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.
Mots-clés : triangular fuzzy number, linear programming problem, multi objective linear fractional programming problem, fuzzy mathematical programming
@article{RO_2014__48_1_109_0, 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}, publisher = {EDP-Sciences}, volume = {48}, number = {1}, year = {2014}, doi = {10.1051/ro/2013056}, mrnumber = {3177880}, zbl = {1293.90071}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ro/2013056/} }
TY - JOUR AU - Veeramani, Chinnadurai AU - Sumathi, Muthukumar TI - Fuzzy Mathematical Programming approach for Solving Fuzzy Linear Fractional Programming Problem JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2014 SP - 109 EP - 122 VL - 48 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2013056/ DO - 10.1051/ro/2013056 LA - en ID - RO_2014__48_1_109_0 ER -
%0 Journal Article %A Veeramani, Chinnadurai %A Sumathi, Muthukumar %T Fuzzy Mathematical Programming approach for Solving Fuzzy Linear Fractional Programming Problem %J RAIRO - Operations Research - Recherche Opérationnelle %D 2014 %P 109-122 %V 48 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2013056/ %R 10.1051/ro/2013056 %G en %F RO_2014__48_1_109_0
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://archive.numdam.org/articles/10.1051/ro/2013056/
[1] Fuzzy goal programming procedure to bilevel multi-objective linear fractional programming problems. Int. J. Math. Math. Sci. (2010) (Article ID 148975). | MR | Zbl
and ,[2] Linear programming with a fractional objective function. Oper. Res. 21 (1973) 22-29. | MR | Zbl
and ,[3] Solving multi-level multi-objective linear programming problemsthrough fuzzy goal programming approach. Appl. Math. Model. 34 (2010) 2377-2387. | MR | Zbl
,[4] Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy Sets System 125 (2002) 335-342. | MR | Zbl
and ,[5] Programming with linear fractional functions. Naval Res. Logist. Quart. 9 (1962) 81-186. | MR | Zbl
and ,[6] Craven, Fractional Programming. Heldermann verlag, Berlin (1988). | MR | Zbl
[7] Effect of tolerance in fuzzy linear fractional programming. Fuzzy Sets Systems 55 (1993) 133-142. | MR | Zbl
, and ,[8] Solution of fuzzy linear fractional programming problem. OPSEARCH 48 (2011) 129-135. | MR | Zbl
, , and ,[9] A fuzzy programming approach to fuzzy linear fractional programming with fuzzy coefficients. J. Fuzzy Math. 4 (1996) 829-834. | MR | Zbl
and ,[10] Fuzzy approaches for multiple objective linear fractional optimization. Fuzzy Sets System 13 (1984) 11-23. | MR | Zbl
,[11] Acceptable optimality in linear fractional programming with fuzzy coefficients. Fuzzy Optimization Decision Making 6 (2007) 5-16. | MR | Zbl
, and ,[12] 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
and ,[13] A goal programming procedure for fuzzy multiobjective linear fractional programming problem. Fuzzy Sets and Systems 139 (2003) 395-405. | MR | Zbl
, and ,[14] A method of solving fully fuzzified linear fractional programming problems. J.t Appl. Math. Comput. 27 (2008) 227-242. | MR | Zbl
and ,[15] Fractional programming I: duality. Manage. Sci. A 22 (1976) 658-667. | MR | Zbl
,[16] Solving Method for Linear Fractional Optimization Problem with Fuzzy Coefficients in the Objective Function. Int. J. Comput. Commun. Control 8 (2013) 136-145.
and ,[17] Solving Fuzzy Multi-Objective Linear Programming Problems with Linear Membership Functions. Australian J. Basic and Appl. Sci. 5 (2011) 1163-1171.
, and ,[18] Description and optimization of fuzzy systems. Int. J. General Systems 2 (1976) 209-215. | Zbl
,[19] Fuzzy Set Theory and its Applications. Kluwer Academic, Boston (1985). | Zbl
,Cité par Sources :