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A Fuzzy-stochastic Approach for Binary Linear Programming under Uncertainties

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Listed:
  • Wei Peng
  • Rene V. Mayorga

Abstract

This paper presents an innovative Fuzzy-Stochastic Approach (FSA) to solve Binary Linear Programming (BLP) problems under uncertainties. An Interval-coefficient Fuzzy Binary Linear Programming (IFBLP) model is applied here to reflect two different types of uncertainty in a BLP problem. In the proposed IFBLP model the interval coefficient is used to reflect parameter uncertainty, and the fuzzy goal & fuzzy constraints are used to represent model structure uncertainty. The proposed FSA would de-fuzzify the fuzzy constraints in an IFBLP model by considering its fuzzy goal; and then derive two linear BLPs with extreme crisp-coefficients from the IFBLP model, which here are called as a best optimum BLP and a worst optimum BLP. The results of the two-extreme linear BLPs are used to bound the outcome distribution of the IFBLP model. The proposed FSA is applied into a long-term traffic noise control planning to present its applicability.

Suggested Citation

  • Wei Peng & Rene V. Mayorga, 2017. "A Fuzzy-stochastic Approach for Binary Linear Programming under Uncertainties," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(3), pages 95-111, June.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:3:p:95-111
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    References listed on IDEAS

    as
    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. J W Chinneck & K Ramadan, 2000. "Linear programming with interval coefficients," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(2), pages 209-220, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Fuzzy; Stochastic Simulation; Uncertainty; Interval-parameter; BLP;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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