NDLI: Centroid uncertainty bounds for interval type-2 fuzzy sets: forward and inverse problems

Content Provider	IEEE Xplore Digital Library
Author	Mendel, J.M. Hongwei Wu
Copyright Year	2004
Description	Author affiliation: Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA (Mendel, J.M.; Hongwei Wu)
Abstract	Interval type-2 fuzzy sets (T2 FS) play a central role in fuzzy sets as models for words and in engineering applications of T2 FSs. These fuzzy sets are characterized by their footprints of uncertainty (FOU), which in turn are characterized by their boundaries-upper and lower membership functions (MF). The centroid of an interval T2 FS, which is an interval T1 FS, provides a measure of the uncertainty in the interval T2 FS. Intuitively, we anticipate that geometric properties about the FOU, such as its area and the center of gravities (centroids) of its upper and lower MFs, associated with the amount of uncertainty in an interval T2 FS. The main purpose of this paper is to demonstrate that our intuition is correct and to quantify the centroid of an interval T2 FS with respect to these geometric properties of its FOU. It is then possible to formulate and solve inverse problems, i.e., going from data to parametric T2 FS models.
Starting Page	947
Ending Page	952
File Size	374445
Page Count	6
File Format	PDF
ISBN	0780383532
ISSN	10987584
DOI	10.1109/FUZZY.2004.1375535
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2004-07-25
Publisher Place	Hungary
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fuzzy sets Inverse problems Frequency selective surfaces Area measurement Measurement uncertainty Gravity Signal processing Image processing Marine vehicles Solid modeling
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Theoretical Computer Science Software

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