An efficient computational approach for solving type-2 intuitionistic fuzzy numbers based Transportation Problems
This paper is concerned with the solution procedure of a Transportation Problem in which costs are triangular intuitionistic fuzzy numbers (TIFN) and availabilities and demands are taken as exact numerical values. According to the existing solution approach, TIFN are first ordered by using an accura...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer
2016-12-01
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| Series: | International Journal of Computational Intelligence Systems |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/25868754/view |
| _version_ | 1811302343455539200 |
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| author | Ali Ebrahimnejad Jose Luis Verdegay |
| author_facet | Ali Ebrahimnejad Jose Luis Verdegay |
| author_sort | Ali Ebrahimnejad |
| collection | DOAJ |
| description | This paper is concerned with the solution procedure of a Transportation Problem in which costs are triangular intuitionistic fuzzy numbers (TIFN) and availabilities and demands are taken as exact numerical values. According to the existing solution approach, TIFN are first ordered by using an accuracy function defined on score functions for membership and non-membership functions of TIFN. Then this ordering is used to develop methods for finding an initial basic feasible solution and the optimal solution of intuitionistic fuzzy Transportation Problems in terms of triangular intuitionistic fuzzy numbers. This solution approach, in spite of its merits, requires a lot of fuzzy arithmetic operations, such as additions and subtractions of TIFN, as well as a lot of comparisons on TIFN. In this paper an efficient computational solution approach is proposed for solving intuitionistic fuzzy Transportation Problems based on classical transportation algorithms to overcome the shortcomings of the aforementioned solution approach. In the approach here presented, the comparison of triangular intuitionistic fuzzy costs is done once and all arithmetic operations are done on real numbers. Finally, for the sake of illustration, two intuitionistic fuzzy Transportation Problems are solved herein to demonstrate the usages and advantages of the proposed solution approach. |
| first_indexed | 2024-04-13T07:26:22Z |
| format | Article |
| id | doaj.art-ed6a9ae69a0d4546bfb93ef7c9c9c546 |
| institution | Directory Open Access Journal |
| issn | 1875-6883 |
| language | English |
| last_indexed | 2024-04-13T07:26:22Z |
| publishDate | 2016-12-01 |
| publisher | Springer |
| record_format | Article |
| series | International Journal of Computational Intelligence Systems |
| spelling | doaj.art-ed6a9ae69a0d4546bfb93ef7c9c9c5462022-12-22T02:56:29ZengSpringerInternational Journal of Computational Intelligence Systems1875-68832016-12-019610.1080/18756891.2016.1256576An efficient computational approach for solving type-2 intuitionistic fuzzy numbers based Transportation ProblemsAli EbrahimnejadJose Luis VerdegayThis paper is concerned with the solution procedure of a Transportation Problem in which costs are triangular intuitionistic fuzzy numbers (TIFN) and availabilities and demands are taken as exact numerical values. According to the existing solution approach, TIFN are first ordered by using an accuracy function defined on score functions for membership and non-membership functions of TIFN. Then this ordering is used to develop methods for finding an initial basic feasible solution and the optimal solution of intuitionistic fuzzy Transportation Problems in terms of triangular intuitionistic fuzzy numbers. This solution approach, in spite of its merits, requires a lot of fuzzy arithmetic operations, such as additions and subtractions of TIFN, as well as a lot of comparisons on TIFN. In this paper an efficient computational solution approach is proposed for solving intuitionistic fuzzy Transportation Problems based on classical transportation algorithms to overcome the shortcomings of the aforementioned solution approach. In the approach here presented, the comparison of triangular intuitionistic fuzzy costs is done once and all arithmetic operations are done on real numbers. Finally, for the sake of illustration, two intuitionistic fuzzy Transportation Problems are solved herein to demonstrate the usages and advantages of the proposed solution approach.https://www.atlantis-press.com/article/25868754/viewIntuitionistic fuzzy transportation problemTriangular intuitionistic fuzzy numberAccuracy function |
| spellingShingle | Ali Ebrahimnejad Jose Luis Verdegay An efficient computational approach for solving type-2 intuitionistic fuzzy numbers based Transportation Problems International Journal of Computational Intelligence Systems Intuitionistic fuzzy transportation problem Triangular intuitionistic fuzzy number Accuracy function |
| title | An efficient computational approach for solving type-2 intuitionistic fuzzy numbers based Transportation Problems |
| title_full | An efficient computational approach for solving type-2 intuitionistic fuzzy numbers based Transportation Problems |
| title_fullStr | An efficient computational approach for solving type-2 intuitionistic fuzzy numbers based Transportation Problems |
| title_full_unstemmed | An efficient computational approach for solving type-2 intuitionistic fuzzy numbers based Transportation Problems |
| title_short | An efficient computational approach for solving type-2 intuitionistic fuzzy numbers based Transportation Problems |
| title_sort | efficient computational approach for solving type 2 intuitionistic fuzzy numbers based transportation problems |
| topic | Intuitionistic fuzzy transportation problem Triangular intuitionistic fuzzy number Accuracy function |
| url | https://www.atlantis-press.com/article/25868754/view |
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