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Fuzzy Goal Programming Approach to Quadratic Bi-Level Multi-Objective Programming Problem

by Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 29 - Number 6
Year of Publication: 2011
Authors: Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri
10.5120/3571-4926

Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri . Fuzzy Goal Programming Approach to Quadratic Bi-Level Multi-Objective Programming Problem. International Journal of Computer Applications. 29, 6 ( September 2011), 9-14. DOI=10.5120/3571-4926

@article{ 10.5120/3571-4926,
author = { Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri },
title = { Fuzzy Goal Programming Approach to Quadratic Bi-Level Multi-Objective Programming Problem },
journal = { International Journal of Computer Applications },
issue_date = { September 2011 },
volume = { 29 },
number = { 6 },
month = { September },
year = { 2011 },
issn = { 0975-8887 },
pages = { 9-14 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume29/number6/3571-4926/ },
doi = { 10.5120/3571-4926 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:15:03.619940+05:30
%A Surapati Pramanik
%A Partha Pratim Dey
%A Bibhas C. Giri
%T Fuzzy Goal Programming Approach to Quadratic Bi-Level Multi-Objective Programming Problem
%J International Journal of Computer Applications
%@ 0975-8887
%V 29
%N 6
%P 9-14
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper deals with fuzzy goal programming approach to quadratic bi-level multi-objective programming problem involving a single decision maker with multiple objectives at the upper level and a single decision maker with multiple objectives at the lower level. The objective functions of each level decision maker are quadratic in nature and the system constraints are linear functions. In the model formulation of the problem, we first determine the individual best solution of the quadratic objective functions subject to the system constraints and construct the quadratic membership functions of the objective functions of both levels. The quadratic membership functions are then transformed into equivalent linear membership functions by first order Taylor series at the individual best solution point. A possible relaxation of each level decision is considered by providing preference bounds on the decision variables for avoiding decision deadlock. Fuzzy goal programming approach is then used to achieve maximum degree of each of the membership goals by minimizing negative deviational variables. To demonstrate the efficiency of the proposed approach, an illustrative numerical example is provided.

References
  1. Candler, W., and Townsley, R. 1982. A linear bilevel programming problem. Computers & Operations Research 9, 59-76.
  2. Fortuni-Amat, J., and McCarl, B. 1981. A representation and economic interpretation of a two-level programming problem. Journal of Operational Research Society 32, 783-792.
  3. Anandalingam, G. 1988. A mathematical programming model of decentralized multi-level systems. Journal of the Operational Research Society 39 (11), 1021-1033.
  4. Lai, Y. J. 1996. Hierarchical Optimization: A satisfactory solution. Fuzzy Sets and Systems 77, 321-335.
  5. Shih, H. S., Lai, Y. J., and Lee, E. S. 1996. Fuzzy approach for multi-level programming problems. Computers & Operations Research 23, 73-91.
  6. Shih, H. S., and Lee, E. S. 2000. Compensatory fuzzy multiple level decision making. Fuzzy Sets and Systems 114, 71-87.
  7. Sakawa, M., Nishizaki. I., and Uemura, Y. 1998. Interactive fuzzy programming for multi-level linear problems. Computers and Mathematics with Applications 36, 71-86.
  8. Pramanik, S., and Roy, T. K. 2007. Fuzzy goal programming approach to multi-level programming problem. European Journal of Operational Research 176, 1151-1166.
  9. Edmunds, T., and Bard, J. 1991. Algorithms for nonlinear bilevel mathematical problems. IEEE Transactions Systems, Man, and Cybernetics 21, 83-89.
  10. Savard, G., and Gauvin, J. 1994. The steepest descent direction for the nonlinear bilevel programming problem. Operations Research Letters 15, 265-272.
  11. Vicente, L., Savard, G., and Júdice, J. 1994. Descent approaches for quadratic bilevel programming. Journal of Optimization Theory and Applications 81 (2), 379-399.
  12. Thirwani, D., and Arora, S. R. 1998. An algorithm for quadratic bilevel programming problem. International Journal of Management and System 14, 89-98.
  13. Pal, B. B., and Moitra, B. N. 2003. A fuzzy goal programming procedure for solving quadratic bilevel programming problems. International Journal of Intelligence Systems 14, 89-98.
  14. 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.
  15. Pramanik, S., and Dey, P. P. 2011. Bi-level linear fractional programming problem based on fuzzy goal programming approach. International Journal of Computer Applications 25 (11), 34-40.
Index Terms

Computer Science
Information Sciences

Keywords

Fuzzy goal programming Quadratic programming Quadratic bi-level programming Quadratic bi-level multi-objective programming

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