Fuzzy Mathematical Programming approach for Solving Fuzzy Linear Fractional Programming Problem
RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 1, pp. 109-122.

In this paper, a solution procedure is proposed to solve fuzzy linear fractional programming (FLFP) problem where cost of the objective function, the resources and the technological coefficients are triangular fuzzy numbers. Here, the FLFP problem is transformed into an equivalent deterministic multi-objective linear fractional programming (MOLFP) problem. By using Fuzzy Mathematical programming approach transformed MOLFP problem is reduced single objective linear programming (LP) problem. The proposed procedure illustrated through a numerical example.

DOI : 10.1051/ro/2013056
Classification : 90C31, 91A35, 94D05
Mots-clés : triangular fuzzy number, linear programming problem, multi objective linear fractional programming problem, fuzzy mathematical programming 
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     author = {Veeramani, Chinnadurai and Sumathi, Muthukumar},
     title = {Fuzzy {Mathematical} {Programming} approach for {Solving} {Fuzzy} {Linear} {Fractional} {Programming} {Problem}},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {109--122},
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Veeramani, Chinnadurai; Sumathi, Muthukumar. Fuzzy Mathematical Programming approach for Solving Fuzzy Linear Fractional Programming Problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 1, pp. 109-122. doi : 10.1051/ro/2013056. http://www.numdam.org/articles/10.1051/ro/2013056/

[1] M. Abousina and A.I. Baky, Fuzzy goal programming procedure to bilevel multi-objective linear fractional programming problems. Int. J. Math. Math. Sci. (2010) (Article ID 148975). | MR | Zbl

[2] G.R. Bitran and A.G. Novaes, Linear programming with a fractional objective function. Oper. Res. 21 (1973) 22-29. | MR | Zbl

[3] I.A. Baky, Solving multi-level multi-objective linear programming problemsthrough fuzzy goal programming approach. Appl. Math. Model. 34 (2010) 2377-2387. | MR | Zbl

[4] M. Chakraborty and S. Gupta, Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy Sets System 125 (2002) 335-342. | MR | Zbl

[5] A. Charnes and W.W. Cooper, Programming with linear fractional functions. Naval Res. Logist. Quart. 9 (1962) 81-186. | MR | Zbl

[6] Craven, Fractional Programming. Heldermann verlag, Berlin (1988). | MR | Zbl

[7] D. Dutta, J.R. Rao and R.N. Tiwari, Effect of tolerance in fuzzy linear fractional programming. Fuzzy Sets Systems 55 (1993) 133-142. | MR | Zbl

[8] S. Jain, A. Mangal, and P.R. Parihar, Solution of fuzzy linear fractional programming problem. OPSEARCH 48 (2011) 129-135. | MR | Zbl

[9] D.F. Li and S. Chen, A fuzzy programming approach to fuzzy linear fractional programming with fuzzy coefficients. J. Fuzzy Math. 4 (1996) 829-834. | MR | Zbl

[10] M.K. Luhandjula, Fuzzy approaches for multiple objective linear fractional optimization. Fuzzy Sets System 13 (1984) 11-23. | MR | Zbl

[11] A. Mehra, S. Chandra and C.R. Bector, Acceptable optimality in linear fractional programming with fuzzy coefficients. Fuzzy Optimization Decision Making 6 (2007) 5-16. | MR | Zbl

[12] B.B. Pal and I. Basu, A goal programming method for solving fractional programming problems via dynamic programming. Optim. A J. Math. Program. Oper. Res. 35 (1995) 145-157. | MR | Zbl

[13] B.B. Pal, B.N. Moitra and U. Maulik, A goal programming procedure for fuzzy multiobjective linear fractional programming problem. Fuzzy Sets and Systems 139 (2003) 395-405. | MR | Zbl

[14] B. Pop and I.M. Stancu-Minasian, A method of solving fully fuzzified linear fractional programming problems. J.t Appl. Math. Comput. 27 (2008) 227-242. | MR | Zbl

[15] S. Schaible, Fractional programming I: duality. Manage. Sci. A 22 (1976) 658-667. | MR | Zbl

[16] B. Stanojevi and M. Stanojevi, Solving Method for Linear Fractional Optimization Problem with Fuzzy Coefficients in the Objective Function. Int. J. Comput. Commun. Control 8 (2013) 136-145.

[17] C. Veeramani, C. Duraisamy and A. Nagoorgani, Solving Fuzzy Multi-Objective Linear Programming Problems with Linear Membership Functions. Australian J. Basic and Appl. Sci. 5 (2011) 1163-1171.

[18] H.J. Zimmermann, Description and optimization of fuzzy systems. Int. J. General Systems 2 (1976) 209-215. | Zbl

[19] H.J. Zimmermann, Fuzzy Set Theory and its Applications. Kluwer Academic, Boston (1985). | Zbl

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