Fuzzy Linear Fractional Set Covering Problem with Imprecise Costs
RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 3, pp. 415-427.

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.

DOI : 10.1051/ro/2014015
Classification : 90C70, 90C10
Mots-clés : fuzzy fractional set covering problem, α-optimal solution, fuzzy solution 
@article{RO_2014__48_3_415_0,
     author = {Gupta, Rashmi and Saxena, Ratnesh Rajan},
     title = {Fuzzy {Linear} {Fractional} {Set} {Covering} {Problem} with {Imprecise} {Costs}},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {415--427},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {3},
     year = {2014},
     doi = {10.1051/ro/2014015},
     mrnumber = {3264387},
     zbl = {1296.90152},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2014015/}
}
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
SP  - 415
EP  - 427
VL  - 48
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2014015/
DO  - 10.1051/ro/2014015
LA  - en
ID  - RO_2014__48_3_415_0
ER  - 
%0 Journal Article
%A Gupta, Rashmi
%A Saxena, Ratnesh Rajan
%T Fuzzy Linear Fractional Set Covering Problem with Imprecise Costs
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2014
%P 415-427
%V 48
%N 3
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2014015/
%R 10.1051/ro/2014015
%G en
%F RO_2014__48_3_415_0
Gupta, Rashmi; Saxena, Ratnesh Rajan. Fuzzy Linear Fractional Set Covering Problem with Imprecise Costs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 3, pp. 415-427. doi : 10.1051/ro/2014015. http://www.numdam.org/articles/10.1051/ro/2014015/

[1] D. Dubois and H. Prade, Ranking fuzzy numbers in the setting of possibility theory. Inf. Sci. 30 (1983) 183-224. | MR | Zbl

[2] M.J. Hwang, C.I. Chiang and Y.H. Liu, Solving a fuzzy set covering problem. Math. Comput. Model. 40 (2004) 861-865. | MR | Zbl

[3] A. Kaufman and M.M. Gupta, Fuzzy Mathematical Models in Engineering and Management Sciences. Elsevier Science Publishers B.V., Amsterdam (1988). | Zbl

[4] A. Kaufman and M.M. Gupta, Introduction to fuzzy arithmetic, theory and applications. New York, Von Nostrand Reinhold (1991). | MR | Zbl

[5] J. Li and Raymond S.K. Kwan, A meta-heuristic with orthogonal experiment for the set covering problem. J. Math. Model. Algorithms 3 (2004) 263-283. | MR | Zbl

[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] A. Mehra, S. Chandra and C.R. Bector, Acceptable optimality in linear fractional programming with fuzzy coefficients. Fuzzy Optim. Decis. Making 6 (2007) 6-16. | MR | Zbl

[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. | MR | Zbl

[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] R.R. Saxena and S.R. Arora, A linearization technique for solving the quadratic set covering problem. Optimization 39 (1996) 35-42. | MR | Zbl

[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] 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] H. Shavandi and H. Mahlooji, Fuzzy hierarchical queueing models for the location set covering problem in congested systems. Scientia Iranica 15 (2008) 378-388. | MR | Zbl

[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] H.C. Wu, Duality theorems in fuzzy mathematical programming problems based on the concept of necessity. Fuzzy Sets and Systems 139 (2003) 363-377. | MR | Zbl

[16] H.J. Zimmermann, Fuzzy set theory and its applications. 4th edition, Nowell, MA Kluwer Academic Publishers (2001). | MR | Zbl

[17] K. Zimmermann, Fuzzy set covering problem. Int. J. General Syst. 20 (1991) 127-131. | Zbl

Cité par Sources :