A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming Problems
We define linear programming problems involving trapezoidal fuzzy numbers (LPTra) as the way of linear programming problems involving interval numbers (LPIn). We will discuss the solution concepts of primal and dual linear programming problems involving trapezoidal fuzzy numbers (LPTra) by convertin...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5564598 |
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| author | Ladji Kané Daouda Diawara Lassina Diabaté Moussa Konaté Souleymane Kané Hawa Bado |
| author_facet | Ladji Kané Daouda Diawara Lassina Diabaté Moussa Konaté Souleymane Kané Hawa Bado |
| author_sort | Ladji Kané |
| collection | DOAJ |
| description | We define linear programming problems involving trapezoidal fuzzy numbers (LPTra) as the way of linear programming problems involving interval numbers (LPIn). We will discuss the solution concepts of primal and dual linear programming problems involving trapezoidal fuzzy numbers (LPTra) by converting them into two linear programming problems involving interval numbers (LPIn). By introducing new arithmetic operations between interval numbers and fuzzy numbers, we will check that both primal and dual problems have optimal solutions and the two optimal values are equal. Also, both optimal solutions obey the strong duality theorem and complementary slackness theorem. Furthermore, for illustration, some numerical examples are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy, and reasonable. |
| format | Article |
| id | doaj-art-0c93ce8a66034fd6af1ae383e505e552 |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-0c93ce8a66034fd6af1ae383e505e5522025-08-20T02:02:54ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55645985564598A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming ProblemsLadji Kané0Daouda Diawara1Lassina Diabaté2Moussa Konaté3Souleymane Kané4Hawa Bado5Department of Applied Mathematics (FSEG), Université des Sciences Sociales et de Gestion de Bamako (USSGB), Quartier du Fleuve Rue 310, Porte 238, MaliDepartment of Applied Mathematics (FSEG), Université des Sciences Sociales et de Gestion de Bamako (USSGB), Quartier du Fleuve Rue 310, Porte 238, MaliDepartment of Applied Mathematics (FSEG), Université des Sciences Sociales et de Gestion de Bamako (USSGB), Quartier du Fleuve Rue 310, Porte 238, MaliDepartment of Applied Mathematics (FSEG), Université des Sciences Sociales et de Gestion de Bamako (USSGB), Quartier du Fleuve Rue 310, Porte 238, MaliDepartment of Applied Mathematics (FSEG), Université des Sciences Sociales et de Gestion de Bamako (USSGB), Quartier du Fleuve Rue 310, Porte 238, MaliDepartment of Applied Mathematics (FSEG), Université des Sciences Sociales et de Gestion de Bamako (USSGB), Quartier du Fleuve Rue 310, Porte 238, MaliWe define linear programming problems involving trapezoidal fuzzy numbers (LPTra) as the way of linear programming problems involving interval numbers (LPIn). We will discuss the solution concepts of primal and dual linear programming problems involving trapezoidal fuzzy numbers (LPTra) by converting them into two linear programming problems involving interval numbers (LPIn). By introducing new arithmetic operations between interval numbers and fuzzy numbers, we will check that both primal and dual problems have optimal solutions and the two optimal values are equal. Also, both optimal solutions obey the strong duality theorem and complementary slackness theorem. Furthermore, for illustration, some numerical examples are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy, and reasonable.http://dx.doi.org/10.1155/2021/5564598 |
| spellingShingle | Ladji Kané Daouda Diawara Lassina Diabaté Moussa Konaté Souleymane Kané Hawa Bado A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming Problems Journal of Mathematics |
| title | A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming Problems |
| title_full | A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming Problems |
| title_fullStr | A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming Problems |
| title_full_unstemmed | A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming Problems |
| title_short | A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming Problems |
| title_sort | mathematical model for solving the linear programming problems involving trapezoidal fuzzy numbers via interval linear programming problems |
| url | http://dx.doi.org/10.1155/2021/5564598 |
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