AN APPROACH TO SOLVE THE FUZZY MULTY OBJECTIVE LINEAR FRACTIONAL GOAL PROGRAMMING PROBLEM

MOUSUMI GUPTA; DEBASISH BHATTACHARJEE

AN APPROACH TO SOLVE THE FUZZY MULTY OBJECTIVE LINEAR FRACTIONAL GOAL PROGRAMMING PROBLEM

MOUSUMI GUPTA¹, DEBASISH BHATTACHARJEE²*
¹Department of Mathematics, National Institute of Technology Agartala, Tripura799055, India
²Department of Mathematics, National Institute of Technology Agartala, Tripura799055, India
* Corresponding Author : dbhattacharjee_nita@yahoo.in

Received : 10-08-2011 Accepted : 03-09-2011 Published : 05-09-2011
Volume : 2 Issue : 1 Pages : 23 - 36
J Stat Math 2.1 (2011):23-36

Cite - MLA : MOUSUMI GUPTA and DEBASISH BHATTACHARJEE "AN APPROACH TO SOLVE THE FUZZY MULTY OBJECTIVE LINEAR FRACTIONAL GOAL PROGRAMMING PROBLEM." Journal of Statistics and Mathematics 2.1 (2011):23-36.

Cite - APA : MOUSUMI GUPTA, DEBASISH BHATTACHARJEE (2011). AN APPROACH TO SOLVE THE FUZZY MULTY OBJECTIVE LINEAR FRACTIONAL GOAL PROGRAMMING PROBLEM. Journal of Statistics and Mathematics, 2 (1), 23-36.

Cite - Chicago : MOUSUMI GUPTA and DEBASISH BHATTACHARJEE "AN APPROACH TO SOLVE THE FUZZY MULTY OBJECTIVE LINEAR FRACTIONAL GOAL PROGRAMMING PROBLEM." Journal of Statistics and Mathematics 2, no. 1 (2011):23-36.

Copyright : © 2011, MOUSUMI GUPTA and DEBASISH BHATTACHARJEE, Published by Bioinfo Publications. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited.

Abstract

It is the purpose of this article to introduce a new weighted FGP technique by using only under deviation variables to fuzzy goals of fuzzy multi objective linear fractional goal programming problem (FMOLFGPP) to achieve highest degree of each of the membership goals by minimizing their under deviational variables. To assess the relative importance of the fuzzy goals properly, the weighting scheme by the decision of decision maker (DM) and Mohamedâ€™s technique (Fuzzy Sets and Systems, 89 (1997) 215-222) has been used. Illustrative numerical examples of FMOLFGPP are provided to demonstrate the feasibility of the proposed method, which clearly shows the proposed approach yields better optimal solution of FMOLFGP problem than the conventional min sum FGP approach in the sense that it gives the values of the fractional objectives closer to their aspiration level.

References

[1] Ali Payan et al., (2010) Applied Mathematical Modelling, 34, 4179–4183
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[2] Bellman R. E., Zadeh L. A., Manage (1970) Sci.17, B 141-164
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[3] Pal B.B., Moitra B.N. (2003) Fuzzy Sets and Systems 139, 395-405.
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[4] Charnes A., Cooper W.W. and Ferguson R. (1955) Management Science, 1, 138-151
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[5] Charnes A. and Cooper W.W. (1962) Naval Research Logistics Quarterly, 9, 181-186
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[6] Chakraborty M. and Gupta S. (2002) Fuzzy Sets and System,125,335-342
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[7] Ching-Ter Chang (2009) International Journal of Systems Science, 40, (8), 867–874
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[8] Romero C. (1986) European J. Oper. Res., 25 183–191.
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[9] Dutta D., Tiwari R.N., Rao J.R. (1992) Fuzzy Sets System, 52 (1), 39–45
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[10] Hannan E.L. (1981) Decision Sciences, 12, 522-531
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[11] Zimmermann H.J. (1978) Fuzzy Sets and System, 1, 45-55
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[12] Stancu-Minasian I.M., Pop B. (2000) 2nd Internat. Conf. on Symmetry and Antisymmetry in Mathematics, Formal Languages and Computer Science, BraUsov, Romania
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[13] Ibrahim A. Baky (2009) Fuzzy Sets and Systems, 160, 2701–2713
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[14] Kornbluth J.S.H. and Steuer R.E. (1981) Management Sc., 27, 1024-1039
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[15] Kornbluth J.S.H., Steuer R.E. (1981) European J. Oper. Res., 8, 58-65
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[16] Ignizio J.P. (1976) Lexington D.C. Health, MA.
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[17] Li H.L. (1994) European Journal of Operational Research, 73, 590-596
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[18] Mohamed Ramadan Hamed (1997) Fuzzy Sets and Systems, 89, 215-222
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[19] Luhandjula M.K. (1984) Fuzzy Sets and Systems, 13 (1), 11–23
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[20] Mahmoud A. Abo-Sinna, Baky I. A. (2010) International Journal of Mathematics and Mathematical Sciences, Article ID 148975, 15
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[21] Narasimhan R. (1980) Decision Sciences, Vol.11, 325-336.
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[22] Ravi V. and Reddy P.J. (1998) Fuzzy Sets and System, 96, 173-182
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[23] Tantawy S.F. (2008) Mathematical and Computer Modelling, 48, 5-6, Pages 969-973
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[24] Shao-Yuan Li et al. (2007) European Journal of Operational Research, 176, 3, 1319-1333
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[25] Mishra S. (2007) European Journal of Operational Research 183, 296–302
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[26] Pramanik S., Kumar Roy T. (2006) European Journal of Operational Research 176, 1151– 1166
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[27] Arora S.R., Gupta R. (2009) European Journal of Operational Research, 194, 368–376.
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[28] Tanaka H., Okuda T. and Asai K. (1974) Journal of Cybernetics, 3, 4, 37–46
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[29] Tiwari R.N., Dharmar S., Rao J.R. (1986) Fuzzy Sets and Systems, 19, 251-259
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[30] Wolf H.(1985) Operation Researech,33,835- 841
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[31] Yahia Zare Mehrjerdi (2011) Applied Soft Computing , Volume 11, Issue 2, 1735-1742
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[32] Zadeh L. A.(1965) Information and Control, 8, 338-353.
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

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