Interactive Fuzzy Stochastic Multi-level 0-1 Programming through Probability Maximization

Masatoshi Sakawa, Takeshi Matsui

Abstract

This paper considers multi-level 0-1 programming problems involving random variable coefficients both in objective functions and constraints. Following the probability maximization model together with the concept of chance constraints, the formulated stochastic multi-level 0-1 programming problems are transformed into deterministic ones. Taking into account vagueness of judgments of the decision makers, we present interactive fuzzy programming. In the proposed interactive method, after determining the fuzzy goals of the decision makers at all levels, a satisfactory solution is derived efficiently by updating satisfactory levels of the decision makers with considerations of overall satisfactory balance among all levels. An illustrative numerical example for a three-level 0-1 programming problem is provided to demonstrate the feasibility of the proposed method.

References

  1. Charnes, A. and Cooper, W. W. (1959). Chance constrained programming. Management Science, 6(1):73-79.
  2. Dantzig, G. B. (1955). Linear programming under uncertainty. Management Science, 1(3-4):197-206.
  3. Hanafi, S. and Freville, A. (1998). An efficient tabu search approach for the 0-1 multidimensional knapsack problem. European Journal of Operational Research, 106(2-3):659-675.
  4. Lai, Y. J. (1996). Hierarchical optimization: a satisfactory solution. Fuzzy Sets and Systems, 77(3):321-335.
  5. Sakawa, M. and Nishizaki, I. (2009). Cooperative and Noncooperative Multi-Level Programming. Springer, New York, 1st edition.
  6. Sakawa, M., Nishizaki, I., and Uemura, Y. (1998). Interactive fuzzy programming for multi-level linear programming problems. Computers & Mathematics with Applications, 36(2):71-86.
  7. Sakawa, M., N. I. and Uemura, Y. (2000). Interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters. Fuzzy Sets and Systems, 115(1):93-103.
  8. Shih, H. S., Lai, Y. J., and Lee, E. S. (1996). Fuzzy approach for multi-level programming problems. Computers and Operations Research, 23(1):73-91.
  9. Stancu-Minasian, I. M. (1984). Stochastic Programming with Multiple Objective Functions. D. Reidel Publishing Company, Dordrecht, 1st edition.
  10. Stancu-Minasian, I. M. (1990). Overview of different approaches for solving stochastic programming problems with multiple objective functions. Kulwer Academic Publishers, Dordrecht/Boston/London, 1st edition.
  11. Zimmermann, H.-J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1):45-55.
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Paper Citation


in Harvard Style

Sakawa M. and Matsui T. (2012). Interactive Fuzzy Stochastic Multi-level 0-1 Programming through Probability Maximization . In Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2012) ISBN 978-989-8565-33-4, pages 383-388. DOI: 10.5220/0004110103830388


in Bibtex Style

@conference{fcta12,
author={Masatoshi Sakawa and Takeshi Matsui},
title={Interactive Fuzzy Stochastic Multi-level 0-1 Programming through Probability Maximization},
booktitle={Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2012)},
year={2012},
pages={383-388},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004110103830388},
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 Stochastic Multi-level 0-1 Programming through Probability Maximization
SN - 978-989-8565-33-4
AU - Sakawa M.
AU - Matsui T.
PY - 2012
SP - 383
EP - 388
DO - 10.5220/0004110103830388