Solution types of two-sided interval linear system and their application on interval linear programming problems

This study proposes a novel technique for solving Linear Programming Problems with triangular fuzzy variables. A modified version of the well-known simplex method and the Existing Method for Solving Interval Linear Programming problems are used for solving linear programming problems with triangular fuzzy variables. Furthermore, for illustration, some numerical examples and one real problem are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy, and reasonable.

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NEW IMPROVED METHOD FOR SOLVING THE FUZZY LINEAR PROGRAMMING PROBLEMS WITH VARIABLES GIVEN AS FUZZY NUMBERS

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.10.12.11 ◽

2021 ◽

Vol 10 (12) ◽

pp. 3699-3723

Author(s):

L. Kané ◽

M. Konaté ◽

L. Diabaté ◽

M. Diakité ◽

H. Bado

Keyword(s):

Linear Programming ◽

Fuzzy Numbers ◽

Optimal Solution ◽

Fuzzy Linear Programming ◽

Interval Linear Programming ◽

Interval Numbers ◽

Programming Technique ◽

Solution Approach ◽

Interval Linear ◽

Linear Programming Problems

The present paper aims to propose an alternative solution approach in obtaining the fuzzy optimal solution to a fuzzy linear programming problem with variables given as fuzzy numbers with minimum uncertainty. In this paper, the fuzzy linear programming problems with variables given as fuzzy numbers is transformed into equivalent interval linear programming problems with variables given as interval numbers. The solutions to these interval linear programming problems with variables given as interval numbers are then obtained with the help of linear programming technique. A set of six random numerical examples has been solved using the proposed approach.

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A Necessary Soft Optimality Test in Interval Linear Programming Problems

Fuzzy Logic and its Applications to Engineering, Information Sciences, and Intelligent Systems ◽

10.1007/978-94-009-0125-4_46 ◽

1995 ◽

pp. 465-473

Author(s):

M. Inuiguchi ◽

M. Sakawa

Keyword(s):

Linear Programming ◽

Interval Linear Programming ◽

Interval Linear ◽

Linear Programming Problems ◽

Optimality Test

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An improved three-step method for solving the interval linear programming problems

Yugoslav journal of operations research ◽

10.2298/yjor180117020a ◽

2018 ◽

Vol 28 (4) ◽

pp. 435-451 ◽

Cited By ~ 1

Author(s):

Mehdi Allahdadi ◽

Chongyang Deng

Keyword(s):

Linear Programming ◽

Optimality Conditions ◽

Optimality Condition ◽

Solution Space ◽

Interval Linear Programming ◽

Step Method ◽

Feasibility Condition ◽

Extra Step ◽

Interval Linear ◽

Linear Programming Problems

Feasibility condition, which ensures that the solution space does not violate any constraints, and optimality condition, which guarantees that all points of the solution space are optimal, are very significant conditions for the solution space of interval linear programming (ILP) problems. Among the existing methods for ILP problems, the best-worst cases (BWC) method and two-step method (TSM) do not ensure feasibility condition, while the modified ILP (MILP), robust TSM (RTSM), improved TSM (ITSM), and three-step method (ThSM) guarantee feasibility condition, whose solution spaces may not be completely optimal. We propose an improved ThSM (IThSM) for ILP problems, which ensures both feasibility and optimality conditions, i.e., we introduce an extra step to optimality.

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