A new distance measure for trapezoidal fuzzy numbers

We propose a new distance measure for the space of all trapezoidal fuzzy numbers using centroid point and left/right spread of trapezoidal fuzzy numbers. Moreover, the metric properties of suggested distance measure are investigated. Indeed, we show that for two arbitrary trapezoidal fuzzy numbers i...

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Main Authors: Ebadi, M. J., Suleiman, Mohamed, Ismail, Fudziah, Ahmadian, Ali, Shahryari, M. R. Balooch, Salahshour, Soheil
Format: Article
Language:English
English
Published: Hindawi Publishing Corporation 2013
Online Access:http://psasir.upm.edu.my/id/eprint/30211/
http://psasir.upm.edu.my/id/eprint/30211/1/A%20new%20distance%20measure%20for%20trapezoidal%20fuzzy%20numbers.pdf
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author Ebadi, M. J.
Suleiman, Mohamed
Ismail, Fudziah
Ahmadian, Ali
Shahryari, M. R. Balooch
Salahshour, Soheil
author_facet Ebadi, M. J.
Suleiman, Mohamed
Ismail, Fudziah
Ahmadian, Ali
Shahryari, M. R. Balooch
Salahshour, Soheil
author_sort Ebadi, M. J.
building UPM Institutional Repository
collection Online Access
description We propose a new distance measure for the space of all trapezoidal fuzzy numbers using centroid point and left/right spread of trapezoidal fuzzy numbers. Moreover, the metric properties of suggested distance measure are investigated. Indeed, we show that for two arbitrary trapezoidal fuzzy numbers if the distance between centroid points and also the distance between left spreads and right spreads go to zero, then two given fuzzy numbers are equal. Consequently, we complete discussion about the relation between fuzzy number and its centroid which is the firstly discussed by Hadi-Vencheh and Allame (2010). To the best of our knowledge, this is first time in the literature that such metric is applied by centroid point.
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spelling upm-302112015-09-09T02:41:05Z http://psasir.upm.edu.my/id/eprint/30211/ A new distance measure for trapezoidal fuzzy numbers Ebadi, M. J. Suleiman, Mohamed Ismail, Fudziah Ahmadian, Ali Shahryari, M. R. Balooch Salahshour, Soheil We propose a new distance measure for the space of all trapezoidal fuzzy numbers using centroid point and left/right spread of trapezoidal fuzzy numbers. Moreover, the metric properties of suggested distance measure are investigated. Indeed, we show that for two arbitrary trapezoidal fuzzy numbers if the distance between centroid points and also the distance between left spreads and right spreads go to zero, then two given fuzzy numbers are equal. Consequently, we complete discussion about the relation between fuzzy number and its centroid which is the firstly discussed by Hadi-Vencheh and Allame (2010). To the best of our knowledge, this is first time in the literature that such metric is applied by centroid point. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30211/1/A%20new%20distance%20measure%20for%20trapezoidal%20fuzzy%20numbers.pdf Ebadi, M. J. and Suleiman, Mohamed and Ismail, Fudziah and Ahmadian, Ali and Shahryari, M. R. Balooch and Salahshour, Soheil (2013) A new distance measure for trapezoidal fuzzy numbers. Mathematical Problems in Engineering, 2013. art. no. 424186. pp. 1-4. ISSN 1024-123X http://www.hindawi.com/journals/mpe/2013/424186/ 10.1155/2013/424186 English
spellingShingle Ebadi, M. J.
Suleiman, Mohamed
Ismail, Fudziah
Ahmadian, Ali
Shahryari, M. R. Balooch
Salahshour, Soheil
A new distance measure for trapezoidal fuzzy numbers
title A new distance measure for trapezoidal fuzzy numbers
title_full A new distance measure for trapezoidal fuzzy numbers
title_fullStr A new distance measure for trapezoidal fuzzy numbers
title_full_unstemmed A new distance measure for trapezoidal fuzzy numbers
title_short A new distance measure for trapezoidal fuzzy numbers
title_sort new distance measure for trapezoidal fuzzy numbers
url http://psasir.upm.edu.my/id/eprint/30211/
http://psasir.upm.edu.my/id/eprint/30211/
http://psasir.upm.edu.my/id/eprint/30211/
http://psasir.upm.edu.my/id/eprint/30211/1/A%20new%20distance%20measure%20for%20trapezoidal%20fuzzy%20numbers.pdf