### Solving fuzzy linear programming problems by using the fuzzy exponential barrier method

#### Abstract

In order to resolve the fuzzy linear programming problem, the fuzzy exponential barrier approach is the major strategy employed in this article. To overcome the problems with fuzzy linear programming, this method uses an algorithm. In this concept, a fuzzy inequality constraint is produced since the objective functions are convex.numerical examples are provided.

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Dubois., Didier., Henri Prade.: The mean value of a fuzzy number, Fuzzy sets and system, 24.3,279-300. 1987.

Fiacco., Anthony,V.: Sensitivity analysis for nonlinear programming using penalty methods, Mathematical Programming, 10(1), 287-311. 1976.

Fiacco., Anthony,V., Garth, P., McCormick.: Nonlinear programming: sequential

unconstrained minimization techniques,Vol. 4. Siam, (1990).

NagoorGani, A., Yogarani,R.: Fuzzy linear programming problem using polynomial penalty method, Bulletin of Pure & Applied Sciences-Mathematics and Statistics 38.1,441-449, (2019).

NagoorGani, A., Yogarani,R.: Solving Fuzzy Linear Programming Problem With A Fuzzy Polynomial Barrier Method, International Journal of Aquatic Science,Vol. 12,pp.169-174, (2021).

Nagoor Gani, A., Yogarani,R.: SOLVING FUZZY LINEAR PROGRAMMING PROBLEM USING A FUZZY LOGARITHMIC BARRIER METHOD, Advances and Applications in Mathematical Sciences,Vol.20, 583-595 (2021).

Nagoor Gani, A., Yogarani,R.: Fuzzy Inverse Barrier Method to Find Primal and Dual Optimality Solutions of Fuzzy Linear Programming Problems, Turkish Journal of Computer and Mathematics Education (TURCOMAT), 12.9, 957-962, (2021).

Hsieh., ChihHsun., Shan-Huo Chen.: Similarity of generalized fuzzy numbers with graded mean integration representation, Proc. 8th Int. Fuzzy Systems Association World Congr. Vol. 2, pp.551-555, (1999).

Li, X., Pan, S.: Solving the finite min-max problem via an exponential barrier method,8.2, (2003).

MAHDAVI., AMIRI,N., NASERI, SH., YAZDANI, AB.: Fuzzy primal simplex algorithms for solving fuzzy linear programming problems, 68-84(2009).

Mahdavi-Amiri, N., Nasseri, S. H.: Duality in fuzzy number linear programming by use of a certain linear ranking function, Applied Mathematics and Computation, 180.1, 206-216, (2006).

Moengin, Parwadi: Exponential barrier method in solving linear programming problems,International Journal of Engineering and Technology, 12.3. 2011.

NagoorGani, A., Assarudeen., Mohamed S.N.: A new operation on triangular fuzzy number for solving fuzzy linear programming problem, Applied Mathematical Sciences, 6(11),25-532. 2012.

Tanaka, H., Asai, K.: Fuzzy linear programming problems with fuzzy numbers, Fuzzy sets and systems, 13(1), 1-10. 1984.

Wright., Stephen, J.: On the convergence of the Newton/log-barrier method, Mathematical Programming, 90.1, 71-100. 2001.

Zimmermann, H.J.: Fuzzy programming and linear programming with several objective Functions, Fuzzy Sets and Systems, 1(1), 45. 1978.

DOI: http://dx.doi.org/10.23755/rm.v46i0.1088

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