Research Article

A Priority based Fuzzy Goal Programming to Multi-Objective Linear Fractional Programming Problem

by  Surapati Pramanik, Partha Pratim Dey
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 30 - Issue 10
Published: September 2011
Authors: Surapati Pramanik, Partha Pratim Dey
10.5120/3679-5180
PDF

Surapati Pramanik, Partha Pratim Dey . A Priority based Fuzzy Goal Programming to Multi-Objective Linear Fractional Programming Problem. International Journal of Computer Applications. 30, 10 (September 2011), 1-6. DOI=10.5120/3679-5180 

                        @article{ 10.5120/3679-5180,
                        author  = { Surapati Pramanik,Partha Pratim Dey },
                        title   = { A Priority based Fuzzy Goal Programming to Multi-Objective Linear Fractional Programming Problem },
                        journal = { International Journal of Computer Applications },
                        year    = { 2011 },
                        volume  = { 30 },
                        number  = { 10 },
                        pages   = { 1-6 },
                        doi     = { 10.5120/3679-5180 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2011
                        %A Surapati Pramanik
                        %A Partha Pratim Dey
                        %T A Priority based Fuzzy Goal Programming to Multi-Objective Linear Fractional Programming Problem%T 
                        %J International Journal of Computer Applications
                        %V 30
                        %N 10
                        %P 1-6
                        %R 10.5120/3679-5180
                        %I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper deals with priority based fuzzy goal programming approach for solving multi-objective linear fractional programming problem. In the model formulation of the problem, we construct the fractional membership functions by determining the optimal solution of the objective functions subject to the system constraints. The fractional membership functions are then transformed into equivalent linear membership functions at the individual best solution point by first order Taylor series. In the solution process, fuzzy goal programming approach is used to solve problem by minimizing negative deviational variables. Then, sensitivity analysis is performed with the change of priorities of the fuzzy goals. Euclidean distance function is used to identify the appropriate priority structure in the decision-making situation. The efficiency of the proposed approach is illustrated by solving a numerical example.

References
  • Ijiri, Y. 1965 Management Goals and Accounting for control. North-Holland Publication, Amsterdam.
  • Ignizio, J. P. 1976 Goal programming and Extensions. Lexington Books, D. C. Heath and Company, London.
  • Lee, S. M. 1972 Goal Programming for Decision Analysis. Auerbach Publishers Inc., Philadelphia.
  • Steuer, R. E. 1986 Multiple criteria optimization: theory, computation and applications. Wiley, NewYork.
  • Charnes, A., and Cooper, W. W. 1962. Programming with linear fractional functions. Naval Research Logistics Quarterly 9, 181-186.
  • Bitran, G. R., and Noveas, A. G. 1973. Linear programming with a fractional objective function. Operations Research 21, 22-29.
  • Kornbluth, J. S. H., and Steuer, R. E. 1981. Goal programming with linear fractional criteria. European Journal of Operational Research 8, 58-65.
  • Luhandjula, M. K. 1984. Fuzzy approaches for multiple objective linear fractional optimization. Fuzzy Sets and Systems 13, 11-23.
  • Dutta, D., Rao, J. R., and Tiwari, R. N. 1992. Multiple objective linear fractional programming - a fuzzy set theoretic approach. Fuzzy Sets and Systems 52, 39-45.
  • Zadeh, L. A. 1976. The concept of a linguistic variable and its application to approximate reasoning, Part III. Information Sciences 9, 43-80.
  • Zadeh, L. A.1975a. The concept of a linguistic variable and its application to approximate reasoning, Part II. Information Sciences 8, 301-352.
  • Zadeh, L. A. 1975b. The concept of a linguistic variable and its application to approximate reasoning, Part I. Information Sciences 8, 199-244.
  • Sakawa, M., and Kato, K. 1988. Interactive decision-making for multi-objective linear fractional programming problems with block angular structure involving fuzzy numbers. Fuzzy Sets and Systems 97, 19-31.
  • Chakraborty, M., and Gupta, S. 2002. Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy Sets and Systems 125, 335-342.
  • Pal, B. B., Moitra, B. N., and Maulik, U. 2003. A goal programming procedure for fuzzy multiobjective linear fractional programming. Fuzzy Sets and Systems 139, 395-405.
  • Minasian, I. M. S., and Pop, B. 2003. On a fuzzy set to solving multiple objective linear fractional programming problem. Fuzzy Sets and Systems 134, 397-405.
  • Sadjadi, S. J., Aryanejad, M. B. and Sarfaraz, A. 2005. A fuzzy approach to solve a multi-objective linear fractional inventory model. Journal of Industrial Engineering Internatioal 1 (1), 43-47.
  • Guzel, N., and Sivri, M. 2005. Taylor series solution of multi-objective linear fractional programming problem. Trakya University Journal Science 6, 80-87.
  • Toksarı, M. D. 2008. Taylor series approach to fuzzy multiobjective linear fractional programming. Information Sciences 178, 1189-1204.
  • S. Pramanik, “Bilevel programming problem with fuzzy parameters: a fuzzy goal programming approach”, Journal of Applied Quantitative Methods, 2011, in press.
  • Pramanik, S., and Roy, T. K. 2008. Multiobjective transportation model with fuzzy parameters: a priority based fuzzy goal programming approach. Journal of transportation System Engineering and Information Technology 8 (3), 40-48.
  • Pramanik, S., and Roy, T. K. 2007. Fuzzy goal programming approach to multilevel programming problems. European Journal of Operational Research 176, 1151-1166.
  • Pramanik, S., and Dey, P. P. 2011. Multi-objective quadratic programming problem: a priority based fuzzy goal programming. International Journal of Computer Applications 26 (10), 30-35.
  • Yu, P. L. 1973. A class of solutions for group decision problems. Management Science 19, 936-946.
  • Pramanik, S., and Roy T. K. 2006. A fuzzy goal programming technique for solving multi-objective transportation problem. Tamsui Oxford Journal of Management Sciences 22 (1), 67-89.
  • Pramanik, S., and Roy, T. K. 2005a. A goal programming procedure for solving unbalanced transportation problem having multiple fuzzy goals. Tamsui Oxford Journal of Management Sciences 21 (2), 39-54.
  • Pramanik, S., and Roy T. K. 2005b. A fuzzy goal programming approach for multi-objective capacitated transportation problem. Tamsui Oxford Journal of Management Sciences 21 (1), 75-88.
Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

Fractional programming Goal programming Multi-objective linear fractional programming Priority based fuzzy goal programming

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