NDLI: Metrics for vague spatial objects based on the concept of mass

Content Provider	IEEE Xplore Digital Library
Author	Dilo, A. de By, R.A. Stein, A.
Copyright Year	2007
Description	Author affiliation: Delft Univ. of Technol., Delft (Dilo, A.)
Abstract	Many spatial phenomena exhibit vagueness. Representation of such phenomena requires vague objects. In previous work, we provided definitions for vague objects: vague points, vague lines, and vague regions. Each of these objects is presented as a fuzzy set in $IR^{2}$ that satisfies well-defined properties. In this paper, we propose a number of geometric measures for vague objects, using the concept of mass distribution. The membership function of a vague object can be seen as a mass distribution. According to this view, a crisp object is a body with constant density, and a vague object is a body of varying density. We provide mathematical definitions for length of a vague line, area of a vague region, centroid of a vague object, as well as a measure for the vagueness of an object. The length of a vague line and the area of a vague region are indeed the mass of the vague line and of the vague region, respectively. Both metrics give an average of the values of the corresponding crisp metric on the alpha-cuts of the vague object. The centroid of a vague object is its centre of mass associated with a membership degree. The last metric functions as a measure of the degree of vagueness for a vague object.
Starting Page	1
Ending Page	6
File Size	12528501
Page Count	6
File Format	PDF
ISBN	1424412099
ISSN	10987584
DOI	10.1109/FUZZY.2007.4295469
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-07-23
Publisher Place	UK
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fuzzy sets Vegetation Fuzzy logic Geographic Information Systems Area measurement Length measurement Multivalued logic Database systems Performance analysis Geoscience
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Theoretical Computer Science Software

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