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Multilevel Programming Problems with Fuzzy Parameters: A Fuzzy Goal Programming Approach

by Surapati Pramanik
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 122 - Number 21
Year of Publication: 2015
Authors: Surapati Pramanik
10.5120/21852-5174

Surapati Pramanik . Multilevel Programming Problems with Fuzzy Parameters: A Fuzzy Goal Programming Approach. International Journal of Computer Applications. 122, 21 ( July 2015), 34-41. DOI=10.5120/21852-5174

@article{ 10.5120/21852-5174,
author = { Surapati Pramanik },
title = { Multilevel Programming Problems with Fuzzy Parameters: A Fuzzy Goal Programming Approach },
journal = { International Journal of Computer Applications },
issue_date = { July 2015 },
volume = { 122 },
number = { 21 },
month = { July },
year = { 2015 },
issn = { 0975-8887 },
pages = { 34-41 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume122/number21/21852-5174/ },
doi = { 10.5120/21852-5174 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:11:10.522351+05:30
%A Surapati Pramanik
%T Multilevel Programming Problems with Fuzzy Parameters: A Fuzzy Goal Programming Approach
%J International Journal of Computer Applications
%@ 0975-8887
%V 122
%N 21
%P 34-41
%D 2015
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper presents fuzzy goal programming approach for solving multilevel programming problems with fuzzy parameters. The proposed approach is based on ? -cut and fuzzy goal programming. In the proposed approach, the tolerance membership functions for the fuzzily described objective functions are defined by determining individual best solution of the objective function of every decision maker. Since the objectives of the level decision makers are potentially conflicting in nature, decision deadlock may arise due to the dissatisfaction of the solution of upper level decision makers. Sometimes upper level decision makers insist to work more than stipulated working hours or overtime duty in order to meet the heavy demand of the market arising for festivals or emergency reasons. In order to survive in the open competitive market, the relaxations of lower level decision makers are very crucial for the upper level decision makers and for the organization. So in the proposed model relaxation of decision for each level decision maker is considered. The relaxation of decision is performed by providing preference bounds on the decision variables for avoiding decision deadlock. Then three fuzzy goal programming models for multilevel programming are formulated. In general, the fuzzy goal programming models offer different solutions. In order to find the best compromise solution Euclidean function is used. An illustrative numerical example is provided to demonstrate the efficiency of the proposed approach.

References
  1. Burton, R. M. 1977. The multilevel approach to organizational issues of the firm. Omega 5, 457-468.
  2. Bard, J. F. and Falk, J. E. 1982. An explicit solution to the multi-level programming problems. Computers and Operations Research 9 (1), 77-100.
  3. Anandalingam, G. 1988. A mathematical programming model of decentralized multi-level systems. Journal of the Operational Research Society 39 (11), 1021-1033.
  4. Anandalingam, G. and Apprey, V. 1991. Multilevel programming and conflicting resolution. European Journal of Operational Research 51, 233-247.
  5. Watada, J. , Wang, S. , and Pedrycz, W. 2009. Building confidence-interval-based fuzzy random regression model. IEEE Transactions on Fuzzy Systems. 11 (6), 1273—1283.
  6. Zadeh, L. A. 1965 Fuzzy sets, Information and Control 8, 338-353.
  7. Lai, Y. J. 1996. Hierarchical optimization: a satisfactory solution. Fuzzy Sets and Systems 77, 321-335.
  8. Shih, H. S. , Lai, Y. J. , and Lee, E. S. 1996. Fuzzy approach for multi-level programming problems. Computers & Operations Research 23 (1), 73-91.
  9. Shih, H. S. and Lee, E. S. 2000. Compensatory fuzzy multiple level decision making. Fuzzy Sets and Systems 114 (1), 71-87.
  10. Sakawa, M. , Nishizaki, I. , and Uemura, Y. 1998. Interactive fuzzy programming for multilevel linear programming problems. Computers and Mathematics with Applications 36 (2), 71-86.
  11. Sakawa, M. , Nishizaki, I. , and Hitaka, M. 1999. Interactive fuzzy programming for multi-level 0-1 programming through genetic algorithms. European Journal of Operational Research 144(3), 580 – 588.
  12. Sinha, S. 2003. Fuzzy mathematical programming applied to multi-level programming problems. Computers and Operations Research 30 (9), 1259 – 1268.
  13. Sinha, S. 2003. Fuzzy programming approach to multi-level programming problems. Fuzzy Sets and Systems 136 (2), 189 – 202.
  14. Pramanik, S. and Roy, T. K. 2007. Fuzzy goal programming approach to multi-level programming problem. European Journal of Operational Research 176(2), 1151-1166.
  15. Baky, I. A. 2010. Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach. Applied Mathematical Modelling 34 (9), 2377-2387.
  16. Han, J. Lu, J. , Hu, Y. , and Zhang G. 2015. Tri-level decision-making with multiple followers: model, algorithm and case study. Information Sciences 311, 182–204.
  17. Sakawa, M. , Nishizaki, I. and Uemura, Y. (2000). Interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters. Fuzzy Sets and Systems. 109: 3–19.
  18. S. Pramanik. 2012. Bilevel programming problem with fuzzy parameter: a fuzzy goal programming approach. Journal of Applied Quantitative Methods. 7(1), 09-24.
  19. Pramanik, S. and Roy, T. K. 2008. Multiobjective transportation model with fuzzy parameters: based on priority based fuzzy goal programming approach. Journal of Transportation Systems Engineering and Information Technology 8(3), 40-48.
  20. S. Pramanik, Dey, P. P. 2011. Bi-level multi-objective programming problem with fuzzy parameters. International Journal of Computer Applications, 30 (10) 13-20.
  21. S. Pramanik, Dey, P. P. , and Giri, B. C. 2011. Decentralized bilevel multiobjective programming problem with fuzzy parameters based on fuzzy goal programming. Bulletin of Calcutta Mathematical Society. 103 (5), 381-390.
  22. Lee, E. S. , and Li, R. J. 1993. Fuzzy multiple objective programming with Pareto optimum. Fuzzy Sets and Systems 53,275 – 288.
  23. Pramanik, S. , Dey, P. P. 2011. Quadratic bi-level programming problem based on fuzzy goal programming approach. International Journal of Software Engineering and Applications 2(4), 41-59.
  24. Dey, P. P. , Pramanik, S. , and Giri, B. C. 2014. TOPSIS approach to linear fractional bi-level MODM problem based on fuzzy goal programming. Journal of Industrial and Engineering International 10(4), 173-184.
  25. Yu, P. L. 1973. A class of solutions for group decision problems. Management Science 19, 936–946.
  26. Zeleny, M. 1982. Multiple criteria decision making. McGraw-Hill, New York.
  27. Lu, J. , Zhang, G. , Montero, J. , and Garmendia, L. 2012. Multifollower trilevel decision making models and system. IEEE Transactions on Industrial Informatics 8(4), 974–985.
Index Terms

Computer Science
Information Sciences

Keywords

Multi-level programming Fuzzy goal programming goal programming.

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