# Fuzzy Linear Fractional Set Covering Problem with Imprecise Costs

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

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## Abstract

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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

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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

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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
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