A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming Problems | Zendy

Ladji Kané | Zendy; Daouda Diawara | Zendy; Lassina Diabaté | Zendy; Moussa Konaté | Zendy; Souleymane Kané | Zendy; Hawa Bado | Zendy

Open Access

A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming Problems

Author(s) -

Ladji Kané,

Daouda Diawara,

Lassina Diabaté,

Moussa Konaté,

Souleymane Kané,

Hawa Bado

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/5564598

Subject(s) - linear programming , mathematics , correctness , interval (graph theory) , fuzzy number , mathematical optimization , duality (order theory) , linear fractional programming , interval arithmetic , fuzzy logic , algorithm , fuzzy set , computer science , discrete mathematics , combinatorics , artificial intelligence , mathematical analysis , bounded function

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.

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