Interactive Fuzzy Decision Making for Multiobjective Fuzzy Random Linear Programming Problems

Hitoshi Yano, Masatoshi Sakawa

Abstract

In this paper, we propose an interactive fuzzy decision making method for multiobjective fuzzy random linear programming problems (MOFRLP), in which the criteria of probability maximization and fractile optimization are considered simultaneously. In the proposed method, it is assumed that the decision maker has fuzzy goals for not only objective functions of MOFRLP but also permissible probability levels in a fractile optimization model for MOFRLP, and such fuzzy goals are quantified by eliciting the corresponding membership functions. Using the fuzzy decision, such two kinds of membership functions are integrated. In the integrated membership space, the satisfactory solution is obtained from among a Pareto optimal solution set through the interaction with the decision maker.

References

  1. Birge, J. R. and Louveaux, F. (1997). Introduction to Stochastic Programming. Springer.
  2. Charnes, A. and Cooper, W. W. (1959). Chance constrained programming. Management Science, 6(1):73-79.
  3. Dantzig, G. B. (1955). Linear programming under uncertainty. Management Science, 1(3-4):197-206.
  4. Dubois, D. and Prade, H. (1980). Fuzzy Sets and Systems: Theory and Applications. Academic Press.
  5. Kall, P. and Mayer, J. (2005). Stochastic Linear Programming Models, Theory, and Computation. Springer.
  6. Katagiri, H., Ishii, H., and Itoh, T. (1997). Fuzzy random linear programming problem. In Proceedings of Second European Workshop on Fuzzy Decision Analysis and Neural Networks for Management, Planning and Optimization. Dortmund.
  7. Kwakernaak, H. (1978). Fuzzy random variable-1. Information Sciences, 15:1-29.
  8. Lai, V. and Hwang, C. (1992). Fuzzy Mathematical Programming. Springer.
  9. Luhandjula, M. and Gupta, M. (1996). On fuzzy stochastic optimization. Fuzzy Sets and Systems, 81:47-55.
  10. Puri, M. and Ralescu, D. (1986). Fuzzy random variables. Journal of Mathematical Analysis and Applications, 14:409-422.
  11. Sakawa, M. (1993). Fuzzy Sets and Interactive Multiobjective Optimization. Plenum Press.
  12. Sakawa, M., Nishizaki, I., and Katagiri, H. (2011). Fuzzy Stochastic Multiobjective Programming. Springer.
  13. Wang, G.-Y. and Qiao, Z. (1993). Linear programming with fuzzy random variable coefficients. Fuzzy Sets and Systems, 57:295-311.
  14. Yano, H. and Matsui, K. (2011). Fuzzy approaches for multiobjective fuzzy random linear programming problems through a probability maximization model. In Lecture Notes in Engineering and Computer Science: Proceedings of The International MultiConference of Engineers and Computer Scientists 2011, pages 1349-1354, Hong Kong.
  15. Zimmermann, H.-J. (2011). Fuzzy Sets, Decision-Making and Expert Systems. Kluwer Academic Publishers, Boston.
Download


Paper Citation


in Harvard Style

Yano H. and Sakawa M. (2012). Interactive Fuzzy Decision Making for Multiobjective Fuzzy Random Linear Programming Problems . In Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2012) ISBN 978-989-8565-33-4, pages 319-328. DOI: 10.5220/0004087003190328


in Bibtex Style

@conference{fcta12,
author={Hitoshi Yano and Masatoshi Sakawa},
title={Interactive Fuzzy Decision Making for Multiobjective Fuzzy Random Linear Programming Problems},
booktitle={Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2012)},
year={2012},
pages={319-328},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004087003190328},
isbn={978-989-8565-33-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2012)
TI - Interactive Fuzzy Decision Making for Multiobjective Fuzzy Random Linear Programming Problems
SN - 978-989-8565-33-4
AU - Yano H.
AU - Sakawa M.
PY - 2012
SP - 319
EP - 328
DO - 10.5220/0004087003190328