A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming Problems. (17th April 2021)

• Record Type: Journal Article
• Authors: Kané, Ladji; Diawara, Daouda; Diabaté, Lassina; Konaté, Moussa; Kané, Souleymane; Bado, Hawa
• Other Names: Qin Xiaolong Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2021(2021)
• Publication Date: 2021-04-17
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2021/5564598
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : 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.