NDLI: Ensuring the Centroid of an Interval Type-2 Fuzzy Set

Content Provider	IEEE Xplore Digital Library
Author	Maowen Nie Woei Wan Tan
Copyright Year	1993
Abstract	In computing with words, establishing a fuzzy set (FS) model for a word to capture its uncertainties is an important issue. An interval type-2 (IT2) FS can be used to model a word. How to establish an IT2 FS from the collected data about a word has been a challenging problem. It has been reported that one way is to extract the centroid of an IT2 FS from the collected data and to obtain geometric parameters of its footprint of uncertainty (FOU) such that its centroid matches the extracted one. How to extract the centroid of an IT2 FS from the collected data about a word has thoroughly been studied. However, there exists no method for obtaining FOU parameters for an IT2 FS such that its centroid matches the desired one. To fill this gap, this paper presents an approach to obtaining FOU parameters for an IT2 FS by establishing equations using the centroid requirement. To propose this approach, a sufficient and necessary condition for ensuring the centroid of an IT2 FS is developed. Using this sufficient and necessary condition, two equations about all of the FOU parameters are established. To obtain the FOU parameters, all of them except two are predetermined so that the established equations can be simplified to two single-variable equations. The other two FOU parameters can then be determined by solving these two single-variable equations using existing root-finding algorithms. Among existing root-finding algorithms, the false position algorithm is recommended. The overall merits of the proposed approach are its simplicity in implementation and its applicability to IT2 FSs with arbitrary FOU shapes. In addition, numerical examples are provided to further illustrate how to apply the proposed approach to obtain FOU parameters for an IT2 FS.
Sponsorship	IEEE Computational Intelligence Society
Starting Page	950
Ending Page	963
Page Count	14
File Size	801277
File Format	PDF
ISSN	10636706
Volume Number	23
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Equations Frequency selective surfaces Uncertainty Mathematical model Switches Gold Data mining Karnik-Mendel method Centroid computing with words interval type-2 fuzzy sets
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Control and Systems Engineering Computational Theory and Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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