A mathematical model for solving the linear programming problems involving trapezoidal fuzzy numbers via interval linear programming problems
type: Item
instance of: scholarly article
title: A mathematical model for solving the linear programming problems involving trapezoidal fuzzy numbers via interval linear programming problems
zbMATH Open document ID: 1477.90124
DOI: 10.1155/2021/5564598
author: Ladji Kane
author: Daouda Diawara
author: Lassina Diabaté
author: Moussa Konaté
author: Souleymane Kané
author: Hawa Bado
published in: Journal of Mathematics
publication date: 2021-06-25T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 90C70
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 7363421
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5564598
OpenAlex ID: W3155732728
cites work: On comparing interval numbers
cites work: Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming.
cites work: Linear Multiple Objective Problems with Interval Coefficients
cites work: Multiobjective programming in optimization of interval objective functions -- a generalized approach
cites work: Algorithms for Linear Programming Problems with Interval Objective Function Coefficients
cites work: ON ARITHMETIC OPERATIONS OF INTERVAL NUMBERS
cites work: Decision-Making in a Fuzzy Environment
cites work: Fuzzy Linear Programming: Solution Techniques and Applications
cites work: Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables
cites work: Some new results in linear programs with trapezoidal fuzzy numbers: finite convergence of the Ganesan and Veeramani's method and a fuzzy revised simplex method
cites work: A method for solving linear programming with interval-valued trapezoidal fuzzy variables
cites work: A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems
cites work: A novel method for solving linear programming problems with symmetric trapezoidal fuzzy numbers
cites work: A revisit of numerical approach for solving linear fractional programming problem in a fuzzy environment
cites work: Sensitivity analysis in fuzzy number linear programming problems
cites work: A new fuzzy arithmetic
description: scientific article; zbMATH DE number 7363421