Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs

Authors

  • B. Stanojević Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade
  • I.M. Stancu-Minasian The Romanian Academy, Institute of Mathematical Statistics and Applied Mathematics, Bucharest, Romania

DOI:

https://doi.org/10.2298/YJOR110522001S

Keywords:

fuzzy programming, triangular fuzzy number, fractional programming, centroid of triangle

Abstract

In our earlier articles, we proposed two methods for solving the fully fuzzified linear fractional programming (FFLFP) problems. In this paper, we introduce a different approach of evaluating fuzzy inequalities between two triangular fuzzy numbers and solving FFLFP problems. First, using the Charnes-Cooper method, we transform the linear fractional programming problem into a linear one. Second, the problem of maximizing a function with triangular fuzzy value is transformed into a problem of deterministic multiple objective linear programming. Illustrative numerical examples are given to clarify the developed theory and the proposed algorithm.

References

Buckley, J.J., and Feuring, T., "Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming", Fuzzy Sets and Systems, 109 (1) (2000) 35-53.

Charnes, A., and Cooper, W.W., "Programming with linear fractional functionals", Naval Res. Logist. Quart., 9 (3-4) (1962) 181-186.

Gradasevic-Filipovic, M., and Saletic, D.Z., “Multicriteria optimization in a fuzzy environment: the fuzzy analytic hierarchy process”, Yugoslav Journal of Operations Research, 20 (1) (2010) 71-85.

Dubois, D., and Prade, H., "Fuzzy numbers: an overview", in: J.C. Bezdek (ed.), Analysis of Fuzzy Information, CRC Press, Boca Raton, 1987, 3-39.

Hadi-Vencheh, A., and Mokhtarian, M.N., "A new fuzzy MCDM approach based on centroid of fuzzy numbers", Expert Systems with Applications, 38 (2011) 5226-5230.

Kerre, E.E., "The use of fuzzy set theory in electrocardiological diagnostics", in: M.M. Gupta, E. Sanchez (eds.), Approximate Reasoning in Decision Analysis, North-Holland Publishing Co., Amsterdam-New York, 1982, 277-282.

Nejad, A.M., and Mashinchi, M., "Ranking fuzzy numbers based on the areas on the left and the right sides of fuzzy number", Computers and Mathematics with Applications, 61 (2011) 431-442.

Pop, B., and Stancu-Minasian, I.M., "A method of solving fully fuzzified linear fractional programming problems", J. Appl. Math. Comput., 27 (1-2) (2008) 227-242.

Pop, B., and Stancu-Minasian, I.M., "On solving fully fuzzified linear fractional programs", AMO-Adv. Model. Optim., 11 (4) (2009) 503-523.

Sharma, D.K., Jana, R.K., and Gaur, A., "Fuzzy goal programming for agricultural land allocation problems", Yugoslav Journal of Operations Research, 17 (1) (2007) 31-42.

Stancu-Minasian, I.M., "A sixth bibliography of fractional programming", Optimization, 55 (4) (2006) 405-428.

Stancu-Minasian, I.M., Fractional Programming. Theory, Methods and Applications, Kluwer Academic Publishers, Dordrecht/Boston/London, 1997.

Tsoukalas, L.H., and Uhrig, R.E, Fuzzy and Neural Approaches in Engineering, John Wiley and Sons Inc., New York, 1997.

Vujic, S., and Cirovic, G., "Production planning in mines using fuzzy linear programming", Yugoslav Journal of Operations Research, 6 (2) (1996).

Wanga, Y.-M., Yanga, J.-B., Xua, D.-L., and Chinc, K.-S., "On the centroids of fuzzy numbers", Fuzzy Sets and Systems, 157 (2006) 919-926.

Zimmermann, H.-J., Fuzzy Set Theory-and its Applications, Kluwer Publishing, Boston, 1985.

Downloads

Published

2012-03-01

Issue

Vol. 22 No. 1 (2012)

Section

Research Articles

License

Copyright (c) 2012 YUJOR

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.