval T2 FSs that are raised to level alpha, for which closed-form formulas are available [15]. In this paper, by studying the join and meet geometrically for general T2 FSs, we show that for many situations closed-form formulas exist for them. We also show that the formulas for computing the union and intersection of general T2 FSs that were derived from the horizontal-slice representation of a T2 FS [19] can also be obtained directly from geometrical interpretations of formulas that were derived by Karnik and Mendel [12] for the vertical-slice representation of a T2 FS.

Published in:

Fuzzy Systems (FUZZ), 2011 IEEE International Conference on

Date of Conference:

27-30 June 2011

Need Help?


IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.