Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T19:12:45.876Z Has data issue: false hasContentIssue false
  • English
  • Français

Fuzzy Linear Fractional Set Covering Problem with Imprecise Costs

Published online by Cambridge University Press:  22 May 2014

Rashmi Gupta  and
Ratnesh Rajan Saxena
Rashmi Gupta
Affiliation:
Department of Mathematics, University of Delhi, 110007 Delhi, India.. [email protected]
Ratnesh Rajan Saxena
Affiliation:
Department of Mathematics, Deen Dayal Upadhyaya College (University of Delhi), Karampura, 110015 New Delhi, India.; [email protected]
Get access

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.

Keywords

Fuzzy fractional set covering problemα-optimal solutionfuzzy solution
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 3 , July 2014 , pp. 415 - 427
Copyright
© EDP Sciences, ROADEF, SMAI, 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Dubois, D. and Prade, H., Ranking fuzzy numbers in the setting of possibility theory. Inf. Sci. 30 (1983) 183–224. Google Scholar
Hwang, M.J., Chiang, C.I. and Liu, Y.H., Solving a fuzzy set covering problem. Math. Comput. Model. 40 (2004) 861–865. Google Scholar
A. Kaufman and M.M. Gupta, Fuzzy Mathematical Models in Engineering and Management Sciences. Elsevier Science Publishers B.V., Amsterdam (1988).
A. Kaufman and M.M. Gupta, Introduction to fuzzy arithmetic, theory and applications. New York, Von Nostrand Reinhold (1991).
Li, J. and Kwan, Raymond S.K., A meta-heuristic with orthogonal experiment for the set covering problem. J. Math. Model. Algorithms 3 (2004) 263–283. Google Scholar
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.
Mehra, A., Chandra, S. and Bector, C.R., Acceptable optimality in linear fractional programming with fuzzy coefficients. Fuzzy Optim. Decis. Making 6 (2007) 6–16. Google Scholar
Metev, B. and Gueorguieva, D., A simple method for obtaining weakly efficient points in multiobjective linear fractional programming problems. Eur. J. Oper. Res. 12 (2000) 325–338. Google Scholar
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.
Saxena, R.R. and Arora, S.R., A linearization technique for solving the quadratic set covering problem. Optimization 39 (1996) 35–42. Google Scholar
Saxena, R.R. and Gupta, R., Enumeration technique for solving linear fractional fuzzy set covering problem, Int. J. Pure Appl. Math. 84 (2013) 477–496. Google Scholar
Saxena, R.R. and Gupta, R., Enumeration technique for solving linear fuzzy set covering problem, Int. J. Pure Appl. Math. 85 (2013) 635–651. Google Scholar
Shavandi, H. and Mahlooji, H., Fuzzy hierarchical queueing models for the location set covering problem in congested systems. Scientia Iranica 15 (2008) 378–388. Google Scholar
Stanojević, B. and Stanojević, M., Solving method for linear fractional optimization problem with fuzzy coefficients in the objective fucntion. Int. J. Comput. Commun. 8 (2013) 146–152. Google Scholar
Wu, H.C., Duality theorems in fuzzy mathematical programming problems based on the concept of necessity. Fuzzy Sets and Systems 139 (2003) 363–377. Google Scholar
H.J. Zimmermann, Fuzzy set theory and its applications. 4th edition, Nowell, MA Kluwer Academic Publishers (2001).
Zimmermann, K., Fuzzy set covering problem. Int. J. General Syst. 20 (1991) 127–131. Google Scholar