Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T00:40:30.932Z Has data issue: false hasContentIssue false
  • English
  • Français

Fuzzy Mathematical Programming approach for Solving FuzzyLinear Fractional Programming Problem

Published online by Cambridge University Press:  10 January 2014

Chinnadurai Veeramani  and
Muthukumar Sumathi
Chinnadurai Veeramani
Affiliation:
Department of Applied Mathematics Computational Sciences, PSG College of Technology, Coimbatore, India.. veerasworld@yahoo.com; ramasumathi.psg@gmail.com
Muthukumar Sumathi
Affiliation:
Department of Applied Mathematics Computational Sciences, PSG College of Technology, Coimbatore, India.. veerasworld@yahoo.com; ramasumathi.psg@gmail.com
Get access

Abstract

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

Keywords

Triangular fuzzy numberLinear programming problemmulti objective linear fractional programming problemfuzzy mathematical programming
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 1 , January 2014 , pp. 109 - 122
Copyright
© EDP Sciences, ROADEF, SMAI, 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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).
Bitran, G.R. and Novaes, A.G., Linear programming with a fractional objective function. Oper. Res. 21 (1973) 22–29. Google Scholar
Baky, I.A., Solving multi-level multi-objective linear programming problemsthrough fuzzy goal programming approach. Appl. Math. Model. 34 (2010) 2377–2387. Google Scholar
Chakraborty, M. and Gupta, S., Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy Sets System 125 (2002) 335–342. Google Scholar
Charnes, A. and Cooper, W.W., Programming with linear fractional functions. Naval Res. Logist. Quart. 9 (1962) 81–186. Google Scholar
Craven, Fractional Programming. Heldermann verlag, Berlin (1988).
Dutta, D., Rao, J.R. and Tiwari, R.N., Effect of tolerance in fuzzy linear fractional programming. Fuzzy Sets Systems 55 (1993) 133–142. Google Scholar
Jain, S., Mangal, A., and Parihar, P.R., Solution of fuzzy linear fractional programming problem. OPSEARCH 48 (2011) 129–135. Google Scholar
Li, D.F. and Chen, S., A fuzzy programming approach to fuzzy linear fractional programming with fuzzy coefficients. J. Fuzzy Math. 4 (1996) 829–834. Google Scholar
Luhandjula, M.K., Fuzzy approaches for multiple objective linear fractional optimization. Fuzzy Sets System 13 (1984) 11–23. Google Scholar
Mehra, A., Chandra, S. and Bector, C.R., Acceptable optimality in linear fractional programming with fuzzy coefficients. Fuzzy Optimization Decision Making 6 (2007) 5–16. Google Scholar
Pal, B.B. and Basu, I., A goal programming method for solving fractional programming problems via dynamic programming. Optim. A J. Math. Program. Oper. Res. 35 (1995) 145–157. Google Scholar
Pal, B.B., Moitra, B.N. and Maulik, U., A goal programming procedure for fuzzy multiobjective linear fractional programming problem. Fuzzy Sets and Systems 139 (2003) 395–405. Google Scholar
Pop, B. and Stancu-Minasian, I.M., A method of solving fully fuzzified linear fractional programming problems. J.t Appl. Math. Comput. 27 (2008) 227–242. Google Scholar
Schaible, S., Fractional programming I: duality. Manage. Sci. A 22 (1976) 658–667. Google Scholar
Stanojevi, B. and Stanojevi, M., Solving Method for Linear Fractional Optimization Problem with Fuzzy Coefficients in the Objective Function. Int. J. Comput. Commun. Control 8 (2013) 136–145. Google Scholar
Veeramani, C., Duraisamy, C. and Nagoorgani, A., Solving Fuzzy Multi-Objective Linear Programming Problems with Linear Membership Functions. Australian J. Basic and Appl. Sci. 5 (2011) 1163–1171. Google Scholar
Zimmermann, H.J., Description and optimization of fuzzy systems. Int. J. General Systems 2 (1976) 209–215. Google Scholar
H.J. Zimmermann, Fuzzy Set Theory and its Applications. Kluwer Academic, Boston (1985).