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Interactive Fuzzy Multi-Objective Stochastic Linear Programming

In: Fuzzy Multi-Criteria Decision Making

Author

Listed:
  • Masatoshi Sakawa

    (Hiroshima University)

  • Kosuke Kato

    (Hiroshima University)

Abstract

Two major approaches to deal with randomness or ambiguity involved in mathematical programming problems have been developed. They are stochastic programming approaches and fuzzy programming approaches. In this chapter, we focus on multiobjective linear programming problems with random variable coefficients in objective functions and/or constraints. Using several stochastic models such as an expectation optimization model, a variance minimization model, a probability maximization model, and a fractile criterion optimization model in chance constrained programming, the stochastic programming problems are transformed into deterministic ones. As a fusion of stochastic approaches and fuzzy ones, after determining the fuzzy goals of the decision maker, several interactive fuzzy satisfying methods to derive a satisfying solution for the decision maker by updating the reference membership levels are presented.

Suggested Citation

  • Masatoshi Sakawa & Kosuke Kato, 2008. "Interactive Fuzzy Multi-Objective Stochastic Linear Programming," Springer Optimization and Its Applications, in: Cengiz Kahraman (ed.), Fuzzy Multi-Criteria Decision Making, pages 375-408, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-76813-7_15
    DOI: 10.1007/978-0-387-76813-7_15
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    Citations

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    Cited by:

    1. M. Sakawa & T. Matsui & H. Katagiri, 2013. "An interactive fuzzy satisficing method for random fuzzy multiobjective integer programming problems through probability maximization with possibility," Fuzzy Information and Engineering, Springer, vol. 5(3), pages 335-350, September.
    2. Masatoshi Sakawa & Hideki Katagiri, 2012. "Stackelberg solutions for fuzzy random two-level linear programming through level sets and fractile criterion optimization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(1), pages 101-117, March.

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