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On some optimisation models in a fuzzy-stochastic environment

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  • Luhandjula, M.K.
  • Joubert, J.W.

Abstract

This paper is on fuzzy stochastic optimisation, an area that is quickly coming to the forefront of mathematical programming under uncertainty. An even stronger motivating factor for the growing interest in this area can be found in the ubiquitous nature of decision problems involving hybrid imprecision. More precisely, we consider a range of situations in which random factors and fuzzy information co-occur in an optimisation setting. Related hybrid optimisation models are discussed and converted into deterministic terms through appropriate tools like probabilistic set, uncertain probability, and fuzzy random variable, making good use of uncertainty principles. We also discuss ways to deal with the resulting problems. Numerical examples carried out using class optimisation software demonstrate the efficiency of the proposed approaches. We shall end this article by pointing out some of the challenges that currently occupy researchers in this emerging field.

Suggested Citation

  • Luhandjula, M.K. & Joubert, J.W., 2010. "On some optimisation models in a fuzzy-stochastic environment," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1433-1441, December.
  • Handle: RePEc:eee:ejores:v:207:y:2010:i:3:p:1433-1441
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    References listed on IDEAS

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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Ammar, E.E., 2009. "On fuzzy random multiobjective quadratic programming," European Journal of Operational Research, Elsevier, vol. 193(2), pages 329-341, March.
    3. Luhandjula, M.K., 2006. "Fuzzy stochastic linear programming: Survey and future research directions," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1353-1367, November.
    4. Zmeskal, Zdenek, 2005. "Value at risk methodology under soft conditions approach (fuzzy-stochastic approach)," European Journal of Operational Research, Elsevier, vol. 161(2), pages 337-347, March.
    5. Zmeskal, Zdenek, 2001. "Application of the fuzzy-stochastic methodology to appraising the firm value as a European call option," European Journal of Operational Research, Elsevier, vol. 135(2), pages 303-310, December.
    6. Katagiri, Hideki & Sakawa, Masatoshi & Kato, Kosuke & Nishizaki, Ichiro, 2008. "Interactive multiobjective fuzzy random linear programming: Maximization of possibility and probability," European Journal of Operational Research, Elsevier, vol. 188(2), pages 530-539, July.
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    Cited by:

    1. Chen, Shih-Pin, 2016. "Time value of delays in unreliable production systems with mixed uncertainties of fuzziness and randomness," European Journal of Operational Research, Elsevier, vol. 255(3), pages 834-844.
    2. Luhandjula, M.K. & Rangoaga, M.J., 2014. "An approach for solving a fuzzy multiobjective programming problem," European Journal of Operational Research, Elsevier, vol. 232(2), pages 249-255.

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