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...
| Main Authors: | , , , , , |
|---|---|
| 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 |
| _version_ | 1848846613020147712 |
|---|---|
| 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. |
| first_indexed | 2025-11-15T09:05:29Z |
| format | Article |
| id | upm-30211 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T09:05:29Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |