# 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

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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