Fuzzy Linear Fractional Set Covering Problem with Imprecise Costs

Rashmi Gupta; Ratnesh Rajan Saxena

RAIRO - Operations Research - Recherche Opérationnelle (2014)

  • Volume: 48, Issue: 3, page 415-427
  • ISSN: 0399-0559

Abstract

top
Set covering problems are in great use these days, these problems are applied in many disciplines such as crew scheduling problems, location problems, testing of VLSI circuits, artificial intelligence etc. In this paper α-acceptable optimal solution is given for the fuzzy linear fractional set covering problem where fuzziness involved in the objective function. At first the fuzzy linear fractional problem is being converted in to crisp parametric linear fractional set covering problem then a linearization technique is used to obtain an optimal solution to this parametric problem. This optimal solution will also be the fuzzy optimal solution for the original problem. An example is also provided to illustrate the algorithm.

How to cite

top

Gupta, Rashmi, and Saxena, Ratnesh Rajan. "Fuzzy Linear Fractional Set Covering Problem with Imprecise Costs." RAIRO - Operations Research - Recherche Opérationnelle 48.3 (2014): 415-427. <http://eudml.org/doc/275061>.

@article{Gupta2014,
abstract = {Set covering problems are in great use these days, these problems are applied in many disciplines such as crew scheduling problems, location problems, testing of VLSI circuits, artificial intelligence etc. In this paper α-acceptable optimal solution is given for the fuzzy linear fractional set covering problem where fuzziness involved in the objective function. At first the fuzzy linear fractional problem is being converted in to crisp parametric linear fractional set covering problem then a linearization technique is used to obtain an optimal solution to this parametric problem. This optimal solution will also be the fuzzy optimal solution for the original problem. An example is also provided to illustrate the algorithm.},
author = {Gupta, Rashmi, Saxena, Ratnesh Rajan},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {fuzzy fractional set covering problem; α-optimal solution; fuzzy solution; -optimal solution},
language = {eng},
number = {3},
pages = {415-427},
publisher = {EDP-Sciences},
title = {Fuzzy Linear Fractional Set Covering Problem with Imprecise Costs},
url = {http://eudml.org/doc/275061},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Gupta, Rashmi
AU - Saxena, Ratnesh Rajan
TI - Fuzzy Linear Fractional Set Covering Problem with Imprecise Costs
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 3
SP - 415
EP - 427
AB - Set covering problems are in great use these days, these problems are applied in many disciplines such as crew scheduling problems, location problems, testing of VLSI circuits, artificial intelligence etc. In this paper α-acceptable optimal solution is given for the fuzzy linear fractional set covering problem where fuzziness involved in the objective function. At first the fuzzy linear fractional problem is being converted in to crisp parametric linear fractional set covering problem then a linearization technique is used to obtain an optimal solution to this parametric problem. This optimal solution will also be the fuzzy optimal solution for the original problem. An example is also provided to illustrate the algorithm.
LA - eng
KW - fuzzy fractional set covering problem; α-optimal solution; fuzzy solution; -optimal solution
UR - http://eudml.org/doc/275061
ER -

References

top
  1. [1] D. Dubois and H. Prade, Ranking fuzzy numbers in the setting of possibility theory. Inf. Sci.30 (1983) 183–224. Zbl0569.94031MR730910
  2. [2] M.J. Hwang, C.I. Chiang and Y.H. Liu, Solving a fuzzy set covering problem. Math. Comput. Model.40 (2004) 861–865. Zbl1067.03509MR2106174
  3. [3] A. Kaufman and M.M. Gupta, Fuzzy Mathematical Models in Engineering and Management Sciences. Elsevier Science Publishers B.V., Amsterdam (1988). Zbl0683.90024
  4. [4] A. Kaufman and M.M. Gupta, Introduction to fuzzy arithmetic, theory and applications. New York, Von Nostrand Reinhold (1991). Zbl0588.94023MR1132439
  5. [5] J. Li and Raymond S.K. Kwan, A meta-heuristic with orthogonal experiment for the set covering problem. J. Math. Model. Algorithms3 (2004) 263–283. Zbl1146.90535MR2231450
  6. [6] J. Li and Raymond S.K. Kwan, A fuzzy evolutionary approach with Taguchi parameter setting for the set covering problem. School of Computing, University of Leads LS 2 9JT, UK, 2002. 
  7. [7] A. Mehra, S. Chandra and C.R. Bector, Acceptable optimality in linear fractional programming with fuzzy coefficients. Fuzzy Optim. Decis. Making6 (2007) 6–16. Zbl1278.90489MR2283121
  8. [8] B. Metev and D. Gueorguieva, A simple method for obtaining weakly efficient points in multiobjective linear fractional programming problems. Eur. J. Oper. Res.12 (2000) 325–338. Zbl0970.90104MR1785803
  9. [9] R. Sahraeian and M.S. Kazemi, A fuzzy set covering-clustering algorithm for facility location problem. IEEE International Conference on Industrial Engeneering Management (2011) 1098–1102. 
  10. [10] R.R. Saxena and S.R. Arora, A linearization technique for solving the quadratic set covering problem. Optimization39 (1996) 35–42. Zbl0867.90082MR1482753
  11. [11] R.R. Saxena and R. Gupta, Enumeration technique for solving linear fractional fuzzy set covering problem, Int. J. Pure Appl. Math.84 (2013) 477–496. 
  12. [12] R.R. Saxena and R. Gupta, Enumeration technique for solving linear fuzzy set covering problem, Int. J. Pure Appl. Math.85 (2013) 635–651. 
  13. [13] H. Shavandi and H. Mahlooji, Fuzzy hierarchical queueing models for the location set covering problem in congested systems. Scientia Iranica15 (2008) 378–388. Zbl1153.90376MR2426710
  14. [14] B. Stanojević and M. Stanojević, Solving method for linear fractional optimization problem with fuzzy coefficients in the objective fucntion. Int. J. Comput. Commun.8 (2013) 146–152. 
  15. [15] H.C. Wu, Duality theorems in fuzzy mathematical programming problems based on the concept of necessity. Fuzzy Sets and Systems139 (2003) 363–377. Zbl1047.90082MR2006781
  16. [16] H.J. Zimmermann, Fuzzy set theory and its applications. 4th edition, Nowell, MA Kluwer Academic Publishers (2001). Zbl0719.04002MR1882395
  17. [17] K. Zimmermann, Fuzzy set covering problem. Int. J. General Syst.20 (1991) 127–131. Zbl0757.90086

NotesEmbed ?

top

You must be logged in to post comments.